{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/israeldi/quantlab/master/assets/images/Program-Logo.png\" width=\"400px\" align=\"right\">\n",
    "\n",
    "# QuantLab: Stochastics\n",
    "### [(Go to Quant Lab)](https://israeldi.github.io/quantlab/)\n",
    "\n",
    "#### Source: Python for Finance (2nd ed.)\n",
    "\n",
    "**Mastering Data-Driven Finance**\n",
    "\n",
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/py4fi_2nd_shadow.png\" width=\"200px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "\n",
    "1. [Random Numbers](#1.-Random-Numbers)\n",
    "2. [Plotting Random Samples](#2.-Plotting-Random-Samples)\n",
    "3. [Simulation](#3.-Simulation)\n",
    "    - 3.1 [Random Variables](#3.1-Random-Variables)\n",
    "    - 3.2 [Stochastic Processes](#3.2-Stochastic-Processes)\n",
    "        - 3.2.1 [Geometric Brownian Motion](#3.2.1-Geometric-Brownian-Motion)\n",
    "4. [Valuation](#4.-Valuation)\n",
    "    - 4.1 [Valuation of European call options in Black-Scholes-Merton model](#4.1-Valuation-of-European-call-options-in-Black-Scholes-Merton-model)\n",
    "    - 4.2 [Vega function and implied volatility estimation](#4.2-Vega-function-and-implied-volatility-estimation)\n",
    "    - 4.3 [Pricing European Options by Monte Carlo](#4.3-Pricing-European-Options-by-Monte-Carlo)\n",
    "    - 4.4 [American Options](#4.4-American-Options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially import all the modules we will be using for our notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import numpy.random as npr \n",
    "\n",
    "# COMMAND PROMPT: pip install matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Directory where we will save our plots\n",
    "directory = \"./images\"\n",
    "if not os.path.exists(directory):\n",
    "    os.makedirs(directory)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Random Numbers\n",
    "#### ([Back to Top](#Table-of-Contents))\n",
    "\n",
    "First we set the `seed` in order to always generate the same random numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "npr.seed(100)\n",
    "np.set_printoptions(precision=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1** Generates $X_1,\\ldots\\,X_n$ where $X_i \\sim U[0,1]$. In this case $n = 10$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "uuid": "8763b99e-6b02-4003-8567-c0f505986e5a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5434, 0.2784, 0.4245, 0.8448, 0.0047, 0.1216, 0.6707, 0.8259,\n",
       "       0.1367, 0.5751])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.2** Generates $2$-dimensional $(X,Y)$, where $X_i$ and $Y_j \\sim U[0,1]$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "uuid": "16f2a7c4-62dd-4d0f-bde9-fafb61e0fb64"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.8913, 0.2092, 0.1853, 0.1084, 0.2197],\n",
       "       [0.9786, 0.8117, 0.1719, 0.8162, 0.2741],\n",
       "       [0.4317, 0.94  , 0.8176, 0.3361, 0.1754],\n",
       "       [0.3728, 0.0057, 0.2524, 0.7957, 0.0153],\n",
       "       [0.5988, 0.6038, 0.1051, 0.3819, 0.0365]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.3** Generates $1$-dimensional $X_1,\\ldots\\,X_n$ where $X_i \\sim U[a,b]$. In other words, we are scaling $U_i \\sim U[0,1]$ and adding a drift term, $X_i = a + U_i*(b-a)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "uuid": "2d14b433-a7da-4aac-a534-56ab4c8a5d84"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.4521, 9.9046, 5.2997, 9.4527, 7.8845, 8.7124, 8.1509, 7.9092,\n",
       "       5.1022, 6.0501])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 5.\n",
    "b = 10.\n",
    "npr.rand(10) * (b - a) + a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.4** Same transformation as in **1.3)** but in $2$ dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "a05adb2b-5704-4189-b0e8-19318ac3f0b9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.7234, 8.8456, 6.2535, 6.4295, 9.262 ],\n",
       "       [9.875 , 9.4243, 6.7975, 7.9943, 6.774 ],\n",
       "       [6.701 , 5.8904, 6.1885, 5.2243, 7.5272],\n",
       "       [6.8813, 7.964 , 8.1497, 5.713 , 9.6692],\n",
       "       [9.7319, 8.0115, 6.9388, 6.8159, 6.0217]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5) * (b - a) + a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Plotting Random Samples\n",
    "#### ([Back to Top](#Table-of-Contents))\n",
    "\n",
    "**2.1)** First we can compute a couple random samples using random number generators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "4618b170-6bd3-4500-905a-0fe402f198c1"
   },
   "outputs": [],
   "source": [
    "sample_size = 10000\n",
    "\n",
    "# Uniformaly distribibuted sample with 3 observations each\n",
    "rn1 = npr.rand(sample_size, 3)\n",
    "\n",
    "# Sampling 500 integers between 0-9 (10 is not included)\n",
    "rn2 = npr.randint(0, 10, sample_size)\n",
    "\n",
    "# Sampling 500 random floats from [0, 1]\n",
    "rn3 = npr.sample(size = sample_size)\n",
    "\n",
    "# Randomly sample values from vector a \n",
    "a = [0, 25, 50, 75, 100]\n",
    "rn4 = npr.choice(a, size = sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false,
    "uuid": "d03c9514-c224-4d2b-ad2a-9285058823b0"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create 2x2 subplots of each of our random number generators\n",
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n",
    "                                             figsize=(10, 8))\n",
    "ax1.hist(rn1, bins=25, stacked=True)\n",
    "ax1.set_title('rand')\n",
    "ax1.set_ylabel('frequency')\n",
    "\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('randint')\n",
    "\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('sample')\n",
    "ax3.set_ylabel('frequency')\n",
    "\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('choice');\n",
    "\n",
    "fig.suptitle('Histograms of simple random numbers', fontsize=16)\n",
    "plt.savefig('./images/stoch_01.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.2)** We can also generate randoom numbers from distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "fb2966ea-91ff-49c7-80e6-24bd6162cc5a"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "\n",
    "# Generate random samples from standard normal\n",
    "rn1 = npr.standard_normal(sample_size)\n",
    "\n",
    "# Generate random samples from normal\n",
    "rn2 = npr.normal(loc= 100, scale=20, size = sample_size)\n",
    "\n",
    "# Generate random samples from chisquare\n",
    "rn3 = npr.chisquare(df= 2, size = sample_size)\n",
    "\n",
    "# Generate random samples from poisson\n",
    "rn4 = npr.poisson(lam= 1, size = sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "3f790711-f965-4a10-b3df-47cc85d708d3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HH6Jz587Q0dHJd98efX39fONWq1atwtpZEm/Tzrxt0tLSkt7z8uVL/Otf/8r1uqmpaanaUdDyfLPQK46Wlha2bduGkJAQREVFYf/+/ahWrRqcnZ3h4+MDLS0tXLx4EQsXLsT169dhaGiI1q1b5/pSeZssedutUChgbGwsnWj/ppxzy6ytrQucVlJSEszMzBAWFoatW7di48aNCAsLQ4MGDbBw4cIie7Le9PLlS+mfhTd98MEHuc4JAlDsRQAvX75EzZo1803nbaizHArKlzOet7d3gaciPHnyRPo97+f25vqrjoLaDeT/vN+0evVqrFu3Dj/99BN++OEHVKlSBQMHDsSiRYsK3UcAxX8GVapUyXfVpYmJCW7dulVMK9SjVCohhChwezUxMcm1veZdrgqFQlqu6myLpBlYkFEuLVq0wJo1a5CRkYELFy5g+/btWLlyJczNzfP9dwsANWrUwLNnz/INf/r0KZo1a4ZatWqhSpUq+e7Xo879ew4cOIC1a9ciICAA9vb2Utd6jx49Stm6/ynrdr6NsmqnsbFxvoxvfokC5duOvOrVq4dly5ZBpVLh0qVL+O6777Bt2zZ07NgRVlZW8PDwQJcuXRASEoJGjRoBAL788ssyOdk47wn8KpUKSUlJBX65GRoaQqFQYM+ePdDW1s73ek4BYGtrC1tbWyiVSkRHR2P9+vWYMWMGYmJicvU4FqZGjRoFflk/efJE6uVTV0GfdVEXLahDneVw+/btAscDAH9//wKv1mzQoMFb5XpTQe0Gim67sbEx5s+fj/nz5yM+Ph6HDh3C1q1b0bx5c0ycOLHUWTIzM5GWlparGHr69KlUyCkUinzn7OYtvIuS83kUtr2WZJ0palscOHCg2tOh8sXSmCTR0dHo0aMHnj9/Dl1dXfTo0UM63yPnhOm8/0117doVUVFRuQ5n3Lx5E3/88Qe6dOkCbW1tdOrUCb/88kuu8aKioorN8/vvv6Nu3bpwcXGRdvpxcXF4/vz5W93ZWp125lVcO99GWbXTwsICsbGxuQ7dRUdHV1g73pSQkABLS0vExcVBS0sLXbp0wZIlS6Cjo4MHDx7g1q1bSE5OxpgxY6RiTKVSISYmpkzuWp6QkIBHjx5Jf584cQJZWVmwsLDI996uXbtCCIGUlBS0b99e+jlz5gy2bdsGHR0dhISEYMSIEQBef1EOGjQI48ePh1KpVLuHtGvXrrhx4wZu3rwpDcvIyMCxY8dKvOwtLCxw/PjxXIcIT548WaJpFJSvuOVQkKZNm8LY2BiJiYm5xnvx4gXWrl1boh7k4nprLCwsoFQqc135eevWLdy9e7fA9z9//hy9evXCf//7XwBA69at4ePjg/r160tX875ND9Gvv/4q/f748WNcunRJOiRuYGCAf/75J9f2mPfmu0XNW19fH61bt853k9hff/0VSqVS7XWmuG2RNAd7yEjSoUMHCCEwbdo0uLu7o0qVKti+fTuMjIykLzIjIyPEx8cjNjYWHTt2hIeHB5ydneHu7o6xY8dCqVRizZo1+PDDD6UT6qdOnYrPPvsMfn5+6N+/Py5duiSdP1bUDql9+/bSlWzm5ua4efMm1q1bB4VCgX/++adc25mXOu0srbJq55gxYxAREQF3d3d4eHjg0aNH+a4CLM92vKl58+bQ19eHj48Ppk2bhho1auDAgQNQKBTo1asX6tSpA319fYSFhUGlUuGff/7B7t27kZCQIB1uKcn5WXllZWXBw8MD06ZNQ3JyMlauXIlevXoV2PvZunVr2NnZYfbs2Zg2bRqaNWuGs2fPYv369ZgwYQK0tLRgYWGBdevWwc/PD4MGDUJycjLCw8PRtWtXte8xNmzYMGzfvh3u7u7w8vKCoaEhtm3bhqdPn0p3zleXh4cH/v3vf2Pq1KlwdXXF9evXsWvXrhJNIy91lkNBdHR0MH36dOlcxR49euDevXtYtWoVGjduXKIeMiMjI8TFxeHs2bPo1q1bvnWgZ8+e6NatG2bPno1Zs2ZBT08Pa9asKfTiChMTEzRq1AhLly7Fq1evUK9ePZw4cQIPHjxA3759pXmmpaXh2LFjJbofm5aWFpYtW4a0tDTo6+sjNDQUxsbGcHZ2BvD6XK/ly5dj/vz5GDlyJBISErB79+587QWAo0ePomfPnvnmMX36dEyZMgVeXl4YNmwYHj58iKCgIHTu3LnQQ8t5FbctkuZgDxlJjI2N8fXXX6Nq1aqYM2cOpk2bhvT0dGzdulX60hk7diwyMjIwYcIEXLt2De3atcP27duRlZWFzz//HEuXLoWZmRm+/fZb6QTwHj164Msvv8S5c+fg4eGB6Oho6VyTou76P2zYMLi7u2PPnj2YOHEidu7cifHjx8PR0RGXLl0q13bmpU47S6us2lmrVi3s3LkT1atXh5eXF7Zt24YvvviiwtrxJh0dHWzatAmNGjXCwoULMWnSJNy6dQsbNmxA8+bNYWhoiJCQELx8+RKTJ0/GokWLYGxsjLVr10KlUuHy5ctvNf/mzZtjwIABmDdvHr788ksMGjQIa9euLfT9K1euxLBhw7Bx40ZMmDABP/zwA7y9vaUTn83NzREUFISrV69i8uTJCAgIQIcOHaQrI9VhYGCAXbt2oWPHjli0aBFmzpwJLS0t7Nq1q8Q3HW3RogW2bNmCpKQkTJ8+HT/88IN0hePbKG45FGbUqFFYuHAhfvnlF7i7u2Pt2rXo378/NmzYUKLCetKkSbhz5w7c3d0LvH2EQqHA+vXrYWVlhaVLlyIgIABDhw7Nd+7km4KCgtC9e3esXLkS48ePx6lTp7By5Up8/PHHAIBBgwahbdu28PLyyndxRVF0dHTg5+eH4OBgzJw5U9r+cg4lNmvWDEuWLEFcXBzc3d1x7NgxBAcH55pGjx49YGlpicWLF2PLli355pFzP8K7d+9iypQpCAkJgb29Pb7++usCDysXlrOobZE0h0LwqaZUzo4dO4aGDRuiZcuW0rCIiAjpfjll/TgSer/NnTsXV69exZEjR+SOQkSkNh6ypHJ3/PhxnDp1Ct7e3qhXrx5u3ryJ1atX49NPP2UxRkREBBZkVAHmzZuHVatWYdWqVXj27Blq164NZ2dnTJ06Ve5oREREGoGHLImIiIhkxpP6iYiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIqEjjxo3D8+fPy2x6kyZNQmRk5FtNY/PmzZg7d24ZJSp7ISEhWLRokdwxiKiCRUZGYtKkSdLfiYmJ8PDwgBBCGpaQkABLS8tc412+fBnDhg3DgAEDMGbMGDx+/Fh6LTw8HP3790ffvn0REhKSa1qFuXLlCpydnTFkyBAMHjwYBw8elF47ceIEBg8eDDs7O3h6eiIlJQUAcOzYMYSGhpa67fT2WJBRkU6fPi13BCKiSsnPzw9Tp06FQqFAVlYWtm3bhnHjxiE1NVV6T0ZGBjw9PTF//nz89NNPsLOzw/z58wEAJ0+exM8//4zIyEgcOXIEsbGx+Omnn4qcpxACnp6e8PT0xMGDB7Fp0yasWLECt2/fxvPnz+Hr64uQkBD85z//wUcffYSVK1cCAD755BNcuHAB8fHx5bdAqEg6cgcg+aWmpsLX1xd37tyBlpYW2rZti0WLFkk7hTFjxmDjxo1ISEjAhg0bkJGRgefPn8PBwQFeXl6IjY3F6tWr8dFHH+HPP/9ERkYG/P390b17dyQmJmLu3Ll4/Pgx6tevj2fPnknz3bdvHyIiIpCZmYnk5GS4u7vD1dUVkZGR2LdvH9LS0mBgYIAtW7ZgyZIliImJQa1atVCrVi0YGhrma0dkZCSOHj0KLS0t3LlzB1WqVEFgYCBatmyJR48eYeHChbh//z6EEHBwcMCECRNw7949jBw5Es2aNcP9+/exYsUKzJo1C927d8elS5eQlZWFOXPmICIiArdu3UK7du0QFBQELS0thIeH49ixY0hPT0daWhp8fHzQt2/fCvvciOi1ovZBSqUSX3zxBRISEqBQKGBlZYWZM2dCR0cH7dq1Q58+fZCQkICVK1fC1dUVY8eOxYkTJ5CSkoLZs2fj559/xh9//IHatWsjPDwcenp6he673nTp0iU8e/YM7du3BwBcu3YN169fR3BwMNzd3aX3/d///R8MDAzQtWtXAICjoyOWLVuGpKQkHD16FPb29tDT0wMADBs2DIcOHcLAgQMLXRYZGRmYOnUqPv74YwBA3bp1UbNmTTx69AhXrlxB+/bt0bhxYwCAi4sLhgwZgoCAACgUCjg6OiI0NBTr1q0rs8+GSkDQe+/7778X48aNE0IIkZWVJebPny9u374thBCiZcuW4tmzZ0KlUolRo0aJv/76SwghxKNHj0Tr1q3Fs2fPxG+//SZat24trl27JoQQYvPmzWLkyJFCCCGmTJkiVq9eLYQQ4vbt26JTp05i//79IiUlRYwYMUI8f/5cCCHE77//Ljp16iSEEGL//v2iW7duQqlUCiGE2LZtmxg9erRIT08XqampYujQocLHxydfO/bv3y+6du0qHj58KIQQYtGiRWLOnDlCCCFGjhwptmzZIoQQ4uXLl2Lw4MHiyJEj4u+//xYtW7YU586dE0II6e9jx44JIYTw9/cXvXv3FkqlUvzzzz+iZ8+e4sKFC+LevXvCzc1NpKWlCSGEOHLkiLC3txdCCBEcHCy++OKLt/9giEgtRe2D5syZIxYvXixUKpVIT08X48aNExs2bBBCvN6/ff/999J0WrZsKbZv3y6EEGLDhg2ic+fO4tGjRyI7O1sMHTpUHDp0qNh918SJE4UQQqxYsUIEBwfny/r3339L7xfi9b4jZ/+bw8rKSsTHx4tx48aJI0eOSMNPnz4tHBwcSrRs9uzZI2xsbERaWprYsGGDWLBggfRaZmamaNmypbSvVSqVokOHDtJ+jSoWD1kSunbtihs3bsDNzQ0bN27EmDFj0KhRo1zvUSgUCA8PR1xcHEJDQ7FixQoIIZCWlgYAqF+/Plq3bg0AaNOmDZKTkwEAMTExGDZsGACgUaNGsLCwAADo6+sjPDwcJ0+exJo1axAeHo5Xr15J82vVqhUMDAwAAGfOnIG9vT10dXWhp6eHwYMHF9qWtm3bom7durlyvHr1ChcvXsTIkSMBAIaGhhg2bBiio6MBADo6OujUqZM0jSpVqsDW1hYA0LBhQ3Tu3BkGBgaoWrUqateujeTkZHz44YcIDAzE4cOHsXLlSuzZsyfXYQgiqliF7YOio6MxatQoKBQK6OrqwtnZWdr2AcDMzCzXdOzs7AC83vZbtmyJOnXqQEtLCw0aNEBycnKx+64ct27dQsOGDYvNrVKpChyura1d4PliWlrqf21v3LgRISEhCA8PR7Vq1QqdV840DQwMYGBggPv376s9Dyo7LMgIH330EY4ePYqJEyciJSUFn332GX7++edc73n16hWGDh2KuLg4tGnTBnPmzIGOjo60w6hWrZr0XoVCIQ1/83fgdfEDAI8ePYKDgwPu37+Prl27wsvLK9f8crroC6KtrV3oawXlUKlU+XZsKpUKWVlZAABdXV0pF/C6IFMoFLn+zisuLg7Ozs5ISUlBz549MWHChEIzEVH5K2wflLcIeXPbB/Lva97c3gva9ovbd72ZobAC6E316tXDkydPpL8zMzORlJSEOnXq5HstMTFR+oezKBkZGZg5cyaOHDmCPXv24F//+leB80pMTESNGjVyLYPs7Owi97FUfliQEXbv3g1fX19YWlpi9uzZsLS0xJ9//gngdfGTlZWFO3fuICUlBV5eXrC1tcXZs2eRkZFR7A7HysoKERERAIAHDx4gNjYWAHD16lWYmJhgypQpsLKywvHjxwG83hkUNI0DBw4gPT0d6enp+PHHH0vUPgMDA3Ts2Ajo8ecAACAASURBVBG7du0CACiVShw4cEA6x6I0zp07h3bt2uGzzz6Dubk5oqKiCsxORPKytLTErl27IIRARkYG9u7d+1bbvrr7riZNmuDvv/8udnodO3bEixcvcPHiRQDA/v370alTJxgZGaFPnz44dOgQXr16hYyMDERGRuKTTz4pdpo5V0/u2bMHDRo0kIZbWlri8uXLuH37NgBgz5496NOnj/S6UqlEeno66tevX+w8qOzxpH6Cg4MDzp49i4EDB6J69eqoX78+Ro8eDQDo27cvXF1dERoail69emHAgAEwMjJCw4YN0bx5c9y5cwe6urqFTjsgIAC+vr4YMGAA6tatK/2n1rNnT+zbtw/9+/dH9erV0aFDB5iYmODOnTv5puHs7Iy7d+/C3t4exsbG+Q6nqmPlypVYtGgRIiMjkZGRgcGDB2PYsGGl7pq3t7fHf//7XwwcOBBVqlRBjx49kJycLF1CTkSawc/PD0uWLMHgwYORmZkJKysreHh4lHp66u677OzssHTpUnh6ehY5vSpVqiA0NBSLFi1CWloajI2NERgYCACwtbXFH3/8geHDhyMzMxN9+vSBg4MDAODbb7/F1atXsXTp0lzTu3DhAo4fP47GjRvDxcVFGj5r1ixYWVlh+fLl8PT0RGZmJho2bCjNCwBOnTqFXr16FblPp/KjEAUdpCYiIqK3Mm7cOHh5eaFDhw5lPu2UlBT4+flhzZo1ZTbN0aNHY968edI/zlSxeMiSiIioHCxatAjr1q1T62auJZWQkIDp06eX2fSOHj0KMzMzFmMyYg8ZERERkczYQ0ZEREQkMxZkRERERDKrlFdZPnmilDtCkWrW1ENSUv4bBWoKTc8HaH5GTc8HaH7GkuYzNc3/uCw5bNiwAb/88gsyMzPh4uICc3NzzJ07FwqFAi1atEBAQECRN+988kSpUZ8NsxRMk7IAmpWHWQpXWB519l/sISsHOjqafVM9Tc8HaH5GTc8HaH5GTc9XkNjYWPz+++/49ttvsWPHDjx69AjLly+Hl5cXdu/eDSEEoqKiip2OJrWdWQqmSVkAzcrDLIV7mzwsyIiI1HTq1Cm0bNkSU6dOhYeHB3r16oW4uDiYm5sDAKytrRETEyNzSiKqjCr8kOXQoUOlZxQ2aNAATk5OWLp0KbS1tWFpaYlp06ZVdCQiIrUkJSXhwYMHCA8Px7179zB58mQIIaRHbenr60OpLPqUipo1Xz+mRlMOwQLMUhhNygJoVh5mKVxp81RoQZaeng4hBHbs2CENGzJkCEJCQvDRRx9h4sSJuHbtGtq0aVORsYiI1GJsbIymTZtCV1cXTZs2RdWqVfHo0SPp9dTUVBgZGRU5jaSkVzA1NdSYc2GZpWCalAXQrDzMUrjC8qhTpFVoQZaQkIC0tDSMGzcOWVlZmD59OjIyMtCwYUMAr5+zFRMTU2xBVrOmnsYdN85L0yr2vDQ9H6D5GTU9H6D5GTU9X15du3bFN998g88++wyPHz9GWloaevTogdjYWFhYWCA6Ohrdu3eXOyYRVUIVWpBVq1YN48ePx/Dhw3H79m24u7vn+m9SX19frYexatIVFQXRtIo9L03PB2h+Rk3PB2h+xpLm04TirXfv3jh37hwcHR0hhIC/vz8aNGiABQsWICgoCE2bNoWdnZ3cMYmoEqrQgqxJkyZo1KgRFAoFmjRpAkNDQ7x48UJ6XZ3ufiIiOc2ZMyffsJ07d8qQhIjeJRV6leW+ffuwYsUKAEBiYiLS0tKgp6eHu3fvQgiBU6dOwczMrCIjEREREcmuQnvIHB0d4evrCxcXFygUCixbtgxaWlqYNWsWsrOzYWlpiY4dO1ZkJCqBcSt+Uet9W+balsm01JkOERHAfQpVfhVakOnq6mLVqlX5hu/du7ciYxARERFpFN4YloiIiEhmLMiIiIiIZFYpHy5Omk3dc83KYjo8J4SIiN4F7CEjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikhkLMiIiIiKZsSAjIiIikpmO3AGIiCqToUOHwsDAAADQoEEDODk5YenSpdDW1oalpSWmTZsmc0IiqoxYkBERqSk9PR1CCOzYsUMaNmTIEISEhOCjjz7CxIkTce3aNbRp00bGlERUGbEgIyJSU0JCAtLS0jBu3DhkZWVh+vTpyMjIQMOGDQEAlpaWiImJKbIgq1lTDwBgampYIZnVoclZBnsfLLdpl/X7y5sm5WGWwpU2DwsyIiI1VatWDePHj8fw4cNx+/ZtuLu7w8jISHpdX18ff//9d5HTSEp6BVNTQzx5oizvuGp5n7KUZNqatFwAzcrDLIUrLI86RRoLMiIiNTVp0gSNGjWCQqFAkyZNYGhoiBcvXkivp6am5irQiIjUxassiYjUtG/fPqxYsQIAkJiYiLS0NOjp6eHu3bsQQuDUqVMwMzOTOSURVUbsISMiUpOjoyN8fX3h4uIChUKBZcuWQUtLC7NmzUJ2djYsLS3RsWNHuWMSUSXEgoyISE26urpYtWpVvuF79+6VIQ0RvUtkOWT57Nkz2NjY4ObNm7hz5w5cXFzg6uqKgIAAqFQqOSIRERERyabCC7LMzEz4+/ujWrVqAIDly5fDy8sLu3fvhhACUVFRFR2JiIiISFYVXpAFBgbC2dkZtWvXBgDExcXB3NwcAGBtbY2YmJiKjkREREQkqwo9hywyMhImJiawsrLCxo0bAQBCCCgUCgCv7+GjVBZ/P5GaNfWgo6NdrlnflqbdqC4vTc+nLnXboc7NJQ+vGlIu85aTpmfU9HxERBWlQguy/fv3Q6FQ4MyZM4iPj4ePjw+eP38uva7uPXySkl6VZ8y3pmk3qstL0/OVRFm2ozLfNLIgmp6xpPlYvJGmGLfiF7Xet2WubTknoXdJhRZku3btkn53c3PDwoUL8dVXXyE2NhYWFhaIjo5G9+7dKzISERERkexkvzGsj48PQkJC4OTkhMzMTNjZ2ckdiYiIiKhCyXYfsh07dki/79y5U64YRERERLKTvYeMiIiI6H3HgoyIiIhIZizIiIiIiGTGZ1kSERH9f+re0oKorLGHjIiIiEhmLMiIiIiIZMZDllSp8fACERG9C9hDRkRERCQzFmREREREMmNBRkRERCQzFmREREREMmNBRkRERCQzXmVJRERUDtS5CnzLXNsKSEKVAXvIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIqASePXsGGxsb3Lx5E3fu3IGLiwtcXV0REBAAlUoldzwiqqRYkBERqSkzMxP+/v6oVq0aAGD58uXw8vLC7t27IYRAVFSUzAmJqLLiVZYEgM+EJFJHYGAgnJ2dsXHjRgBAXFwczM3NAQDW1tY4ffo0+vbtK2dEIqqkWJAREakhMjISJiYmsLKykgoyIQQUCgUAQF9fH0qlstjp1KypBwAwNTUsv7Al9L5k0aR25ihJJk3KzyyFK20eFmRERGrYv38/FAoFzpw5g/j4ePj4+OD58+fS66mpqTAyMip2OklJr2BqaognT4ov3irC+5RFU9r5JnUzvU+fU0loUhag8DzqFGksyIiI1LBr1y7pdzc3NyxcuBBfffUVYmNjYWFhgejoaHTv3l3GhERUmbEgI/r/eFdtKikfHx8sWLAAQUFBaNq0Kezs7OSORESVFAsyIqIS2rFjh/T7zp07ZUxCRO8K3vaCiIiISGYsyIiIiIhkxoKMiIiISGYsyIiIiIhkVuqC7MqVK2WZg4iIiOi9VeqrLFeuXImkpCQMGTIEQ4YMgampaVnmIiIiInpvlLog++abb3D//n0cPHgQ48ePR7169TB06FD06dMHVapUKcuMRERERO+0tzqH7MMPP4SDgwPs7e3x559/YseOHbC3t8fRo0cLfH92djZ8fX3h7OwMFxcX/PHHH7hz5w5cXFzg6uqKgIAAqFSqt4lEREREVOmUuods7969OHToEJ48eQIHBwfs3r0bdevWRWJiIoYOHYq+ffvmG+f48eMAgD179iA2NharV6+GEAJeXl6wsLCAv78/oqKiChyXiIiI6F1V6oLs/Pnz8PT0hLm5ea7hderUQUBAQIHjfPLJJ+jVqxcA4MGDBzAyMkJMTIw0DWtra5w+fbrYgqxmTT3o6GiXNnqF0LSnz+el6fk0lTqPVzq8akgFJFGPpn/Omp6PiKiilLog8/b2xjfffANzc3P8/fffCAkJwZw5c/DBBx8U+Tw3HR0d+Pj44OjRowgODsbp06ehUCgAAPr6+lAqi39qe1LSq9LGrhCa9vT5vDQ9X2WnKctW0z/nkuZj8UZE77JSF2SzZs3CoEGDALzuFTMzM8OcOXOwZcuWYscNDAzErFmzMGLECKSnp0vDU1NTYWRkVNpIREREhVKnh1sTqZN7y1zbCkhC5anUJ/W/ePECzs7OAABdXV2MGDECSUlJRY5z4MABbNiwAQBQvXp1KBQKtGvXDrGxsQCA6OhomJmZlTYSERERUaVU6oKsevXqOHnypPT3mTNnUL169SLH6devH65du4aRI0di/PjxmDdvHvz9/RESEgInJydkZmYWebiTiIiI6F1U6kOWX3zxBWbPno05c+YAAOrVq4cvv/yyyHH09PSwdu3afMN37txZ2hhERERElV6pC7LWrVvjyJEjSEpKQpUqVWBgYFCWuYiIiIjeG6UuyK5du4bw8HAkJydDCCEN/+abb8okGBEREdH7otQFmY+PD5ycnNCiRQvpthVEREREVHKlLsiqVauGUaNGlWUWIiIiovdSqQsyS0tL7NixA5aWlqhatao0vH79+mUSjIiIiOh9UeqC7ODBgwCArVu3SsMUCgWioqLePhURERHRe6TUBdkvv1TOOx4TERERaZpS3xg2OTkZfn5+GD16NJKSkuDr64uXL1+WZTYiIiKi90KpC7IFCxagffv2ePHiBfT19VG7dm3MmjWrLLMRERERvRdKfcjy3r17cHJywrfffgtdXV3MmDEDn376aVlmIyKiSooPxCYqmVIXZNra2lAqldI9yG7fvg0trVJ3uBERabzs7Gz4+fnhr7/+gkKhwBdffIGqVati7ty5UCgUaNGiBQICArgvJKISK3VBNn36dLi5ueHhw4eYMmUKLl26hGXLlpVlNiIijXL8+HEAwJ49exAbG4vVq1dDCAEvLy9YWFjA398fUVFR6Nu3r8xJiaiyKXVBZm1tjXbt2uHKlSvIzs7GokWL8MEHH5RlNiIijfLJJ5+gV69eAIAHDx7AyMgIMTExMDc3B/B6v3j69OkiC7KaNfUAAKamhuWeV11yZSlovpq0XCqCOod21VHRy02TPidNygKUPk+pC7LQ0NBcf8fHxwMApk2bVtpJEhFpPB0dHfj4+ODo0aMIDg7G6dOnpVM39PX1oVQqixw/KekVTE0N8eRJ0e+rKHJmyTtfTVoulU1FLjdN+pw0KQtQeB51irQyOdEhMzMTv/zyC549e1YWkyMi0miBgYH4z3/+gwULFiA9PV0anpqaCiMjIxmTEVFlVeoesrw9YVOnTsW4cePeOhARkaY6cOAAEhMTMWnSJFSvXh0KhQLt2rVDbGwsLCwsEB0dje7du8sdk4gqoVIXZHmlpqbiwYMHZTU5IiKN069fP/j6+mLkyJHIysrCvHnz0KxZMyxYsABBQUFo2rQp7Ozs5I5JRJVQqQsyW1tb6bwJIQRevnzJHjIZ8F4/RBVHT08Pa9euzTd8586dMqQhondJqQuyHTt2SL8rFAoYGRnBwMCgTEIRERERvU9KXZCdO3euyNcdHBxKO2kiInoPlNUtH4jeBaUuyE6cOIHz58/D1tYWOjo6OHnyJExNTdGkSRMALMiIiIiI1FXqguz58+c4ePAgatWqBQBQKpXw8PDA8uXLyywcERER0fug1PchS0xMRM2aNaW/q1atiuTk5DIJRURERPQ+KXUPWa9evTBmzBjY2dlBCIEff/wRn376aVlmIyIiInovlLog8/X1xU8//YRz586hatWqmDZtGnr27FmW2YiIiIjeC2/16KTatWujRYsW8PLygq6ublllIiIiInqvlLog2759O9asWYNt27YhLS0N/v7+2Lx5c1lmIyIiInovlLog+/7777F582ZUr14dxsbG2LdvH/bv31+W2YiIiIjeC6UuyLS0tHIdpqxatSq0tbXLJBQRERHR+6TUJ/Wbm5sjMDAQaWlpOHbsGCIiItC9e/eyzEZlhHfDJiIi0mylLsjmzJmDvXv3olWrVjhw4ABsbGzg7Oxc5DiZmZmYN28e7t+/j4yMDEyePBnNmzfH3LlzoVAo0KJFCwQEBEBL662uNSAiIiKqVEpdkE2YMAFbtmwptgh706FDh2BsbIyvvvoKL168gIODA/71r3/By8sLFhYW8Pf3R1RUFPr27VvaWERERESVTqm7ov755x88fPiwROP0798fn3/+OQBACAFtbW3ExcXB3NwcAGBtbY2YmJjSRiIiIiKqlErcQ/bjjz9i4MCBePz4MXr37o0PPvgAVatWhRACCoUCUVFRhY6rr68PAEhJSYGnpye8vLwQGBgIhUIhva5UKovNULOmHnR0NPsCAlNTQ7kjkEw06bPXpCwF0fR8REQVpcQFWXBwMPr164fk5GT88ssvUiGmrocPH2Lq1KlwdXXF4MGD8dVXX0mvpaamwsjIqNhpJCW9KmnsCmVqaognT4ovLOndpCmfvaavhyXNx+KNiN5lJS7IOnfujPbt20MIgT59+kjDcwqz+Pj4Qsd9+vQpxo0bB39/f/To0QMA0KZNG8TGxsLCwgLR0dG8UpOIiIjeOyU+h2z58uWIj49H7969ER8fL/0kJCQUWYwBQHh4OF6+fImwsDC4ubnBzc0NXl5eCAkJgZOTEzIzM2FnZ1fqxhARERFVRqW+ynL9+vUlHsfPzw9+fn75hu/cubO0MYiIiIgqPd7wi4iIiEhmLMiIiIiIZMaCjIiIiEhmpT6HjIiIiDSDOs8s3jLXtgKSUGmxICMiUgOfxUtE5YkFGRGRGvgsXiIqT/xXjohIDXwWLxGVJ/aQERGpoSyfxQto1qOgNCkLlZ+y/Jw1aZ3RpCxA6fOwICMiUlNZPYtXk54zqklZqHyV1eesSeuMJmUBCs+jTpHGQ5ZERGrIeRbv7Nmz4ejoCOB/z+IFgOjoaJiZmckZkYgqMfaQEZUxXn7+bnrzWbxhYWEAgPnz52PJkiUICgpC06ZN+SxeIio1FmRERGrgs3iJqDzxkCURERGRzNhDRkREJaLOYXkiKhkWZEQyUPcLjeeaERG9H3jIkoiIiEhmLMiIiIiIZMaCjIiIiEhmLMiIiIiIZMaCjIiIiEhmvMqSiIgkvKXFu4tXd2s29pARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMeGNYDcYbNBIREb0f2ENGREREJDNZCrLLly/Dzc0NAHDnzh24uLjA1dUVAQEBUKlUckQiIiIikk2FF2SbNm2Cn58f0tPTAQDLly+Hl5cXdu/eDSEEoqKiKjoSERERkawq/Byyhg0bIiQkBHPmzAEAxMXFwdzcHABgbW2N06dPo2/fvkVOo2ZNPejoaJd71rdhamoodwR6B7zteqTp66Gm5yMiqigVXpDZ2dnh3r170t9CCCgUCgCAvr4+lEplsdNISnpVbvnKgqmpIZ48Kb4dRMV5m/VI09fDkuZj8UZE7zLZT+rX0vpfhNTUVBgZGcmYhoiIiKjiyV6QtWnTBrGxsQCA6OhomJmZyZyIiIiIqGLJXpD5+PggJCQETk5OyMzMhJ2dndyRiIgKxavEiag8yHJj2AYNGmDv3r0AgCZNmmDnzp1yxCAiKpFNmzbh0KFDqF69OoD/XSVuYWEBf39/REVFFXtREhFRQXinfiIiNZXVVeKAZl2koElZSH7qrA+atM5oUhag9HlYkBERqamsrhLXpCtgNSkLaYbi1gdNWmc0KQtQeB51ijQWZDLgMyqJ3g28SpyIyorsJ/UTEVVWvEqciMoKCzIiolLiVeJEVFZ4yJKIqAR4lTgRlQcWZCWgzrlfW+baVkASIiIiepewICMiIiIJOx/kwXPIiIiIiGTGgoyIiIhIZizIiIiIiGTGgoyIiIhIZizIiIiIiGTGqyzLGB+LRGWprK524lVTRFSWuE8pe+whIyIiIpIZCzIiIiIimfGQJRHRe4CnUxBptne+IFN3J8Rj3VRZ8YuWiKjy4yFLIiIiIpmxICMiIiKSGQsyIiIiIpm98+eQEZF6yvJcNJ6TSURUMuwhIyIiIpIZe8iIiDQY74hO9H5gDxkRERGRzFiQEREREcmMBRkRERGRzFiQEREREcmMBRkRERGRzHiVJRGVOXWuDDy8akgFJHk/8HmmpIk0cb1U54pkua5s1oiCTKVSYeHChbh+/Tp0dXWxZMkSNGrUSO5YRETF4v6LiMqCRhyyPHbsGDIyMhAREQFvb2+sWLFC7khERGrh/ouIyoJGFGQXLlyAlZUVAKBTp064evWqzImIiNTD/RcRlQWNOGSZkpICAwMD6W9tbW1kZWVBR6fgeKamhmpPuyzPU+E5L0RlqyTbsqYq7f5L3bZzv0NUsd52myvtfk0jesgMDAyQmpoq/a1SqQrdmRERaRLuv4ioLGhEQdalSxdER0cDAC5duoSWLVvKnIiISD3cfxFRWVAIIYTcIXKuUvrjjz8ghMCyZcvQrFkzuWMRERWL+y8iKgsaUZARERERvc804pAlERER0fuMBRkRERGRzFiQlQOlUgkPDw+MGjUKTk5O+P333+WOVKCjR4/C29tb7hi5qFQq+Pv7w8nJCW5ubrhz547ckQp0+fJluLm5yR0jn8zMTMyePRuurq5wdHREVFSU3JHyyc7Ohq+vL5ydneHi4oI//vhD7kjl7tmzZ7CxscHNmzdx584duLi4wNXVFQEBAVCpVBWaZcOGDXBycsKwYcPw3XffyZYnMzMT3t7ecHZ2hqurq2zL5s1tubD5h4aGwtHREc7Ozrhy5UqF5YmPj4erqyvc3Nwwfvx4PH36FACwd+9eDBs2DCNGjMDx48crJEuOw4cPw8nJSfpbjizPnj3D5MmTMXLkSDg7O+Pu3buyZYmPj8eIESPg4uICX19faZ0pVRZBZW7t2rVi69atQgghbt68KRwcHOQNVIDFixcLOzs74eXlJXeUXP7zn/8IHx8fIYQQv//+u/Dw8JA5UX4bN24U9vb2Yvjw4XJHyWffvn1iyZIlQgghkpKShI2NjbyBCnD06FExd+5cIYQQv/32m0Z+xmUpIyNDTJkyRfTr10/cuHFDTJo0Sfz2229CCCEWLFgg/vvf/1ZYlt9++01MmjRJZGdni5SUFBEcHCxbnqNHjwpPT08hhBCnTp0S06ZNq/AsebflguZ/9epV4ebmJlQqlbh//74YNmxYheUZOXKkuHbtmhBCiG+//VYsW7ZMPH78WNjb24v09HTx8uVL6ffyziKEEHFxcWL06NHSMLmy+Pj4iB9++EEIIcSZM2fE8ePHZcsyZcoUceLECSGEEDNnzhRRUVGlzsIesnIwduxYODs7A3jdG1C1alWZE+XXpUsXLFy4UO4Y+VSGu543bNgQISEhcscoUP/+/fH5558DAIQQ0NbWljlRfp988gkWL14MAHjw4AGMjIxkTlS+AgMD4ezsjNq1awMA4uLiYG5uDgCwtrZGTExMhWU5deoUWrZsialTp8LDwwO9evWSLU+TJk2QnZ0NlUqFlJQU6OjoVHiWvNtyQfO/cOECLC0toVAoUL9+fWRnZ+P58+cVkicoKAitW7cG8L/vkitXrqBz587Q1dWFoaEhGjZsiISEhHLPkpSUhKCgIMybN08aJleWixcvIjExEWPHjsXhw4dhbm4uW5bWrVvjxYsXEEIgNTUVOjo6pc7Cguwtfffdd7C3t8/1c/v2bVSrVg1PnjzB7NmzMXPmTI3Kd+XKFQwcOBAKhUK2XIUp7K7nmsTOzk5jb/ypr68PAwMDpKSkwNPTE15eXnJHKpCOjg58fHywePFiDB48WO445SYyMhImJibSPxnA60I5Z9vT19eHUqmssDxJSUm4evUq1q5diy+++AKzZs2SLY+enh7u37+PAQMGYMGCBXBzc6vwLHm35YLmn3efVJ658ubJKeIvXryInTt3YuzYsUhJSYGh4f/uBK+vr4+UlJRyzZKdnY358+fD19cX+vr60nvkyAIA9+/fh5GREbZt24Z69eph06ZNsmVp3Lgxli5digEDBuDZs2ewsLAodRbN/FapRIYPH47hw4fnG379+nXMnDkTc+bMkf7jkkNh+TQV73r+9h4+fIipU6fC1dVVo4udwMBAzJo1CyNGjMAPP/wAPT09uSOVuf3790OhUODMmTOIj4+Hj49Prt6V1NTUCu0hNDY2RtOmTaGrq4umTZuiatWqePTokSx5tm3bBktLS3h7e+Phw4cYM2YMMjMzZcmSQ0vrf30UOfPPu09KTU3N9WVb3n788UesX78eGzduhImJiSx54uLicOfOHSxcuBDp6em4ceMGli5diu7du8uybIyNjWFrawsAsLW1xerVq9GuXTtZsixduhS7du1CixYtsGvXLqxYsQKWlpalysIesnJw48YNfP7551i1ahVsbGzkjlOp8K7nb+fp06cYN24cZs+eDUdHR7njFOjAgQPYsGEDAKB69epQKBS5vgjfJbt27cLOnTuxY8cOtG7dGoGBgbC2tkZsbCwAIDo6GmZmZhWWp2vXrvj1118hhEBiYiLS0tLQo0cPWfIYGRlJX1I1atRAVlYW2rRpI9uyAVDgdnhGHgAAIABJREFU/Lt06YJTp05BpVLhwYMHUKlUMDExqZA8Bw8elNafjz76CADQoUMHXLhwAenp6VAqlbh582a57yc7dOiAH374ATt27EBQUBCaN2+O+fPny5IFeL0enzx5EgBw7tw5NG/eXLYsNWrUkHpQa9eujZcvX5Y6C7seysGqVauQkZGBpUuXAnjd67N+/XqZU1UOffv2xenTp+Hs7Czd9ZzUFx4ejpcvXyIsLAxhYWEAgE2bNqFatWoyJ/uffv36wdfXFyNHjkRWVhbmzZunUfnKm4+PDxYsWICgoCA0bdoUdnZ2FTbv3r1749y5c3B0dIQQAv7+/mjQoIEsecaOHYt58+bB1dUVmZmZmDFjBtq1ayfbsgEK/my0tbVhZmYGJycn6SrwipCdnY2lS5eiXr16mD59OgCgW7du8PT0hJubG1xdXSGEwIwZM2Q7T9nU1FSWLD4+PvDz88OePXtgYGCAVatWoUaNGrJkWbJkCWbMmAEdHR1UqVIFixcvLvVy4Z36iYiIiGT2bh4nICIiIqpEWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJARERERyYwFGREREZHMWJBRuYiNjYW9vX2Br61duxYHDhyo4ERERCVz7949tG7dGkOGDJF+Pv30U+zbt6/I8ebPn4+YmJgKSknvCh25A9D75/PPP5c7AhGRWqpVq4aDBw9KfycmJsLe3h7/r717D6uqTvQ//t6AoHIJUezoQT04ad6yU5lakZfMqHnGvAzKZcIUnTOZYlheAAUsrxw92AyOmjRNJ7AhU2eko6fOiJWpDFqmjogzZzzqeCEviQpoinvv3x/+3OMF3aiw1gI+r+eZ53Ev9l7r43Za+8N3ffd3devWjU6dOlX5mjlz5hgVT+oRFTK5Z6tWreK3v/0tHh4eNGvWjPT0dADOnz/PpEmT+L//+z8uXrzI7Nmz6dGjB4mJiXTo0IExY8Zct5+vv/6a+fPn43A4APjFL35BeHg4x48fJzExkRMnTtC6dWs8PT157rnnGDZsGA8++CAFBQUEBQUBuB4HBgYyd+5cdu3aRUVFBU6nk9mzZ/PYY4+RmJjImTNnOHz4MP369eO1115j4cKFbN++HbvdTpcuXZgxYwZ+fn7GvpEiYnn3338/7dq14+DBg+Tn57Nu3To8PT0JDQ0lJSWF4OBgYmNj+dnPfsazzz7LrFmz2LFjB40aNSIkJIR58+bh4+NT5XZfX182bNjA4sWLsdvt+Pn5kZSURPfu3cnMzOTo0aOcPHmSo0ePEhQUxKJFi7j//vvNfkukhuiSpdyTffv2sXDhQt59910++eQTnnnmGZYuXQrAd999x6hRo1i7di1RUVFkZmbedl+ZmZmMHj2aNWvWMHfuXP70pz8BkJaWxsMPP8y6detITk52bb+dXbt2ceLECT766CPWr1/P0KFDycrKcv38hx9+YN26dUyZMoXly5fj6enJmjVryMvLo2XLlixcuPAe3hURqa++/fZb/v73v7N//36++uorVq1axSeffEKHDh1ITEy87rk7d+5k27Zt5OXlsWbNGtq0acNf/vKXW27fv38/aWlpZGZm8sknnzBx4kReffVVysvLgSu/tP7yl7/k008/JSAggI8++siMt0BqiUbI5J4UFBQQFhZGq1atABg1ahRwZQ5ZmzZtePjhhwHo1KkTq1evvu2+XnjhBd566y02btzIk08+yeuvv+7aV3JyMgChoaE8+eSTbnM98sgj3HfffeTm5nL48GEKCwvx9fV1/fyxxx5z/fmLL76grKzMNeejsrKS5s2bV/MdEJH67IcffmDw4MEA2O12mjVrxoIFC1izZg3Dhg2jadOmAIwcOZJly5Zx6dIl12s7duyIp6cnw4cPJywsjPDwcLp37865c+eq3L5ixQp69+5NmzZtAHjiiScICgpiz549APTs2dM1ct+lSxfOnj1r5FshtUyFTO6Jp6cnNpvN9fiHH37g6NGjADRq1Mi13Waz4XQ6b7uvqKgo+vfvz5YtW/jqq69YvHgxeXl5+Pj4XPfaa/d7rWtPhF988QVz5sxh9OjRDBgwgPbt25OXl+f6+dWTKIDD4SA5OZm+ffsCUFFRwcWLF6vz1xeReu7GOWRX3fgLpsPh4PLly9dtCwgIYO3atezYsYM//elPJCQkMHLkSNeVgxu3e3nd/JHsdDpd+23cuLFre3XOqVK36JKl3JNevXpRUFDAiRMnAMjNzWXBggV3ta+oqCiKi4sZNmwYs2bN4ty5c5w9e5Z+/fqRm5sLXLkMWlBQ4HpNUFAQf/7znwH44x//6Nq+ZcsW+vfvT0xMDA899BAbNmzAbrdXedywsDBWrFjBpUuXcDgcpKSkkJGRcVd/BxFpGMLCwlizZg3nz58HIDs7m8cffxxvb2/Xcz7//HNGjRrFI488Qnx8PEOGDGHfvn233N67d2+2bNnC4cOHgStXIEpKSlxXGqR+0wiZ3JMHH3yQKVOmMHbsWACCg4OZO3cuBw8evON9TZ48mblz5/L222/j4eHBhAkTCAkJISkpiZkzZzJo0CCaN2/uujwKMGPGDN566y0CAgJ48sknCQ4OBq6Uu8mTJzNo0CA8PT3p0aMH//M//+P6wsC1Xn31VdLT0xk6dCh2u53OnTvfNBdERORaERERlJSUMHz4cBwOB+3atbtp7mmfPn3YtGkTP/nJT2jatCn33Xcfs2bNolWrVlVuDwkJIS0tjQkTJmC322ncuDHLli3D39/fpL+lGMnm1Jin1DFXv305bNgws6OIiIjUCF2yFBERETGZRshERERETKYRMhERERGTqZCJiIiImKxOfsvy5Mmyaj+3WbOmlJaer8U0ylEXMyiH9TK4yxEcbNw3zSorK0lOTubo0aNcunSJcePG8cADD5CYmIjNZqNDhw6kpaXh4eHB4sWL+eKLL/Dy8iI5OZnu3bvfdt93cv4C6/zb3MiqucC62ayaC6ybrb7kqs75q04Wsjvh5eVpdgRAOayWAZTDahnAOjny8vIIDAxkwYIFnDlzhiFDhtCpUycSEhLo1asXqamp5Ofn07p1a7Zt28bHH39MSUkJ8fHxbu9Icaes8p7cyKq5wLrZrJoLrJutIeWq94VMROROPf/884SHhwNXVkr39PSkqKiInj17AlfWl9qyZQuhoaGEhYVhs9lo3bo1drud06dPu252LyJSXSpkIiI3uHrf0/LyciZOnEhCQgLp6emu24T5+vpSVlZGeXk5gYGB172urKzstoWsWbOmd/zbtZGXa++EVXOBdbNZNRdYN1tDyaVCJiJShZKSEsaPH09MTAyDBg267pZgFRUVBAQE4OfnR0VFxXXb3a2qfqfzYYKD/e943pkRrJoLrJvNqrnAutnqS67qlDd9y1JE5AanTp0iLi6OKVOmEBERAUCXLl0oLCwEYNOmTfTo0YNHH32UzZs343A4OHbsGA6HQ5crReSuaIRMROQGy5Yt49y5cyxZsoQlS5YAMH36dGbPnk1GRgbt27cnPDzcdZ/UyMhIHA4HqampJicXkbpKhUxE5AYzZsxgxowZN23Pycm5aVt8fDzx8fFGxBKRekyXLEVERERMpkImIiIiYrJavWS5a9cuFi5cSHZ2NsXFxcyaNQtPT0+8vb1JT0+nRYsWrFy5ktzcXLy8vBg3bhz9+/ev0QyD3lhbree9l/hMjR5XRKS+ipu/0e1zdE4VuTO1VsiysrLIy8ujSZMmAMyZM4eUlBQ6d+5Mbm4uWVlZjB07luzsbFavXs3FixeJiYnhqaeewtvbu7ZiiYiIiFhOrV2ybNu2LZmZma7HGRkZdO7cGQC73Y6Pjw+7d+/mkUcewdvbG39/f9q2bcu+fftqK5KIiIiIJdXaCFl4eDhHjhxxPW7ZsiUAO3bsICcnhxUrVvDVV19dt4iir68v5eXlbvd9Nytdu2PESsBWWW3YCjmskAGUw2oZwDo5RESMZOiyF+vXr2fp0qUsX76coKCgu1rlGu58pevqqO2VgK2y2rAVclghg3JYL4O7HCpqIlKfGfYty7Vr15KTk0N2djZt2rQBoHv37nzzzTdcvHiRsrIy9u/fT8eOHY2KJCIiImIJhoyQ2e125syZQ6tWrVwLKD7++ONMnDiR2NhYYmJicDqdTJo0CR8fHyMiiYjUCdX5pri+0ShS99VqIQsJCWHlypUAbNu2rcrnjBgxghEjRtRmDBERERFL08KwIiIiIiZTIRMRERExmQqZiIiIiMlUyERERERMpkImIiIiYjIVMhERERGTGbpSv4hIXbJr1y4WLlxIdnY2kyZN4tSpUwAcPXqUhx9+mEWLFjFu3DhKS0tp1KgRPj4+vPvuuyanFpG6SIXs/4ubv9Htc7T4okjDkZWVRV5eHk2aNAFg0aJFAJw9e5aRI0eSlJQEwKFDh1i3bh02m820rCJS9+mSpYhIFdq2bUtmZuZN2zMzM3nppZdo2bIlp06d4ty5c7zyyitER0fz+eefm5BUROoDjZCJiFQhPDycI0eOXLft+++/p6CgwDU6VllZSVxcHCNHjuTs2bNER0fTvXt3mjdvfsv9NmvWFC8vzxrNasUbr5udyezj34pVc4F1szWUXCpkIiLV9Omnn/KTn/wET88rhapFixZERUXh5eVF8+bN6dy5MwcOHLhtISstPV/juU6eLKvxfd4rMzMFB/tb8j2xai6wbrb6kqs65U2XLEVEqqmgoIA+ffq4Hm/dupXXXnsNgIqKCv73f/+X9u3bmxVPROowjZCJiFTTgQMHaNOmjetx37592bx5MyNGjMDDw4PXX3+doKAgExOKSF2lQiYicgshISGsXLnS9XjdunU3PWf69OlGRhKRekqXLEVERERMpkImIiIiYjIVMhERERGTqZCJiIiImEyFTERERMRkKmQiIiIiJlMhExERETGZCpmIiIiIyVTIRERERExWq4Vs165dxMbGAnDo0CGio6OJiYkhLS0Nh8MBwOLFi4mIiCAqKordu3fXZhwRERERS6q1QpaVlcWMGTO4ePEiAPPmzSMhIYEPP/wQp9NJfn4+RUVFbNu2jY8//piMjAzefPPN2oojIiIiYlm1di/Ltm3bkpmZydSpUwEoKiqiZ8+eAPTp04ctW7YQGhpKWFgYNpuN1q1bY7fbOX36tNub8zZr1hQvL8/ain5LwcH+pr6+plghhxUygHJYLQNYJ4eIiJFqrZCFh4dz5MgR12On04nNZgPA19eXsrIyysvLCQwMdD3n6nZ3hay09HzthHbj5Mmyu35tcLD/Pb2+plghhxUyKIf1MrjLoaImIvWZYZP6PTz+caiKigoCAgLw8/OjoqLiuu3+/jrpioiISMNiWCHr0qULhYWFAGzatIkePXrw6KOPsnnzZhwOB8eOHcPhcLgdHRMRERGpb2rtkuWNpk2bRkpKChkZGbRv357w8HA8PT3p0aMHkZGROBwOUlNTjYojIiIiYhm1WshCQkJYuXIlAKGhoeTk5Nz0nPj4eOLj42szhoiIiIilaWFYEZFbuHYtxb179/L0008TGxtLbGws69evB7SWoojUDMMuWYqI1CVZWVnk5eXRpEkT4MrSPaNHjyYuLs71nGvXUiwpKSE+Pp7Vq1ebFVlE6jAVMhGRKty4luKePXs4cOAA+fn5tGvXjuTkZL755ps7XkuxNtZRtOKSIGZnMvv4t2LVXGDdbA0llwqZiEgVblxLsXv37gwfPpxu3bqxdOlSfv3rX+Pv73/HaynWxjqKVlhD7kZmZrLKuno3smousG62+pKrOuVNc8hERKph4MCBdOvWzfXnvXv3ai1FEakxKmQiItUwZswY16T9goICunbtqrUURaTG6JKliEg1zJw5k1mzZtGoUSNatGjBrFmz8PPz01qKIlIjVMhERG7h2rUUu3btSm5u7k3P0VqKIlITdMlSRERExGQqZCIiIiImUyETERERMZkKmYiIiIjJVMhERERETKZCJiIiImIyFTIRERERk6mQiYiIiJhMhUxERETEZCpkIiIiIiZTIRMRERExmQqZiIiIiMlUyERERERMpkImIiIiYjIVMhERERGTeRl5sMrKShITEzl69CgeHh7MmjULLy8vEhMTsdlsdOjQgbS0NDw81BNFRESk4TC0kH355ZdcvnyZ3NxctmzZwttvv01lZSUJCQn06tWL1NRU8vPzGThwoJGxRESqtGvXLhYuXEh2djbFxcXMmjULT09PvL29SU9Pp0WLFsyePZsdO3bg6+sLwJIlS/D39zc5uYjUNYYWstDQUOx2Ow6Hg/Lycry8vNi5cyc9e/YEoE+fPmzZssVtIWvWrCleXp5GRL5OcPC9nWTv9fU1xQo5rJABlMNqGcA6ObKyssjLy6NJkyYAzJkzh5SUFDp37kxubi5ZWVkkJSVRVFTEu+++S1BQkMmJRaQuM7SQNW3alKNHj/LCCy9QWlrKsmXL2L59OzabDQBfX1/Kysrc7qe09HxtR63SyZPus91KcLD/Pb2+plghhxUyKIf1MrjLYXRRa9u2LZmZmUydOhWAjIwMWrZsCYDdbsfHxweHw8GhQ4dITU3l1KlTREREEBERYWhOEakfDC1k77//PmFhYbzxxhuUlJTw8ssvU1lZ6fp5RUUFAQEBRkYSEalSeHg4R44ccT2+WsZ27NhBTk4OK1as4Pz587z00kuMHj0au93OyJEj6datG506dbrlfmtjhN8qo4rXMjuT2ce/FavmAutmayi53Bay3bt307179xo5WEBAAI0aNQLgvvvu4/Lly3Tp0oXCwkJ69erFpk2b6N27d40cS0Skpq1fv56lS5eyfPlygoKCXCXs6mXN3r17s2/fvtsWstoY4bfC6OaNzMxklRHfG1k1F1g3W33JVZ3y5vbrjAsXLmTQoEG8++67nDx5stoHr8qoUaMoKioiJiaGl19+mUmTJpGamkpmZiaRkZFUVlYSHh5+T8cQEakNa9euJScnh+zsbNq0aQPAwYMHiY6Oxm63U1lZyY4dO+jatavJSUWkLnI7QvbBBx9w9OhR1q5dy5gxY2jVqhVDhw5lwIABrtGu6vL19eWXv/zlTdtzcnLuaD8iIkay2+3MmTOHVq1aER8fD8Djjz/OxIkTGTx4MCNGjKBRo0YMHjyYDh06mJxWROqias0h++d//meGDBmCl5cXubm5ZGdns2jRIiZPnqwlKkSk3goJCWHlypUAbNu2rcrnjB07lrFjxxoZS0TqIbeFbOXKleTl5XHy5EmGDBnChx9+yD/90z9x/Phxhg4dqkImIiIico/cFrKvv/6aiRMnutYKu+r+++8nLS2t1oKJiIiINBRuJ/W/8cYbfPnllwAcPnyYqVOncurUKQBNwBcRERGpAW4L2eTJk13fKLr//vvp0aOHa6FEEREREbl3bgvZmTNniIqKAsDb25sRI0ZQWlpa68FEREREGgq3haxJkyauS5YABQUFrkUQRUREROTeuZ3U/+abbzJlyhTXZcpWrVrx7//+77UeTERERKShcFvIOnfuzH/9139RWlpKo0aN8PPzMyKXiIiISIPhtpDt3buXZcuWcfbsWZxOp2v7Bx98UKvBRERERBoKt4Vs2rRpREZG0qFDB2w2mxGZRERERBoUt4WscePGvPTSS0ZkEREREWmQ3BaysLAwsrOzCQsLw8fHx7W9devWtRpMREREpKFwW8jWrl0LwG9/+1vXNpvNRn5+fu2lEhEREWlA3BayjRs3GpFDREREpMFyuzDs2bNnmTFjBiNHjqS0tJSkpCTOnTtnRDYRERGRBsFtIUtJSeGhhx7izJkz+Pr60rJlSyZPnmxENhEREZEGwW0hO3LkCJGRkXh4eODt7c2kSZP47rvvjMgmIiIi0iC4LWSenp6UlZW51iA7ePAgHh5uXyYiUuft2rWL2NhYAA4dOkR0dDQxMTGkpaXhcDgAWLx4MREREURFRbF7924z44pIHeZ2Un98fDyxsbGUlJTw6quvsnPnTubOnWtENhER02RlZZGXl0eTJk0AmDdvHgkJCfTq1YvU1FTy8/Np3bo127Zt4+OPP6akpIT4+HhWr15tcnIRqYvcFrI+ffrQrVs3du/ejd1u56233qJFixZGZBMRMU3btm3JzMxk6tSpABQVFdGzZ0/gynlxy5YthIaGEhYWhs1mo3Xr1tjtdk6fPk1QUNAt99usWVO8vDxrNGtwsH+N7q8mmJ3J7OPfilVzgXWzNZRcbgvZ4sWLr3tcXFwMwIQJE2o0iIiIlYSHh3PkyBHXY6fT6Zq64evrS1lZGeXl5QQGBrqec3X77QpZaen5Gs968mRZje/zXpmZKTjY35LviVVzgXWz1Zdc1SlvdzQZrLKyko0bN/L999/fyctEROq8a+fOVlRUEBAQgJ+fHxUVFddt9/e35m/zImJtbkfIbhwJGz9+PHFxcXd9wHfeeYeNGzdSWVlJdHQ0PXv2JDExEZvNRocOHUhLS9OXBkTEcrp06UJhYSG9evVi06ZN9O7dm7Zt27JgwQLGjBnDd999h8PhuO3omIjIrbgtZDeqqKjg2LFjd3WwwsJCvv32W373u99x4cIF3nvvvSonyg4cOPCu9l/b4ua7v2vBe4nPGJBERIw2bdo0UlJSyMjIoH379oSHh+Pp6UmPHj2IjIzE4XCQmppqdkwRqaPcFrJnnnnGNW/C6XRy7ty5ux4h27x5Mx07dmT8+PGUl5czdepUVq5cedNEWXeFrDYmxdaU210ntsrERCvksEIGUA6rZQDr5AAICQlh5cqVAISGhpKTk3PTc+Lj44mPjzc6mojUM24LWXZ2tuvPNpvNNW/ibpSWlnLs2DGWLVvGkSNHGDduXJUTZd3vp+YnxdaUW03ys8rERCvksEIG5bBeBnc5rFTURERqmttCtn379tv+fMiQIdU+WGBgIO3bt8fb25v27dvj4+Nz3ar/VyfKioiIiDQkbgvZF198wddff80zzzyDl5cXX375JcHBwYSGhgJ3Vsgee+wxPvjgA0aPHs2JEye4cOECTzzxxE0TZUVEREQaEreF7PTp06xdu5bmzZsDUFZWxiuvvMK8efPu+GD9+/dn+/btRERE4HQ6SU1NJSQk5KaJsiIiIiINidtCdvz4cZo1a+Z67OPjw9mzZ+/6gFdXvb5WVRNlRURERBoKt4WsX79+vPzyy4SHh+N0Olm/fj0vvviiEdlEREREGgS3hSwpKYn//u//Zvv27fj4+DBhwgSeeuopI7KJiIhUi9aJlLquWkvit2zZkg4dOpCQkIC3t3dtZxIRERFpUNwWsv/8z//k7bff5v333+fChQukpqbym9/8xohsIiIiIg2C20L2+9//nt/85jc0adKEwMBAVq1axerVq43IJiIiItIguC1kHh4e112m9PHxwdPTmrctEhEREamL3E7q79mzJ+np6Vy4cIENGzbw0UcfafFWERERkRrkdoRs6tSptGvXjgcffJA//OEP9O3bl2nTphmRTURERKRBcDtCNnbsWN577z2ioqKMyCMiIiLS4LgdIfvhhx8oKSkxIouIiIhIg3TLEbL169fz4x//mBMnTtC/f39atGiBj48PTqcTm81Gfn6+kTlFRERE6q1bFrJf/epXPPfcc5w9e5aNGze6ipiISEO1Zs0afv/73wNw8eJFiouLycjIID09nVatWgEQHx9Pz549zYwpInXQLQvZI488wkMPPYTT6WTAgAGu7VeLWXFxsSEBRUSsYtiwYQwbNgyAN998k5/+9Kfs2bOHKVOmEB4ebnI6EanLbjmHbN68eRQXF9O/f3+Ki4td/9u3b5/KmIg0aH/+85/529/+RmRkJEVFRaxevZqYmBjmz5/P5cuXzY4nInWQ229ZLl261Igc9YZucCtS/73zzjuMHz8egKeeeopnn32WkJAQ0tLSyM3N5aWXXrrla5s1a4qXV80urh0c7F+j+6sJymTdDLdi1WwNJZfbQiYiIv9w7tw5Dhw44Fog+6c//SkBAQEADBgwgM8+++y2ry8tPV/jmU6eLKvxfd4rZbpZcLC/6RluxarZ6kuu6pQ3t8teiIjIP2zfvp0nnngCuDKn9sUXX+S7774DoKCggK5du5oZT0TqKI2QiYjcgQMHDhASEgKAzWZj9uzZTJgwgcaNG/OjH/2IESNGmJxQROoiFTIRkTswduzY6x6HhYURFhZmUhoRqS90yVJERETEZCpkIiIiIiZTIRMRERExmSmF7Pvvv6dv377s37+fQ4cOER0dTUxMDGlpaTgcDjMiiYiIiJjG8EJWWVlJamoqjRs3Bq7cESAhIYEPP/wQp9Opm5aLiIhIg2N4IUtPTycqKoqWLVsCUFRU5LoRb58+fdi6davRkURERERMZeiyF2vWrCEoKIinn36a5cuXA/+4WTmAr68vZWXuV76tjVuPGKk6t1cC+OQ/BtfK8a1wGworZADlsFoGsE4OEREjGVrIVq9ejc1mo6CggOLiYqZNm8bp06ddP6+oqHDdguR2auPWI1ZUG7eLsMJtKKyQQTmsl8FdDhU1EanPDC1kK1ascP05NjaWmTNnsmDBAgoLC+nVqxebNm1y3R9OREREpKEwfdmLadOmkZmZSWRkJJWVlYSHh5sdSURERMRQpt06KTs72/XnnJwcs2KIiIiImM70ETIRERGRhk6FTERERMRkKmQiIiIiJlMhExERETGZaZP6xb3qLCD7XuIzBiQRERGR2qRCJiJyB4YOHYqfnx8AISEhREZGMmfOHDw9PQkLC2PChAkmJxSRukiFTESkmi5evIjT6bxu2Z7BgweTmZlJmzZt+Ld/+zf27t1Lly5dTEwpInWR5pCJiFTTvn37uHDhAnFxcYwcOZLt27dz6dIl2rZti81mIywsjK1bt5odU0TqII2QiYhUU+PGjRkzZgzDhw+mwV2CAAALhUlEQVTn4MGD/PznP7/u/ru+vr4cPnz4tvto1qwpXl6eNZrLivf5VCbrZrgVq2ZrKLlUyEREqik0NJR27dphs9kIDQ3F39+fM2fOuH5eUVFxXUGrSmnp+RrPZYUbw99ImW4WHOxveoZbsWq2+pKrOuVNlyxFRKpp1apVzJ8/H4Djx49z4cIFmjZtyt///necTiebN2+mR48eJqcUkbpII2QiItUUERFBUlIS0dHR2Gw25s6di4eHB5MnT8ZutxMWFsbDDz9sdkwRqYNUyEREqsnb25v/+I//uGn7ypUrTUgjIvWJLlmKiIiImEyFTERERMRkKmQiIiIiJlMhExERETGZCpmIiIiIyVTIREREREymQiYiIiJiMhUyEREREZNpYdgGIG7+RrfPeS/xGQOSiIiISFU0QiYiIiJiMkNHyCorK0lOTubo0aNcunSJcePG8cADD5CYmIjNZqNDhw6kpaXh4aGeKCIiIg2HoYUsLy+PwMBAFixYwJkzZxgyZAidOnUiISGBXr16kZqaSn5+PgMHDjQyloiIiIipDB2Kev7553nttdcAcDqdeHp6UlRURM+ePQHo06cPW7duNTKSiIiIiOkMHSHz9fUFoLy8nIkTJ5KQkEB6ejo2m83187KyMrf7adasKV5enrWata4IDva31H6serxbUQ5rZQDr5BARMZLh37IsKSlh/PjxxMTEMGjQIBYsWOD6WUVFBQEBAW73UVp6vjYj1iknT7ovsEbupzqCg/0NPZ5y1I0M7nKoqIlIfWboJctTp04RFxfHlClTiIiIAKBLly4UFhYCsGnTJnr06GFkJBERERHTGVrIli1bxrlz51iyZAmxsbHExsaSkJBAZmYmkZGRVFZWEh4ebmQkEREREdMZeslyxowZzJgx46btOTk5RsYQEbljVS3b06pVK37xi1/wL//yLwBER0fz4x//2NygYhlalFvuhFbqFxGphqqW7Rk/fjyjR48mLi7O7HgiUsepkImIVMPzzz/vmlJxddmePXv2cODAAfLz82nXrh3Jycn4+fnddj+18S1xK37hQZmqx0qZrJTlWg0llwqZiEg1VLVsz6VLlxg+fDjdunVj6dKl/PrXv2batGm33U9tfEvcCt+QvZEyVY9VMlnlm9Y3qi+5qlPedI8iEZFqKikpYeTIkQwePJhBgwYxcOBAunXrBsDAgQPZu3evyQlFpK7SCFkdV51JoyJy764u25OamsoTTzwBwJgxY0hJSaF79+4UFBTQtWtXk1OKSF2lQiYiUg3XLtuzZMkSABITE5k7dy6NGjWiRYsWzJo1y+SUIlJXqZCJiFTDrZbtyc3NNSGNiNQ3mkMmIiIiYjIVMhERERGTqZCJiIiImEyFTERERMRkKmQiIiIiJlMhExERETGZlr2QaqvuIrTvJT5Ty0lERETqF42QiYiIiJhMhUxERETEZCpkIiIiIibTHDKp0zSvTURE6gMVMgGqX2yMPF59LlEqkiIici1dshQRERExmUbIpMYZPdomIiJS16mQifx/Df0yqoiImEeFTEREpAHQ3FVrs0QhczgczJw5k7/85S94e3sze/Zs2rVrZ3YskZvU1VE0o3PX1ffpbuj8JSI1wRKFbMOGDVy6dImPPvqInTt3Mn/+fJYuXWp2LDFZTc5FM3Jem9G5a6rY6Lfnu6Pzl4jUBEsUsm+++Yann34agH/9139lz549JicSEakenb9E7p4VfxGsTqZP/mNwjR/X5nQ6nTW+1zs0ffp0nnvuOfr27QtAv3792LBhA15eluiLIiK3pPOXiNQES6xD5ufnR0VFheuxw+HQyUxE6gSdv0SkJliikD366KNs2rQJgJ07d9KxY0eTE4mIVI/OXyJSEyxxyfLqt5T++te/4nQ6mTt3Lj/60Y/MjiUi4pbOXyJSEyxRyEREREQaMktcshQRERFpyFTIREREREymQiYiIiJisnpbyBwOB6mpqURGRhIbG8uhQ4cMz1BZWcmUKVOIiYkhIiKC/Px8wzNc6/vvv6dv377s37/ftAzvvPMOkZGRDBs2jI8//tiUDJWVlbzxxhtERUURExNj+Puxa9cuYmNjATh06BDR0dHExMSQlpaGw+EwJUdxcTExMTHExsYyZswYTp06ZXiGqz755BMiIyMNOb5VWeH85U5V/3Zmstr59lp2u52kpCSioqKIjo7mr3/9q9mRrmOFz4aqDB06lNjYWGJjY0lKSjI7jkttfY7V28VyrHA7k7y8PAIDA1mwYAFnzpxhyJAhDBgwwNAMV1VWVpKamkrjxo1NOT5AYWEh3377Lb/73e+4cOEC7733nik5vvzySy5fvkxubi5btmzh7bffJjMz05BjZ2VlkZeXR5MmTQCYN28eCQkJ9OrVi9TUVPLz8xk4cKDhOebMmUNKSgqdO3cmNzeXrKysWj8B3pgBYO/evaxatYqG/l0jK5y/bqeqfzuzWel8e6PPP/8cgNzcXAoLC1m0aJFl/j2t8NlQlYsXL+J0OsnOzjY7ynVq83Os3o6QWeF2Js8//zyvvfYaAE6nE09PT8MzXJWenk5UVBQtW7Y0LcPmzZvp2LEj48eP55VXXqFfv36m5AgNDcVut+NwOCgvLzd0Ec+2bdteV/6Kioro2bMnAH369GHr1q2m5MjIyKBz587Ald/mfXx8DM9QWlpKRkYGycnJtX5sq7PC+et2bvy3swIrnW9v9OyzzzJr1iwAjh07RkBAgMmJ/sEKnw1V2bdvHxcuXCAuLo6RI0eyc+dOsyMBtfs5Vm9HyMrLy/Hz83M99vT05PLly4Z++Pr6+rqyTJw4kYSEBMOOfa01a9YQFBTE008/zfLly03JAFc+cI8dO8ayZcs4cuQI48aN49NPP8Vmsxmao2nTphw9epQXXniB0tJSli1bZtixw8PDOXLkiOux0+l0/f19fX0pKyszJcfVk/GOHTvIyclhxYoVhmaw2+1Mnz6dpKQkQ8qg1Vnh/HU7N/7/xwqscr69FS8vL6ZNm8Yf//hHfvWrX5kdB7DOZ0NVGjduzJgxYxg+fDgHDx7k5z//OZ9++qnp/w3U5udYvR0hs8rtTEpKShg5ciSDBw9m0KBBhh8fYPXq1WzdupXY2FiKi4uZNm0aJ0+eNDxHYGAgYWFheHt70759e3x8fDh9+rThOd5//33CwsL47LPPWLt2LYmJiVy8eNHwHAAeHv/4T7CiosLU35zXr19PWloay5cvJygoyNBjFxUVcejQIWbOnMnrr7/O3/72N+bMmWNoBiuxyvmrrrHC+fZ20tPT+eyzz0hJSeH8+fNmx7HMZ0NVQkNDefHFF7HZbISGhhIYGGiJbLX5OVZvC5kVbmdy6tQp4uLimDJlChEREYYf/6oVK1aQk5NDdnY2nTt3Jj09neDgYMNzPPbYY3z11Vc4nU6OHz/OhQsXCAwMNDxHQEAA/v7+ANx3331cvnwZu91ueA6ALl26UFhYCMCmTZvo0aOHKTnWrl3r+v9ImzZtDD9+9+7dWbduHdnZ2WRkZPDAAw8wffp0w3NYhRXOX3WNVc63VfnDH/7AO++8A0CTJk2w2WzX/TJmFqt8NlRl1apVzJ8/H4Djx49TXl5uiWy1+TlWb3/lGjhwIFu2bCEqKsp1OxOjLVu2jHPnzrFkyRKWLFkCXJkMa7XJk0bp378/27dvJyIiAqfTSWpqqinzPEaNGkVycjIxMTFUVlYyadIkmjZtangOgGnTppGSkkJGRgbt27cnPDzc8Ax2u505c+bQqlUr4uPjAXj88ceZOHGi4VnkCiucv+oaK59vn3vuOZKSkvjZz37G5cuXSU5OtkQuK4uIiCApKYno6GhsNhtz5861xChxbX6O6dZJIiIiIiYzf8xUREREpIFTIRMRERExmQqZiIiIiMlUyERERERMpkImIiIiYjIVMhERERGTqZCJiIiImOz/AUnhG2giqghRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create 2x2 subplots of each of our random number generators\n",
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n",
    "                                             figsize=(10, 8))\n",
    "ax1.hist(rn1, bins=25)\n",
    "ax1.set_title('standard normal')\n",
    "ax1.set_ylabel('frequency')\n",
    "\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('normal(100, 20)')\n",
    "\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('chi square')\n",
    "ax3.set_ylabel('frequency')\n",
    "\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('Poisson');\n",
    "\n",
    "fig.suptitle('Histograms of random samples for different distributions', fontsize=16)\n",
    "plt.savefig('./images/stoch_02.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Simulation\n",
    "#### ([Back to Top](#Table-of-Contents))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.1.1)** Consider, for example, the Black-Scholes-Merton setup for option pricing. In their setup, the level of a\n",
    "stock index $S_T$ at a future date $T$ given a level $S_0$ as of today is given according to:\n",
    "\n",
    "$$S_{T}=S_{0}exp\\{(r-\\frac{1}{2}\\sigma^{2})T+\\sigma\\sqrt{T}z\\}$$\n",
    "\n",
    "where,\n",
    "\n",
    "- $S_T$ is the index level at date $T$\n",
    "- $r$ constant riskless short rate\n",
    "- $\\sigma$ constant volatility (standard deviation of returns of $S$)\n",
    "- $z$ standard normal random variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "ac34499c-4675-457e-a0ac-40b8efcdb72e"
   },
   "outputs": [],
   "source": [
    "S0 = 100  \n",
    "r = 0.05  \n",
    "sigma = 0.25  \n",
    "T = 2.0  \n",
    "I = 10000\n",
    "\n",
    "ST1 = S0 * np.exp((r - 0.5 * sigma ** 2) * T + sigma * math.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false,
    "uuid": "7fc0b66a-9ce3-4c5e-bb99-d5e0363a6678"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation of Geometric Brownian Motion\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(ST1, bins=50)\n",
    "plt.title('Statically simulated geometric Brownian motion (via npr.standard_normal())')\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency');\n",
    "plt.savefig('./images/stoch_03.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.1.2)** Alternatively since we know that the equation in **3.1.1)** represents a log-normal distribution, we can use the `numpy`'s lognormal random generator by specifying location and scale parameters.\n",
    "\n",
    "Recall by definition of log-normal, \n",
    "\\begin{align*}\n",
    "\\mu & =(r-\\frac{1}{2}\\sigma^{2})T\\\\\n",
    "\\sigma & =\\sigma\\sqrt{T}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "c37a0783-81b1-449f-924e-f792ba5017aa"
   },
   "outputs": [],
   "source": [
    "ST2 = S0 * npr.lognormal(mean = (r - 0.5 * sigma ** 2) * T, sigma = sigma * math.sqrt(T), size= I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "fea07d0c-7fc1-4ab8-8b21-fc36e73c3151"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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68MEHtX379jzbz2/MXdu3a0EsISFBbdq00UMPPaSEhARt2LDBFYok5QpN1x8HSXr11Ve1bNky3X333Xr66afVuHHjXOtce/218V3Qz0G5cuXy/fs1hR2n/Fz/Xk6nM9f610JvQft2bfkv37tz587auXOnDh06pKSkJHXp0iXX+nv27FFkZKTS09PVpk0bPffccwXWV65cOdep0OuvP7t+7P7ylOm1YFkQd71y9zMi5d+Twnp/fT1F+Zn55JNP9Nprr6lixYquD0Bd338vL6983//6flz/GCUXRwk3LCAgQPPmzdN3333nWnb27FllZmaqfv36kq7+QsvJydHRo0eVnp6uYcOGqUOHDtq2bZuysrJcv0yurfdLLVu21JYtW1z/8C5ZskSvv/66Nm3apPbt26t///4KDg7WN998I4fD4bbWvn376ptvvtGePXvyvX5k//796tatm+rWrasXXnhBTz/9tA4cOHDDfTl48KCuXLminJwc/etf/8qzzu7duxUQEKA//elPatu2rWsdh8Mhb29vORwOGWMUFBSkChUquC60PnXqlLp166bdu3erbdu2Wrt2rS5evCin01ngxdgPP/yw1q1bp7S0NElXr027JjQ0VIsXL3Ydi7Fjx2rmzJkKCgpSuXLltG7dOklXPyH31Vdf6aGHHipyH1q1aqVNmzbp0KFDkq7OzPXo0UNXrlyR3W7PN6Ber3Xr1lqzZo2rvvHjx+sf//hHoa87d+6cvv/+ewUHBxdY1/HjxyXJda3Xfffdp9/97neqWrWqlixZojZt2ig0NFTr1q3T+fPnde+99xZ53xMSEjRkyBB17dpVNptNO3fuLHSM3oj77rtPhw8f1q5duyRdvQYqKSlJLVq0yDWOfik0NFSrVq1yzdAtWrRIDz744K/6UENQUJCrf9LVYPmHP/xBsbGx6tSpkypVqpRr/aSkJDVp0kTPPPOMWrRoofXr199QP9avX6+0tDQ5nU4tW7ZM7du3/1U1FzSm3f2MFMRd729UQkKCevXqpb59+yooKEgbNmzI06cqVarI399fJ0+ezLX8+PHjuWb6r3+MkotTk7hhQUFBeuedd/Tmm2/q9OnTqlChgvz8/DRx4kTXL4COHTuqf//+mjNnjh555BF16dJF/v7+qlWrlu655x4dPXpUtWrVcq03d+5c1/YbNGigESNGuP73HBgYqKlTpyo9PV3Dhw9X9+7dZbfbFRISonXr1uX7P9Rrbr/9djVp0kR169bNd2ahYcOG6tKlix5//HFVrlxZFStWdH3Y4Ndq06aNHnzwQXXp0kWBgYFq2bJlnlDXpk0brVixQp07d1alSpXUtGlTBQQE6OjRo6pdu7YaNWqkLl266NNPP9XcuXM1ZcoUvf/++8rJydHLL7/s+mDCgQMH9Pjjj8vf318NGzZUampqnnpat26tJ554QhEREapYsaLq1avn+ofyT3/6k2bMmKFevXrJ4XDo3nvvVWxsrMqVK6e5c+dq8uTJmj17thwOh4YMGaJWrVopMTGxSH2oV6+eJk6cqFdffVXGGHl7e2vevHmqXLmy6tWrJ7vdrj59+ujNN98scBuRkZE6efKkevfuLWOMWrRoUeAtOp566inXDEBWVpYGDx6s1q1b68SJE7nWu+eeezRu3Di99NJLcjgcqlixoubPn+86ld6xY0ctXLhQjRo1kpeXlypWrKjHHnusSPt8zSuvvKIhQ4botttuU6VKlfTggw/me0r2twoICNCsWbM0adIkXb58WTabTdOmTVNQUJDrwxfXxtE1ffr00alTp9S3b185nU7Vrl1bb7zxxq9637CwME2ZMiXX7Tr69u2rjz/+WOPHj8+zfrdu3bRu3Tp17dpV5cqVU+vWrXXhwgWlp6fnOn1XmDvuuEPPP/+8UlNT9eCDD+rFF1/Md71PP/1Uu3fvzvWpTXdjWlKBPyMFcdf777//vsj79EtRUVGKi4vTqlWrZLfb1bhxY/3444951rt2SrV///6uZQkJCZo1a1aBj1Fy2Yy7c0PALSIlJUV9+vTR4sWLXddplBU//PCDvv/+e9c9pT788EPt3LnT7fVWQGGioqI0bNgwNW3atFjeb/bs2UpNTVVcXNxN33Zp+xk5fvy4Xn75Za1cuVI2m02JiYlavHix63YV1z9GycapSdzyli1bpq5du2rQoEFlLoRJV2cuv/vuO3Xr1k3du3fXli1bXLcMAW7UxIkT9c4777i9zrO0KG0/IzVr1lTPnj21ZMkSORwOvf/++64Z/Osfo+RjRgwAAMAizIgBAABYhCAGAABgEYIYAACARUrl7SvOnk2zuoQSp2rVykpNzXtndtCbwtAf9+iPe/SnYPTGvbLUn8BAvwKfY0bsFuHtnf9d1UFvCkN/3KM/7tGfgtEb9+jPVQQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIt6e2nB2drZiY2N18uRJeXl5adKkSfL29lZsbKxsNpvq1auncePGycvLS3PmzFF8fLy8vb01evRoNW3a1FNlAQAAlBgeC2LffvutcnJytGTJEm3atElvvfWWsrOzNWzYMLVs2VJxcXFav369qlevrm3btmn58uU6deqUoqOjtXLlSk+VhRIoavqGIq+7MLaDBysBAKB4eezUZFBQkBwOh5xOp9LT0+Xt7a09e/aoRYsWkqR27dpp8+bN2r59u0JDQ2Wz2VS9enU5HA6lpKR4qiwAAIASw2MzYpUrV9bJkyfVpUsXpaamav78+UpKSpLNZpMk+fj4KC0tTenp6apSpYrrddeWBwQEFLjtqlUry9vb7qnSS63AQD+rS/C4G93HstCb34L+uEd/3KM/BaM37tEfDwaxv/71rwoNDdX//M//6NSpU3rqqaeUnZ3tej4jI0P+/v7y9fVVRkZGruV+fu4PTGrqJU+VXWoFBvrp7Nk0q8vwuBvZx7LSmxtFf9yjP+7Rn4LRG/fKUn/cBU6PnZr09/d3BarbbrtNOTk5atSokRITEyVJGzduVEhIiJo3b66EhAQ5nU4lJyfL6XS6nQ0DAAC4VXhsRuzpp5/W6NGj1b9/f2VnZ+uVV15RkyZNNHbsWM2cOVN16tRRWFiY7Ha7QkJCFBERIafTqbi4OE+VhFtAUS/s56J+AEBp4LEg5uPjo1mzZuVZ/vHHH+dZFh0drejoaE+VAgAAUCJxQ1cAAACLEMQAAAAs4rFTk4CVuJYMAFAaMCMGAABgEYIYAACARQhiAAAAFiGIAQAAWIQgBgAAYBGCGAAAgEUIYgAAABYhiAEAAFiEIAYAAGARghgAAIBF+IojeExRv2YIAICyihkxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAInzpN8q0on4x+cLYDh6uBABQFjEjBgAAYBGCGAAAgEUIYgAAABYhiAEAAFjEYxfrr1q1Sp999pkk6cqVK9q3b58WLVqkKVOmyG63KzQ0VC+99JKcTqfGjx+vAwcOqHz58po8ebJq167tqbIAAABKDI8Fsd69e6t3796SpAkTJujxxx/XuHHjNHv2bNWsWVODBw/W3r17deLECWVlZWnp0qXasWOHpk+frnnz5nmqLAAAgBLD46cmf/jhB/33v//VH/7wB2VlZalWrVqy2WwKDQ3V5s2btX37drVt21aS1KxZM+3evdvTJQEAAJQIHr+P2IIFCzRkyBClp6fL19fXtdzHx0fHjx/Ps9xutysnJ0fe3gWXVrVqZXl72z1ad2kUGOhndQm3rFu9t7f6/v1W9Mc9+lMweuMe/fFwELt48aIOHz6sVq1aKT09XRkZGa7nMjIy5O/vr8uXL+da7nQ63YYwSUpNveSxmkurwEA/nT2bZnUZt6xbubeMHffoj3v0p2D0xr2y1B93gdOjpyaTkpLUunVrSZKvr6/KlSunY8eOyRijhIQEhYSEqHnz5tq4caMkaceOHapfv74nSwIAACgxPDojdvjwYdWoUcP1eMKECRo+fLgcDodCQ0N13333KTg4WJs2bVJkZKSMMZo6daonSwIAACgxPBrEnnvuuVyPmzVrpmXLluVa5uXlpYkTJ3qyDAAAgBKJG7oCAABYhCAGAABgEYIYAACARQhiAAAAFiGIAQAAWIQgBgAAYBGCGAAAgEUIYgAAABYhiAEAAFiEIAYAAGARghgAAIBFCGIAAAAW8eiXfuPWFDV9g9UlFLui7vPC2A4ergQAcCthRgwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACzCd00CNxHfSQkA+DWYEQMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwiEc/NblgwQJt2LBB2dnZ6tevn1q0aKHY2FjZbDbVq1dP48aNk5eXl+bMmaP4+Hh5e3tr9OjRatq0qSfLAgAAKBE8NiOWmJio77//Xp9++qkWLVqk06dPa9q0aRo2bJg++eQTGWO0fv167dmzR9u2bdPy5cs1c+ZMTZgwwVMlAQAAlCgeC2IJCQmqX7++hgwZohdffFGPPPKI9uzZoxYtWkiS2rVrp82bN2v79u0KDQ2VzWZT9erV5XA4lJKS4qmyAAAASgyPnZpMTU1VcnKy5s+frxMnTuiPf/yjjDGy2WySJB8fH6WlpSk9PV1VqlRxve7a8oCAgAK3XbVqZXl72z1VeqkVGOhndQkoopJ2rEpaPSUN/XGP/hSM3rhHfzwYxKpUqaI6deqofPnyqlOnjipUqKDTp0+7ns/IyJC/v798fX2VkZGRa7mfn/sDk5p6yVNll1qBgX46ezbN6jJQRCXpWDF23KM/7tGfgtEb98pSf9wFTo+dmnzggQf073//W8YYnTlzRpmZmWrdurUSExMlSRs3blRISIiaN2+uhIQEOZ1OJScny+l0up0NAwAAuFV4bEasffv2SkpKUp8+fWSMUVxcnGrUqKGxY8dq5syZqlOnjsLCwmS32xUSEqKIiAg5nU7FxcV5qiQAAIASxaO3rxg5cmSeZR9//HGeZdHR0YqOjvZkKQAAACUON3QFAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACzibXUBQFkUNX1DkdddGNvBg5UAAKzEjBgAAIBFCGIAAAAWIYgBAABYhCAGAABgEYIYAACARQhiAAAAFiGIAQAAWIQgBgAAYBGCGAAAgEW4sz5cfs3d3gEAwG/n0SDWq1cv+fr6SpJq1KihiIgITZkyRXa7XaGhoXrppZfkdDo1fvx4HThwQOXLl9fkyZNVu3ZtT5YFAABQIngsiF25ckXGGC1atMi1LDw8XLNnz1bNmjU1ePBg7d27VydOnFBWVpaWLl2qHTt2aPr06Zo3b56nygIAACgxPBbE9u/fr8zMTEVFRSknJ0fR0dHKyspSrVq1JEmhoaHavHmzzp49q7Zt20qSmjVrpt27d3uqJAAAgBLFY0GsYsWKevbZZ9W3b18dOXJEzz//vPz9/V3P+/j46Pjx40pPT3edvpQku92unJwceXsXXFrVqpXl7W33VOmlVmCgn9UlwAOK47gydtyjP+7Rn4LRG/fojweDWFBQkGrXri2bzaagoCD5+fnp/PnzruczMjLk7++vy5cvKyMjw7Xc6XS6DWGSlJp6yVNll1qBgX46ezbN6jLgAZ4+rowd9+iPe/SnYPTGvbLUH3eB02O3r1ixYoWmT58uSTpz5owyMzNVuXJlHTt2TMYYJSQkKCQkRM2bN9fGjRslSTt27FD9+vU9VRIAAECJ4rEZsT59+mjUqFHq16+fbDabpk6dKi8vLw0fPlwOh0OhoaG67777FBwcrE2bNikyMlLGGE2dOtVTJQEAAJQoHgti5cuX11/+8oEsOzgAABmTSURBVJc8y5ctW5brsZeXlyZOnOipMgAAAEos7qwPAABgEYIYAACARQhiAAAAFik0iO3atas46gAAAChzCr1Y/4033lBqaqrCw8MVHh6uwMDA4qgLAADglldoEPvb3/6mkydPavXq1Xr22Wd11113qVevXnr00UdVrly54qgRAADgllSka8Tuvvtu9ezZU926ddPBgwe1aNEidevWTV9//bWn6wMAALhlFTojtmzZMn3xxRc6e/asevbsqU8++US/+93vdObMGfXq1UsdO3YsjjoBAABuOYUGse+++05Dhw5VixYtci2vVq2axo0b57HCAAAAbnWFnpr8n//5H3377beSpOPHj2vkyJH6+eefJUlhYWGerQ4AAOAWVmgQGz58uGrWrCnp6ixYSEiIRo4c6fHCAAAAbnWFnpo8f/68IiMjJV39/sgnnnhCn376qccLA3BV1PQNRVpvYWwHD1cCALjZCp0Rq1SpkuvUpCRt2bJFlSpV8mhRAAAAZUGhM2ITJkzQiBEjXKcj77rrLv35z3/2eGEAAAC3ukKD2L333qs1a9YoNTVV5cqVk6+vb3HUBQAAcMsrNIjt3btX8+fP14ULF2SMcS3/29/+5tHCAAAAbnWFBrGYmBhFRESoXr16stlsxVETAABAmVBoEKtYsaKefPLJ4qgFAACgTCk0iIWGhmrRokUKDQ1VhQoVXMurV6/u0cIAAABudYUGsdWrV0uSPvzwQ9cym82m9evXe64qAACAMqDQILZhQ9FuJgkAAIBfp9Abul64cEFjxozRoEGDlJqaqlGjRunixYvFURsAAMAtrdAgNnbsWAUHB+v8+fPy8fHRnXfeqeHDhxdHbQAAALe0QoPYiRMnFBERIS8vL5UvX16vvPKKTp8+XRy1AQAA3NIKDWJ2u11paWmue4gdOXJEXl6FvgwAAACFKPRi/ejoaA0cOFCnTp3Sn/70J+3YsUNTp04tjtoAAABuaYUGsXbt2qlJkybatWuXHA6HJk6cqDvuuKM4agMAALilFRrE5syZk+vxvn37JEkvvfSSZyoCAAAoI37VxV7Z2dnasGGDzp0756l6AAAAyoxCZ8Sun/kaMmSIoqKiPFYQAABAWfGrP/6YkZGh5ORkT9QCAABQphQ6I9ahQwfXrSuMMbp48WKRZ8TOnTun3r17a+HChfL29lZsbKxsNpvq1auncePGycvLS3PmzFF8fLy8vb01evRoNW3a9LftEQAAQClRaBBbtGiR6+82m03+/v7y9fUtdMPZ2dmKi4tTxYoVJUnTpk3TsGHD1LJlS8XFxWn9+vWqXr26tm3bpuXLl+vUqVOKjo7WypUrf8PuAAAAlB6FBrGkpCS3z/fs2TPf5TNmzFBkZKTeffddSdKePXvUokULSVdvibFp0yYFBQUpNDRUNptN1atXl8PhUEpKigICAty+Z9WqleXtbS+s9DInMNDP6hJgod9y/Bk77tEf9+hPweiNe/SnCEEsPj5e3333nTp06CBvb299++23CgwMVFBQkKT8g9iqVasUEBCgtm3buoKYMcZ1itPHx0dpaWlKT09XlSpVXK+7trywIJaaeqnoe1hGBAb66ezZNKvLgIVu9PgzdtyjP+7Rn4LRG/fKUn/cBc5Cg1hKSopWr16t22+/XZKUlpamF198UdOmTSvwNStXrpTNZtOWLVu0b98+xcTEKCUlxfV8RkaG6xRnRkZGruV+fqRjAABQNhT6qckzZ86oatWqrscVKlTQhQsX3L5m8eLF+vjjj7Vo0SLde++9mjFjhtq1a6fExERJ0saNGxUSEqLmzZsrISFBTqdTycnJcjqdhc6GAQAA3CoKnRF75JFH9NRTTyksLEzGGP3zn/9Ujx49fvUbxcTEaOzYsZo5c6bq1KmjsLAw2e12hYSEKCIiQk6nU3FxcTe0EwAAAKWRzRhjClvpyy+/VFJSkipUqKDQ0FC1adOmOGorUFk5p/xr3Ixz7VHTN9ykamCFhbEdbuh1Zek6jRtBf9yjPwWjN+6Vpf64u0asSDd0vfPOO1WvXj0NGzZM5cuXv2mFAQAAlGWFBrGPPvpIb731lv76178qMzNTcXFx+uCDD4qjNgAAgFtaoUHss88+0wcffKBKlSqpSpUqWrFiBTddBQAAuAkKDWJeXl65TkdWqFBBdjs3UwUAAPitCv3UZIsWLTRjxgxlZmbqm2++0dKlS9WqVaviqA0AAOCWVuiM2MiRI1W7dm01aNBAn3/+uR5++GHFxMQUR20AAAC3tEJnxJ577jktXLhQkZGRxVEPAABAmVHojNjly5d16tSp4qgFAACgTClwRuyf//ynunbtqp9++knt27fXHXfcoQoVKri+vHv9+vXFWScAAMAtp8Ag9vbbb6tTp066cOGCNmzY4ApgKH24Yz4AACVTgUHs/vvvV3BwsIwxevTRR13LrwWyffv2FUuBAIqmqIH7Rr8KCQBw8xV4jdi0adO0b98+tW/fXvv27XP92b9/PyEMAADgJij0Yv158+YVRx0AAABlTpG+9BsAAAA3H0EMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsIi3pzbscDg0ZswYHT58WDabTRMmTFCFChUUGxsrm82mevXqady4cfLy8tKcOXMUHx8vb29vjR49Wk2bNvVUWQAAACWGx4LYv/71L0nSkiVLlJiYqDfffFPGGA0bNkwtW7ZUXFyc1q9fr+rVq2vbtm1avny5Tp06pejoaK1cudJTZQEAAJQYHgtijz32mB555BFJUnJysvz9/bV582a1aNFCktSuXTtt2rRJQUFBCg0Nlc1mU/Xq1eVwOJSSkqKAgABPlQYAAFAieCyISZK3t7diYmL09ddf6+2339amTZtks9kkST4+PkpLS1N6erqqVKnies215e6CWNWqleXtbfdk6aVSYKCf1SWgFMhvnDB23KM/7tGfgtEb9+iPh4OYJM2YMUPDhw/XE088oStXrriWZ2RkyN/fX76+vsrIyMi13M/P/YFJTb3ksXpLq8BAP509m2Z1GSgFrh8njB336I979Kdg9Ma9stQfd4HTY5+a/Pzzz7VgwQJJUqVKlWSz2dSkSRMlJiZKkjZu3KiQkBA1b95cCQkJcjqdSk5OltPp5LQkAAAoEzw2I9apUyeNGjVKAwYMUE5OjkaPHq26detq7NixmjlzpurUqaOwsDDZ7XaFhIQoIiJCTqdTcXFxnioJAACgRPFYEKtcubJmzZqVZ/nHH3+cZ1l0dLSio6M9VQoAAECJ5PFrxACUTlHTNxRpvYWxHTxcCQDcurizPgAAgEUIYgAAABYhiAEAAFiEa8SAMqao134BADyPGTEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIt5WF4AbFzV9g9UlAACA34AZMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCPcRA/CbFPV+dgtjO3i4EgAofZgRAwAAsIhHZsSys7M1evRonTx5UllZWfrjH/+oe+65R7GxsbLZbKpXr57GjRsnLy8vzZkzR/Hx8fL29tbo0aPVtGlTT5QEAABQ4ngkiH3xxReqUqWKXn/9dZ0/f149e/ZUw4YNNWzYMLVs2VJxcXFav369qlevrm3btmn58uU6deqUoqOjtXLlSk+UBAAAUOJ4JIh17txZYWFhkiRjjOx2u/bs2aMWLVpIktq1a6dNmzYpKChIoaGhstlsql69uhwOh1JSUhQQEOCJsgAAAEoUjwQxHx8fSVJ6erqGDh2qYcOGacaMGbLZbK7n09LSlJ6eripVquR6XVpaWqFBrGrVyvL2tnuidAAeEhjoZ3UJN6w0114c6E/B6I179MeDn5o8deqUhgwZov79+6t79+56/fXXXc9lZGTI399fvr6+ysjIyLXcz6/wg5KaeskjNQPwnLNn06wu4YYEBvqV2tqLA/0pGL1xryz1x13g9MinJn/++WdFRUVpxIgR6tOnjySpUaNGSkxMlCRt3LhRISEhat68uRISEuR0OpWcnCyn08lpSQAAUGZ4ZEZs/vz5unjxoubOnau5c+dKkl577TVNnjxZM2fOVJ06dRQWFia73a6QkBBFRETI6XQqLi7OE+UAAACUSDZjjLG6iF+rrExlFqaoN9IESoLSekPXsnT65EbQn4LRG/fKUn+K/dQkAAAACkcQAwAAsAhBDAAAwCIEMQAAAIsQxAAAACxCEAMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsIi31QUAKBuipm8o0noLYzt4uBIAKDmYEQMAALAIQQwAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAi3AfMQAlSlHvNyZxzzEApR8zYgAAABYhiAEAAFiEIAYAAGARghgAAIBFCGIAAAAW4VOTAEqton7Ckk9XAiipmBEDAACwiEeD2M6dOzVw4EBJ0tGjR9WvXz/1799f48aNk9PplCTNmTNHffr0UWRkpHbt2uXJcgAAAEoUjwWx9957T2PGjNGVK1ckSdOmTdOwYcP0ySefyBij9evXa8+ePdq2bZuWL1+umTNnasKECZ4qBwAAoMTx2DVitWrV0uzZszVy5EhJ0p49e9SiRQtJUrt27bRp0yYFBQUpNDRUNptN1atXl8PhUEpKigICAjxVFoAyiGvJAJRUHgtiYWFhOnHihOuxMUY2m02S5OPjo7S0NKWnp6tKlSquda4tLyyIVa1aWd7eds8UDqDMCgz0+1XLcRX9KRi9cY/+FOOnJr28/u8saEZGhvz9/eXr66uMjIxcy/38Cj8oqamXPFIjgLLt7Nm0PMsCA/3yXY6r6E/B6I17Zak/7gJnsX1qslGjRkpMTJQkbdy4USEhIWrevLkSEhLkdDqVnJwsp9PJaUkAAFBmFNuMWExMjMaOHauZM2eqTp06CgsLk91uV0hIiCIiIuR0OhUXF1dc5QAAAFjOZowxVhfxa93qU5lFvbAYwM2V38X6Zen0yY2gPwWjN+6Vpf6UiFOTAAAAyI0gBgAAYBGCGAAAgEUIYgAAABYhiAEAAFiEIAYAAGCRYruPGACUdHwnJYDixowYAACARQhiAAAAFuHUJAD8SpzCBHCzMCMGAABgEYIYAACARQhiAAAAFiGIAQAAWIQgBgAAYBGCGAAAgEUIYgAAABYhiAEAAFiEIAYAAGAR7qwPAB7CHfgBFIYgVkyK+gsZQNlDYAPKLk5NAgAAWIQZMQAoJX7NzDqzZ0DpwIwYAACARQhiAAAAFuHUJADcgvgAAFA6MCMGAABgEWbEAKAMY+YMsBZBDABw0xDsgF+HU5MAAAAWYUbsN+KO+QDKAn7XAZ5RIoKY0+nU+PHjdeDAAZUvX16TJ09W7dq1rS4LAOAhpeEUZmmoEaVfiQhi33zzjbKysrR06VLt2LFD06dP17x586wuCwBgsdIwE1fSAxvfyFCylYggtn37drVt21aS1KxZM+3evdviikrHDz8AoPS42f+ueCI0lfRQWVSlaT9KRBBLT0+Xr6+v67HdbldOTo68vfMvLzDQz+M1/f0v4R5/DwAAPK0k/3vmqX/PS/I+X69EfGrS19dXGRkZrsdOp7PAEAYAAHCrKBFBrHnz5tq4caMkaceOHapfv77FFQEAAHiezRhjrC7i2qcmf/zxRxljNHXqVNWtW9fqsgAAADyqRAQxAACAsqhEnJoEAAAoiwhiAAAAFuGjiaVUr169XLf8qFGjhiIiIjRlyhTZ7XaFhobqpZdesrjC4rdz50698cYbWrRokY4eParY2FjZbDbVq1dP48aNk5eXl+bMmaP4+Hh5e3tr9OjRatq0qdVlF5tf9mfv3r164YUX9Pvf/16S1K9fP3Xt2rVM9ic7O1ujR4/WyZMnlZWVpT/+8Y+65557GD//K7/+3HXXXYwfSQ6HQ2PGjNHhw4dls9k0YcIEVahQgbHzv/LrT05ODmPnegalzuXLl014eHiuZT169DBHjx41TqfTPPfcc2bPnj0WVWeNd99913Tr1s307dvXGGPMCy+8YLZu3WqMMWbs2LFm3bp1Zvfu3WbgwIHG6XSakydPmt69e1tZcrG6vj/Lli0zH3zwQa51ymp/VqxYYSZPnmyMMSY1NdU8/PDDjJ9fyK8/jJ+rvv76axMbG2uMMWbr1q3mxRdfZOz8Qn79YezkxanJUmj//v3KzMxUVFSUBg0apKSkJGVlZalWrVqy2WwKDQ3V5s2brS6zWNWqVUuzZ892Pd6zZ49atGghSWrXrp02b96s7du3KzQ0VDabTdWrV5fD4VBKSopVJRer6/uze/duxcfHa8CAARo9erTS09PLbH86d+6sl19+WZJkjJHdbmf8/EJ+/WH8XPXYY49p0qRJkqTk5GT5+/szdn4hv/4wdvIiiJVCFStW1LPPPqsPPvhAEyZM0KhRo1SpUiXX8z4+PkpLS7OwwuIXFhaW6ybAxhjZbDZJ/9eP67/BoSz16fr+NG3aVCNHjtTixYtVs2ZNvfPOO2W2Pz4+PvL19VV6erqGDh2qYcOGMX5+Ib/+MH7+j7e3t2JiYjRp0iR1796dsXOd6/vD2MmLIFYKBQUFqUePHrLZbAoKCpKfn5/Onz/vej4jI0P+/v4WVmg9L6//G9rX+nH9NzhkZGTIz8/zX5dVEnXs2FFNmjRx/X3v3r1luj+nTp3SoEGDFB4eru7duzN+rnN9fxg/uc2YMUNfffWVxo4dqytXrriWM3au+mV/QkNDGTvXIYiVQitWrND06dMlSWfOnFFmZqYqV66sY8eOyRijhIQEhYSEWFyltRo1aqTExERJ0saNGxUSEqLmzZsrISFBTqdTycnJcjqdCggIsLhSazz77LPatWuXJGnLli1q3Lhxme3Pzz//rKioKI0YMUJ9+vSRxPj5pfz6w/i56vPPP9eCBQskSZUqVZLNZlOTJk0YO/8rv/689NJLjJ3r8KnJUqhPnz4aNWqU+vXrJ5vNpqlTp8rLy0vDhw+Xw+FQaGio7rvvPqvLtFRMTIzGjh2rmTNnqk6dOgoLC5PdbldISIgiIiLkdDoVFxdndZmWGT9+vCZNmqRy5crpjjvu0KRJk+Tr61sm+zN//nxdvHhRc+fO1dy5cyVJr732miZPnsz4Uf79iY2N1dSpU8v8+OnUqZNGjRqlAQMGKCcnR6NHj1bdunX53fO/8uvPXXfdxe+e63BnfQAAAItwahIAAMAiBDEAAACLEMQAAAAsQhADAACwCEEMAADAIgQxACXeDz/8oNdee+1XvaZBgwa/+X07dOigEydO/ObtXBMbG6tVq1bdtO0BKP24jxiAEi84OFjBwcFWlwEANx0zYgBKvMTERA0cOFCSNHDgQP35z39WRESEOnbsqG+//VaSdOLECfXr10/h4eG5bgiZkZGhmJgY9e7dW+Hh4VqzZo0kadq0aRoxYoQk6e9//7siIiLkcDjyfX+Hw6Fp06apV69e6tGjh/76179Kkl566SWtXbvWtV7v3r21Z88eHT16VM8884x69eqlfv36ae/evTe9JwBuDQQxAKVOdna2li5dqlGjRmnWrFmSpEmTJql3795avXq1mjdv7lp33rx5aty4sVatWqXFixdr/vz5On78uF555RXt3r1ba9as0cyZM/X666/Lbrfn+37Lli2TJH322WdasWKF1q9fr++++07h4eH65z//KUk6cuSIrly5osaNGysmJkYjRozQZ599pkmTJumVV17xcEcAlFacmgRQ6rRt21aSVK9ePdcX3m/btk1/+ctfJEk9evTQmDFjJEmbN2/W5cuXtXLlSknSpUuXdPDgQdWsWVPTpk1TZGSkxo4dq1q1ahX4flu2bNG+ffu0detW1zYOHDigvn37atKkSUpPT9eaNWvUvXt3ZWRkaPfu3Ro1apTr9ZcuXVJqaurNbwSAUo8gBqDUqVChgiTJZrPlWn7tG9tsNpvrOafTqddff12NGzeWdPVLrG+77TZJ0uHDhxUQEKDdu3e7fT+Hw6ERI0aoU6dOkqSUlBRVrlxZ5cuX1yOPPKINGzZo7dq1WrBggZxOp8qXL6/Vq1e7Xn/69GlVqVLlJuw5gFsNpyYB3BIeeughffHFF5KkdevWKSsrS5LUqlUrffrpp5Kkn376ST169NCpU6d05swZvfXWW1q6dKn27dvnutYsP61atdKyZcuUnZ2tjIwM9e/fXzt37pQkhYeH68MPP9Rtt92mu+++W35+fvr973/vCmKbNm3SgAEDPLnrAEoxZsQA3BLi4uI0YsQILVmyRMHBwfLx8ZF09YL68ePHq1u3bq6ZrVq1amnw4MF65plnVLNmTU2cOFFDhw7VF198IX9//zzbjoyM1NGjR9WrVy/l5OSod+/eatmypSTpgQceUFpamiIjI13rv/766xo/frzef/99lStXTm+++Wae2TsAkCSbuTaXDwAAgGLFqUkAAACLEMQAAAAsQhADAACwCEEMAADAIgQxAAAAixDEAAAALEIQAwAAsAhBDAAAwCL/H28nbUS1CV1TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(ST2, bins=50)\n",
    "plt.title('Statically simulated geometric Brownian motion (via npr.lognormal())')\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency');\n",
    "plt.savefig('./images/stoch_04.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.1.3)** In order to conclude that the two simulations above are indeed the same, we can compute some statistics on the two distributions and compare them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "e5e17dcf-21f4-42ee-bcec-21103aaa8bb3"
   },
   "outputs": [],
   "source": [
    "import scipy.stats as scs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "uuid": "d6f800c9-f38f-4fe1-8cb5-fe9253f1194c"
   },
   "outputs": [],
   "source": [
    "def print_statistics(a1, a2):\n",
    "    ''' Prints selected statistics.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    a1, a2: ndarray objects\n",
    "        results objects from simulation\n",
    "    '''\n",
    "    sta1 = scs.describe(a1)  \n",
    "    sta2 = scs.describe(a2)  \n",
    "    print('%14s %14s %14s' % \n",
    "        ('statistic', 'data set 1', 'data set 2'))\n",
    "    print(45 * \"-\")\n",
    "    print('%14s %14.3f %14.3f' % ('size', sta1[0], sta2[0]))\n",
    "    print('%14s %14.3f %14.3f' % ('min', sta1[1][0], sta2[1][0]))\n",
    "    print('%14s %14.3f %14.3f' % ('max', sta1[1][1], sta2[1][1]))\n",
    "    print('%14s %14.3f %14.3f' % ('mean', sta1[2], sta2[2]))\n",
    "    print('%14s %14.3f %14.3f' % ('std', np.sqrt(sta1[3]), np.sqrt(sta2[3])))\n",
    "    print('%14s %14.3f %14.3f' % ('skew', sta1[4], sta2[4]))\n",
    "    print('%14s %14.3f %14.3f' % ('kurtosis', sta1[5], sta2[5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "980679e8-56af-49e3-85f3-4b4d1ed90312"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         32.327         28.230\n",
      "           max        414.825        409.110\n",
      "          mean        110.730        110.431\n",
      "           std         40.300         39.878\n",
      "          skew          1.122          1.115\n",
      "      kurtosis          2.438          2.217\n"
     ]
    }
   ],
   "source": [
    "print_statistics(ST1, ST2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Stochastic Processes\n",
    "#### ([Back to Top](#Table-of-Contents))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.2.1 Geometric Brownian Motion\n",
    "\n",
    "Below we have the Stochastic differential equation in Black-Scholes-Merton:\n",
    "\n",
    "$$dS_{t}=rS_{t}dt+\\sigma S_{t}dZ_{t},$$\n",
    "which can be discretized exactly by an Euler scheme,\n",
    "$$S_{t}=S_{t-\\Delta t}exp\\{(r-\\frac{1}{2}\\sigma^{2})\\Delta t+\\sigma\\sqrt{\\Delta t}z_{t}\\}$$\n",
    "Thus translating into python,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "uuid": "a6b64214-0041-49cb-b7a8-7b4965d1d03a"
   },
   "outputs": [],
   "source": [
    "S0 = 100      # initial value\n",
    "I = 10000     # number of paths to simulate\n",
    "sigma = 0.25  \n",
    "M = 50        # number of time intervals\n",
    "dt = T / M    # length of time interval in fractions of a year\n",
    "S = np.zeros(shape= (M + 1, I))  # 2-dim array to store index levels\n",
    "S[0] = S0     # initializing first row of array with initial value when t = 0\n",
    "\n",
    "# The for loop provides 10,000 different paths for each time step depending\n",
    "# on the previous time step. Note this is done in a vectorized way\n",
    "for t in range(1, M + 1):\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt +\n",
    "            sigma * math.sqrt(dt) * npr.standard_normal(I))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "969180df-b1f3-4f6d-8ec6-21cadbec06f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The last array of array S represents all simulated values for S_T\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(S[-1], bins=50)\n",
    "plt.title('Dynamically simulated geometric Brownian motion at maturity')\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency');\n",
    "plt.savefig('./images/stoch_05.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following is a comparison of the statistics resulting from the dynamic simulation as well as from the static\n",
    "simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "37d83fc1-6b2d-4d94-a5d1-75d2ba569283"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         20.265         19.718\n",
      "           max        369.431        373.244\n",
      "          mean        109.811        110.696\n",
      "           std         39.750         40.142\n",
      "          skew          1.146          1.095\n",
      "      kurtosis          2.353          2.120\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], ST2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also the figure below shows the first 10 simulated paths:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "c424f261-aa3f-4b04-9b5d-bb6824107fa0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.title('Dynamically simulated geometric Brownian motion paths')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level');\n",
    "plt.savefig('./images/stoch_06.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the dynamic simulation approach not only allows us to visualize paths as displayed in the figure above,\n",
    "but also to value options with **American/Bermudan** exercise or options whose payoff is path-dependent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Valuation\n",
    "#### ([Back to Top](#Table-of-Contents))\n",
    "\n",
    "### 4.1 Valuation of European call options in Black-Scholes-Merton model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bsm_call_value(S0, K, T, r, sigma):\n",
    "    ''' Valuation of European call option in BSM model.\n",
    "    Analytical formula.\n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    S0: float\n",
    "        initial stock/index level\n",
    "    K: float\n",
    "        strike price\n",
    "    T: float\n",
    "        maturity date (in year fractions)\n",
    "    r: float\n",
    "        constant risk-free short rate\n",
    "    sigma: float\n",
    "        volatility factor in diffusion term\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    value: float\n",
    "        present value of the European call option\n",
    "    '''\n",
    "    from math import log, sqrt, exp\n",
    "    from scipy import stats\n",
    "\n",
    "    S0 = float(S0)\n",
    "    d1 = (log(S0 / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))\n",
    "    d2 = (log(S0 / K) + (r - 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))\n",
    "    # stats.norm.cdf --> cumulative distribution function\n",
    "    #                    for normal distribution\n",
    "    value = (S0 * stats.norm.cdf(d1, 0.0, 1.0) -\n",
    "             K * exp(-r * T) * stats.norm.cdf(d2, 0.0, 1.0))\n",
    "    return value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Vega function and implied volatility estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bsm_vega(S0, K, T, r, sigma):\n",
    "    ''' Vega of European option in BSM model.\n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    S0: float\n",
    "        initial stock/index level\n",
    "    K: float\n",
    "        strike price\n",
    "    T: float\n",
    "        maturity date (in year fractions)\n",
    "    r: float\n",
    "        constant risk-free short rate\n",
    "    sigma: float\n",
    "        volatility factor in diffusion term\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    vega: float\n",
    "        partial derivative of BSM formula with respect\n",
    "        to sigma, i.e. Vega\n",
    "\n",
    "    '''\n",
    "    from math import log, sqrt\n",
    "    from scipy import stats\n",
    "\n",
    "    S0 = float(S0)\n",
    "    d1 = (log(S0 / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))\n",
    "    vega = S0 * stats.norm.pdf(d1, 0.0, 1.0) * sqrt(T)\n",
    "    return vega\n",
    "\n",
    "def bsm_call_imp_vol(S0, K, T, r, C0, sigma_est, it=100):\n",
    "    ''' Implied volatility of European call option in BSM model.\n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    S0: float\n",
    "        initial stock/index level\n",
    "    K: float\n",
    "        strike price\n",
    "    T: float\n",
    "        maturity date (in year fractions)\n",
    "    r: float\n",
    "        constant risk-free short rate\n",
    "    sigma_est: float\n",
    "        estimate of impl. volatility\n",
    "    it: integer\n",
    "        number of iterations\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    simga_est: float\n",
    "        numerically estimated implied volatility\n",
    "    '''\n",
    "    for i in range(it):\n",
    "        sigma_est -= ((bsm_call_value(S0, K, T, r, sigma_est) - C0) /\n",
    "                      bsm_vega(S0, K, T, r, sigma_est))\n",
    "    return sigma_est"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Pricing European Options by Monte Carlo\n",
    "\n",
    "The payoff of a European call option on an index at maturity is given by $h(S_T)\\equiv max\\{S_T-K, 0\\}$, where $S_T$ is the index level at maturity date $T$ and $K$ is the strike price. Given a risk-neutral measure for the relevant stochastic process (e.g., geometric Brownian motion), the price of such an option is given by the formula:\n",
    "\n",
    "$$C_{0}=e^{-rT}\\mathbb{E}_{0}^{Q}[h(S_{T})]=e^{-rT}\\intop_{0}^{\\infty}h(s)q(s)ds$$\n",
    "\n",
    "The equation below provides the respective Monte Carlo estimator for the European option, where $\\tilde{S}_{T}^{i}$ is the $T$-th simulated index level at maturity.\n",
    "\n",
    "$$\\tilde{C}_{0}=e^{-rT}\\frac{1}{I}\\sum_{i=1}^{I}h(\\tilde{S}_{T}^{i})$$\n",
    "\n",
    "Consider the following parameterization for the geometric Brownian motion and the valuation function `gbm_mcs_stat()`, taking as a parameter only the strike price. Here, only the index level at maturity is simulated. As a reference, consider the case with a strike price of $K = 105$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_sn(M, I, anti_paths=True, mo_match=True):\n",
    "    ''' Function to generate random numbers for simulation.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    M: int\n",
    "        number of time intervals for discretization\n",
    "    I: int\n",
    "        number of paths to be simulated\n",
    "    anti_paths: boolean\n",
    "        use of antithetic variates\n",
    "    mo_math: boolean\n",
    "        use of moment matching\n",
    "    '''\n",
    "    if anti_paths is True:\n",
    "        sn = npr.standard_normal((M + 1, int(I / 2)))\n",
    "        sn = np.concatenate((sn, -sn), axis=1)\n",
    "    else:\n",
    "        sn = npr.standard_normal((M + 1, I))\n",
    "    if mo_match is True:\n",
    "        sn = (sn - sn.mean()) / sn.std()\n",
    "    return sn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 1.0\n",
    "I = 50000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "693f44be-b3dd-4820-9610-a127f0e9b31b"
   },
   "outputs": [],
   "source": [
    "def gbm_mcs_stat(K):\n",
    "    ''' Valuation of European call option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level at maturity)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K: float\n",
    "        (positive) strike price of the option\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0: float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    sn = gen_sn(1, I)\n",
    "    # simulate index level at maturity\n",
    "    ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "                 + sigma * math.sqrt(T) * sn[1])\n",
    "    # calculate payoff at maturity\n",
    "    hT = np.maximum(ST - K, 0)\n",
    "    # calculate MCS estimator\n",
    "    C0 = math.exp(-r * T) * np.mean(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "f325da52-3e45-4e9e-a4a2-067efb1c3bb7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.010189184997577"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The Monte Carlo estimator value for the European call option.\n",
    "gbm_mcs_stat(K=105.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, consider the dynamic simulation approach and allow for European put options in addition to the call option. The function `gbm_mcs_dyna()` implements the algorithm. The code also compares option price estimates for a call and a put stroke at the same level:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The number of time intervals for the discretization.\n",
    "M = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "511974d5-5ceb-4b68-bf7f-e01eaa43f7c6"
   },
   "outputs": [],
   "source": [
    "def gbm_mcs_dyna(K, option='call'):\n",
    "    ''' Valuation of European options in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level paths)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K: float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0: float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    \n",
    "    # simulation of index level paths\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    \n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * math.sqrt(dt) * sn[t])\n",
    "    \n",
    "    # case-based calculation of payoff\n",
    "    if option == 'call':\n",
    "        hT = np.maximum(S[-1] - K, 0)\n",
    "    else:\n",
    "        # Put option\n",
    "        hT = np.maximum(K - S[-1], 0)\n",
    "    # calculation of MCS estimator\n",
    "    C0 = math.exp(-r * T) * np.mean(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "44ae2961-ec7c-4e69-b6ff-17b8093a894b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.987266071170579"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The Monte Carlo estimator value for the European call option (Dynamic Simulation Approach)\n",
    "gbm_mcs_dyna(K=110., option='call')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "bedb79ae-4f01-41ea-b16a-22ea9781fc0e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.623515262341943"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The Monte Carlo estimator value for the European put option (Dynamic Simulation Approach)\n",
    "gbm_mcs_dyna(K=110., option='put')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The question is how well these simulation-based valuation approaches perform relative to the benchmark value from the Black-Scholes-Merton valuation formula. To find out, the following code generates respective option values/estimates for a range of strike prices, using the analytical option pricing formula for European calls. First, we compare the results from the static simulation approach with precise analytical values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiates empty list objects to collect the results.\n",
    "stat_res = []  \n",
    "dyna_res = []  \n",
    "anal_res = []\n",
    "\n",
    "# Creates an ndarray object containing the range of strike prices.\n",
    "k_list = np.arange(80., 120.1, 5.)  \n",
    "np.random.seed(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulates/calculates and collects the option values for all strike prices.\n",
    "for K in k_list:\n",
    "    stat_res.append(gbm_mcs_stat(K))  \n",
    "    dyna_res.append(gbm_mcs_dyna(K))  \n",
    "    anal_res.append(bsm_call_value(S0, K, T, r, sigma))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "e9e52ba0-6ccb-46df-a089-49505d6c7919"
   },
   "outputs": [],
   "source": [
    "# Transforms the list objects to ndarray objects.\n",
    "stat_res = np.array(stat_res)  \n",
    "dyna_res = np.array(dyna_res)  \n",
    "anal_res = np.array(anal_res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure below shows the results. All valuation differences are smaller than 1% absolutely. There are both negative and positive value differences:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, stat_res, 'ro', label='static')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(bottom=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - stat_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125);\n",
    "fig.suptitle('Analytical option values vs. Monte Carlo estimators (static simulation)')\n",
    "plt.savefig('./images/stoch_15.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A similar picture emerges for the dynamic simulation and valuation approach, whose results are reported in the figure below. Again, all valuation differences are smaller than 1% absolutely, with both positive and negative deviations. As a general rule, the quality of the Monte Carlo estimator can be controlled for by adjusting the number of time intervals $M$ used and/or the number of paths $I$ simulated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SlXS/9u3bM23aNE6fPs2+ffuYPn06AEOHDiUkJITt27cTERHB119/TUREBE5ODx/mGhQUxMSJE6lVqxaVK1fOkDxllTgppTAYDDg7O2d7vt3PZDLRuXNnRowYYXl8/fp1S4KfJiAggDNnzpCYmGj5owXmbrnx48fz6aefMnr06BzP47Rk7MH6PlifrMZ+5VTPHj160KpVK3bs2MG2bduYO3cua9euzbSP+92fBALodJk/zh/lukyrS07HkHbcTk5OLFq0iMOHD7Nr1y6mTp1KgwYNLF2caR5Mih+M3f117d69O6GhodSvXx9vb2/Kly9veS3tWkr7HFBKsWTJkhyv/wd/L2lfqLLy4GeMUooTJ05k6vrM7vx/sJz795VVudlduw/q1asXvr6+NGvWjMDAQA4ePJhl3O6vd1bPpcUwp+vIZDI90nUs8o9ER2Tw448/4unpybZt29iyZQtbtmxh8+bNJCUlWcaVZGX79u0MGjSIDh06oNFoOHjwIEajMdP7QkND2bx5M0ePHrV889XpdBiNxkwfNo0bN2bTpk0kJiYC8Nlnn/Htt9+yfft2goODCQ0NxcvLiy1btmRZVhp3d3dq1qzJ4sWLAfMs09WrV1sG4d6+fZuYmBgAtmzZgrOzMz4+Pmi12iw/SJs1a8ayZcvQ6/WYTCYWL15MkyZNcvq1ZlKmTBlq1qzJhAkTCAkJAeD8+fMkJiYyZMgQWrduzd69e0lNTc30R9TT09PyTfn27dv89ttvluOsVasW33zzDWBObHv27ElUVBRbt27ljTfeoHbt2rz77rsEBQURGxubqV6urq688sorjB49mnbt2lG4cGEMBgOtW7cmKSmJnj17MnHiRE6fPv3IA9Fr1qxJcnIys2bNIjg4ONNrZ8+e5dChQwCcOnWKffv2Ub9+/Rz3qdVqLeU3adKE9evXc/36dcDcIpzVeJsyZcrQqVMnxo4dazmnEhMTmTRpEsWLF6dQoUKPfB7fr2nTpkRERFhaPBYuXEi9evUyJQw51bNHjx4cP36cLl26EBYWRkJCAvHx8RmO80nkdDz377tp06YsXrwYpRSpqamsWLEiy0HqsbGxdOzYkSpVqjBgwADeeOONLFufK1WqxMWLFy2PmzVrxvLlywHzOLT7ZxqWK1eOWrVqMXXqVHr27PlIx/Q4139OatasyenTpzl16hQAUVFRlkQ6zdOe//fz8PBAr9fz559/AmTZQhwfH8+RI0cYPnw47dq149q1a1y4cMHyOZDVOdGwYUN27Nhh+Z2njZFNa6nOycWLF3Mc3yvyn7SoiQyWLl3Km2++maFFycPDgz59+vDdd99lu93QoUMZNGgQxYoVo3DhwtSrV48LFy5kel/JkiXx9/enSpUqlm+cpUuXxs/Pj8DAQJYuXWp5b4sWLfjzzz8tH94vvPACYWFhxMbGMmHCBCIiItBqtVSvXp2TJ0/meFzh4eFMnjyZiIgIUlNT6dSpE126dOHy5cu4urqyZs0awsPDKVSoEJ9//jlarRZvb2+0Wi0hISHMmjXLsq+BAwcyY8YMgoKCMBgMBAQEMH78+Ef7Bd8nNDSU9957jy+//BIwL/fQsmVLAgMD8fDwoEKFCrzwwgucP38+wx/9Pn36MHz4cF5++WXKly+fIakJDw8nLCyMTp06kZqaSseOHXn11VcxGo3ExMTQsWNH3NzcKFasGGFhYdnWa9GiRUyaNAkwJ9Jjx45l+PDh6HQ6NBoNU6dOxcXFhaioKJYtW8b8+fNzPNbOnTuzePFiSzdUmhIlSjBnzhzCwsJITk5Go9Ewbdo0vLy8Mg2wvl+jRo149913cXZ2Zvz48bz99tv069cPjUaDu7s7c+fOzdC6kWbixIl88cUX9OjRA61WS2pqKi+99JJlGZZHPY/vFxISwtWrVwkNDcVkMlGxYsVMkw3AnKxkV8/hw4czdepUZs+ejZOTE4MHD6Z8+fKYTCZmz57NoEGDMixh86hyOp5WrVoxY8YM9Ho948aNY8qUKXTq1Am9Xk+zZs3417/+lWl/vr6+BAYG0rVrV9zc3ChUqFCm1jSAl156if/+978YjUa0Wi0TJ05kzJgxBAYG8uyzz2ZqsUpLUFu0aPHQY+rXr99jX//ZKVWqFOHh4YwaNcoyCP/+ax1yPv8fV9GiRRkxYgRvv/02JUqUoH379pneU6xYMd555x2Cg4MpXrw4np6e1KlTh/Pnz9OoUSNeeuklhg4dypQpUyzbvPDCC0ycOJHBgwdjNBopVKgQ8+bNo2jRog+t07Zt27Ksh7AdGpVTe6oQuez27duEhISwePFiypYtm9/VyXbWlRDi6YwfP55GjRrRoUOHHN9nMpmYPHky5cqVs4yJE3njzp079OzZk1WrVmUYsiFsi3R9ijyzYsUKOnToQN++fW0iSRNCWM+IESNYsWJFjmt0JSYm0qBBAy5evEjv3r3zsHYCzIsejx07VpI0GyctakIIIYQQNkpa1IQQQgghbJQkakIIIYQQNkoSNSGEEEIIGyWJmhBCCCGEjZJETQghhBDCRkmiJoQQQghhoyRRE0IIIYSwUZKoCSGEEELYKEnUhBBCCCFslCRqQgghhBA2ShI1IYQQQggbJYmaEEIIIYSNkkRNCCGEEMJGSaImhBBCCGGjJFETQgghhLBRkqgJIYQQQtgoSdSEEEIIIWyUJGpCCCGEEDZKEjUhhBBCCBsliZoQQgghhI2SRE0IIYQQwkZJoiaEEEIIYaMkURNCCCGEsFGSqAkhhBBC2ChJ1IQQQgghbJQkakIIIYQQNkoSNSGEEEIIGyWJmhBCCCGEjZJETQghhBDCRkmiJoQQQghhoyRRE0IIIYSwUZKoCSGEEELYKF1+V8Aabty4k99VsCpPTzfi4pLyuxriCUn87JfEzr5J/OybI8evdOmi2b4mLWp2SKfT5ncVxFOQ+NkviZ19k/jZt4IaP0nU7Ihr5Eo8WzQCnQ7PFo1wjVyZ31USQgghhBU5ZNenI3KNXInHgH6Wx7rjR/EY0I8EICU4JP8qJoQQQgirkRY1O+E2+/+yfn7OJ3lcEyGEEELkFZtrUdPr9YwdO5bLly+TmprKwIEDKVu2LAMGDKBSpUoA9OzZkw4dOuRvRfOY9mTsYz0vhBBCCPtnc4na2rVrKV68ODNnzuTvv/8mKCiIQYMG8eabb9KvX7+H78BBGX180R0/mun5Y8qPLz90pWdPPT4+pnyomRBCCCGsxea6Ptu3b897770HgFIKrVbLkSNHiI6OplevXowdO5bExMR8rmXeSxryfpbPf+I6ms8/d6Fp0yIEBrqxcKEzdxx7dRIhhBCiwNAopVR+VyIriYmJDBw4kG7dupGamkrVqlXx9/fnyy+/JCEhgVGjRmW7rcFgdMxpvMuWwbRpcOwY+PnBmDEkB/Vg7VpYsAB++QWUgsKFITQU3nwTmjcHJ5tLx4UQQgjxKGwyUbt69SqDBg3itddeIyQkhISEBDw8PAD4888/CQsL47vvvst2e0df8LZ06aJZHuPlyxpWrHBmyRJnzp83Z2cVK5ro2VNP9+56nnvO5kJdIGUXP2H7JHb2TeJn36wRv//97ytKlixJUFDWqyesWrWcrl27s3v3Tq5d+4vOnbvk2r7vl28L3l66dIno6GiMRiMXL158pG1u3rxJv379GDFiBCEh5oPr378/hw4dAmDXrl1Ur17danW2Z889pxg6NJU9e+6yenUS3bvruXFDw/TprtSpU4Ru3QqzerWO5OT8rqkQQghh+777bgEADRs2fqwkLTdZbTLBTz/9xJdffsm9e/dYvnw5PXr0YOTIkXTu3DnH7ebNm0dCQgJffPEFX3zxBQCjR49m6tSpODs7U6pUKcLCwqxVbYfg5ASNGxtp3NjI1KmwZo0zS5c6Ex2tIzpaR/Hiii5d9Lz2mp4aNUxoNPldYyGEEPZs0iRXfvwxd1OKTp0MTJqUkuN77t5NZPr0KSQm3uHmzRt06dKNqKhf8Pauypkzp0lKSiQsbAbPPluWefPmEht7jISEeF54wYexYyda9vPVV59TqlRpunbtRkJCAkOG/JsWLVqRkBBPePh0/Pyqc/78OQYOfJdvv/0v27b9itFoJCioK0FBXXPc99OyWqI2f/58li5dSu/evSlZsiSRkZG8+eabD03Uxo0bx7hx4zI9v2zZMmtV1aEVLQq9e+vp3VvPqVNOLF2qY8UKZxYscGHBAhf8/Iy89pqerl0NlCwpXaNCCCHsx6VLl3jppXa0aNGamzdvMHjwO5QqVZpq1arz3nvv89VXn7Np08906RJC0aJFmT37C0wmE336dOPGjeuW/XTs2JlJkz6ga9dubNq0kXbt2tOjR29WrVrB8OGj+emnHwE4eTKWPXt28vXX32IymZg3by6JiYk57vtpWS1Rc3Jywt3d3fL4mWeewUlGtecrb28TEyakMnZsKlu2aFmyxJlfftExblwhPvxQ8fLLBl57TU/LlkZ0NrdwixBCCFs1aVLKQ1u/rKFEiRKsWLGEX3/diptbEQwGAwA+PlUBKFOmDLdu3cLVtRBxcXFMnDgWNzc37t27Z3kvwHPPlcfNrQhnz55h06aNTJ+e9WLyFy6cp1q16mi1WrRaLe++OxSDwZDjvp+W1f4ce3t7s2jRIgwGA8ePH2fJkiX4+vpaqzjxGHQ6aNfOSLt2Rm7c0LBqlY6lS51Zt87879lnTXTrpqdnTz1VqkgrmxBCCNu0bNki/P0DCA4OYf/+39i1azsAmgfG9OzevYPr168xefI04uLiiInZyoNzKV99NYhvv/0vpUs/Q/HixQEyvadixUqsXr0Kk8mEyWRi+PD/0LVrt4fu+2lYrYlrwoQJXLt2DVdXV8aOHYu7uzsTJ+Zen63IHaVLK/71Lz3R0Un88std3ngjlaQkDZ9+6kqjRu506lSYJUt0FMCl64QQQti4Jk2aExGxgsGD32HFiiVotVr0en2m91WrVp0rVy4zaNDbjB8/inLlnuPmzRsZ3tO8eSt+/30vHTumD9GqVMmLyZPHWx57e1elQYNGDBzYn4ED+9OuXSB+fv4P3ffTsMnlOZ6Wo0+/tvYU83v3YMMGHUuWOLNtmxalNLi5KTp3NtCzp54GDYwyAeEpyBIB9ktiZ98kfvbN2vFLTk5m8OB3+Prrb/N8qFZOy3NYrevT19c3U9Nj6dKliYmJsVaRIpcULgxduhjo0sXAxYsali93Ztky88zRpUudqVzZvDZbt256ypZ1uDxfCCFEAXP48EFmzpzKm2++bXPj6fOkRU2v17N582YOHDjAmDFjrF2cw39jyo9vhSYT7Nih/Wcsm47kZA1OTopWrcyzRtu1M+DqmqdVslvyrd5+Sezsm8TPvjly/PJtwds0zs7OBAYGsnv37rwoTliBkxM0a2bkiy+SOXIkkZkzk6ld20RUlI7+/QsTEODOBx+4cuSIbX0TEUIIIeyZ1bo+V69ebflZKcWpU6dwdna2VnEiD3l4wOuv63n9dT2xsU4sXerMDz/omD/fhfnzXahRw9zK1qWLHk/P/K6tEEIIYb+s1vX5YBenp6cnPXv25Pnnn7dGcRk4atNoGlts/tXrYfNmHUuX6ti0SYfRqMHFRREYaJ6A0KKFEa02v2tpG2wxfuLRSOzsm8TPvjly/HLq+pRZn3bI1k/Wa9c0rFxpXpvt5ElzdlaunInu3fX06KHHy8vhTrnHYuvxE9mT2Nk3iZ99c+T45Wmi1rp160yzPe8XFRWVm8VlyVEDmcZeTlalYP9+J5YscSYy0pnERPN50bixgR499HTqZKBIkXyuZD6wl/iJzCR29k3il79cI1fiNvv/0J6MxejjS9KQ90kJDnnk7R8Wv5SUFHr1CmHlyh9zo7rZunXrJt9881+GDx+da/vM00Tt8uXLOb7+3HPP5WZxWXL0C9EeP2ySkmD9enMr2/bt5qGR7u6KoCDzHRDq1jVRaPXTXcT2wh7jJ8wkdvZN4pd/XCNX4jGgX6bnE75a8Mif87aSqFlDvnR9pqam8uuvv3L37l0AjEYjly5d4r333rNGcRk4+oVo7x82586lr812+bJ5luiQZ5cw669emd77OBexvbD3+BVkEjv7JvHLP54tGqE7fjTT8wY/f+Kid5QYLLsAACAASURBVD7SPrKKX1JSEpMnj+POnTs891x5YmKi8fDwYOnSCLRaLV988SlVq1YjMvIHvL2rcubMaZKSEgkLm8Gzz5Zl3ry5xMYeIyEhnhde8GHs2In8739fcfnyJf7++28SEuLp0iWU6OgtXLx4ng8++JCSJUsyceJYvv76W3bs2MY338xHKYWPjy8jRox5onXY8mV5jsGDB/P9998za9Ystm3bxpw5czh9+rS1ihN2pFIlxahRqfz2211WrEiiSxc9/a5Nz/K9bnOyvjGuEEII+6E9GftYzz+q1atX4eVVhc8/n0/nzl1xd3cnIKAWe/fuwmg0smfPTpo3bwmYbyM1Z84X1K3bgE2bfubu3USKFi3K7Nlf8N//LuTo0cPcuHEdAFdXVz755DNatGjNrl07+PjjWfTu/QZRUb9YyjYYDMya9TEzZ87mf/9bSPny5bl+/fpTHU9WrJaonT17lu+//562bdvy1ltv8cMPP1jlAIT90mqhZUsj8+Yl4+90LOs3HY9l/Xodycl5WzchhBC5x+jj+1jPP6qLFy/g51cdgOrV/dHpdHTqFMxPP61j9+6d1K1b37I0mI9PVQDKlClDamoKrq6FiIuLY+LEscycOZV79+5hMBj+ea+5XkWLulOpktc/P3uQmppiKTs+/m+KFi2Kp2cJAHr1ep1nn332qY4nK1ZL1EqWLIlGo8HLy4sTJ07884tJtVZxws5ld7EeVX68+WZhqld35z//KcTWrVr+uY6EEELYiaQh72f9/HvDnmq/Xl5eHDlyGICTJ2MxGAzUrFmLy5cvsW7dGl55Jf0G6w9OdNy9ewfXr1/jww+n8s47g0hJSSZtNNij3M/a07MEiYmJJCTEAzB79kyOHTvyVMeTFaslat7e3oSFhdGgQQO+/fZbvv766yzvaC8EZH8Raz8YyqBBqXh4KJYtc6Z7dzcCAoowerQre/ZoMZnyuKJCCCEeW0pwCAlfLcDg54/S6TD4+efKGOTOnbty5cplBg7sT0TED5bWs3bt2nP79i0qV66S7bbVqlXnypXLDBr0NuPHj6Jcuee4efPGI5ft5OTEsGGjGDFiCAMH9kcpRbVq1Z/qeLJitckERqORP/74g7p16xIVFcWuXbvo1q0bPj4+1iguA0cfLOqoA2JdI1fiNueT9Fmf7w2zXMQmE+zdqyUyUsePP+q4edP8HaN8eRNBQXqCgw34+5se6VtQfnPU+BUEEjv7JvGzb48TvyVLvsfDoxgdO3Z++JttQL7M+vz3v//Nq6++SuvWrXFxcbFGEdly9AuxoH/YGAwQE6MlMtKZn37SceeOOTvz9jYSFGSgSxc9VarY7qK6BT1+9kxiZ98kfvbtUeP30UeTuHnzBjNmzMrz/ONJ5UuiFh0dzbp169i7dy/NmjXj1VdfpUGDBtYoKhNHvxDlwyZdcrL51lWRkeZbVyUnm5O2gAAjwcF6goIMPPecbSVtEj/7JbGzbxI/++bI8cvXW0glJycTHR3N119/TVxcHFu3bs3x/Xq9nrFjx3L58mVSU1MZOHAgL7zwAqNHj0aj0eDt7c3EiRNzXKfEUQOZxpFP1qeRmAgbNuiIjHQmOlqLwWBO2ho2NBAUZODVVw2UKpX/SZvEz35J7OybxM++OXL8ckrUdNYs+M8//2T9+vVs3LiRsmXL0rdv34dus3btWooXL87MmTP5+++/CQoKwtfXlyFDhtCgQQMmTJhAVFQUbdu2tWbVhR1yd4fQUAOhoQZu3dKwbp25pW3XLi27d+v44ANF8+bmlrZXXjFQNPvrQgghhLAJVmtR69SpE1qtls6dO/PKK6/wzDPPPNJ2d+/eRSmFu7s7cXFxhISEkJqaSkxMDBqNhs2bN7Njxw4mTpyY7T4cNeNO48jfKqzh6lUNq1frWL3amT/+MN8k3tVV8dJLBrp0MfDSSwYKF867+kj87JfEzr5J/OybI8cvX7o+T5w4QdWqVZ94+8TERAYOHEi3bt2YMWMG27dvB2DXrl2sWrWK8PDwbLc1GIzodNonLls4rj//hGXLYOlSOPbPGrtFi0JQEPToAW3bwj+zu4UQQoh8Z/Uxak/i6tWrDBo0iNdee42QkBCaN29OTEwMAJs3b2bnzp1MmDAh2+0dNeNO48jfKvKKUnDsmBORkeaWtgsXzGMeS5Qw0bGjuaWtYUMjT3DLtoeS+NkviZ19k/jZN0eOX77c6/NJ3bx5k379+jFixAhCQsxraPn5+bFnzx4AYmJiqFu3bn5WUTgAjQaqVzcxblwq+/bdZf36u7z1VipaLXz/vQtBQW7Url2ECRNcOXDACdv7OiOEEKIgsLkWtSlTprBhwwYqV65see6DDz5gypQp6PV6KleuzJQpU9Bqs+/adNSMO40jf6vIbwYD7NihZfVqHevWORMfb5456uVlIjjYvLBu1apPdzsEiZ/9ktjZN4mffXPk+OXLGLVjx44xb9484uPjub+I77//3hrFZeCogUzjyCerLUlJga1bzQvr/vyzjqQkc9Lm52ekSxcDQUF6KlR4/MtH4me/JHb2TeJn3xw5fvmSqHXq1Inu3bvj7e2d4Uao9evXt0ZxGThqINM48slqq+7ehZ9/Nq/RtmWLFr3efE7XrWukSxc9r75q4JlnHu1SkvjZL4mdfZP42TdHjl++rKNWqFAhevfuba3dC5GnihSBLl3Mkwzi4mD9emciI3Vs367lt98KMW6comlTI8HBBl55RU/x4vldYyGEEI7AapMJmjZtysKFCzl79ixXrlyx/BPC3nl6Qu/eelatusehQ3f56KNkatc2EROjY+jQQvj7u9O3byEiI3XcvZu+nWvkSjxbNAKdDs8WjXCNXJl/ByGEEMIuWK3rs3Xr1pkL02iIioqyRnEZOGrTaBpHbv61Z+fPa1i92pmICB3Hj5snu7i5Kdq3NzDk2SU0++KNTNskfLWAlOCQPK6peFJy7dk3iZ99c+T45eu9PvODowYyjSOfrI4iNta8RltEhDPnzztxkAACOJzpfQY/f+Kid+ZDDcWTkGvPvkn87Jsjxy9f1lG7ffu25f6cdevWZfDgwdy8edNaxQlhU3x9TYwZk8revXf5+ee7VNccy/J9TrGxJCTkceWEEELYDaslahMmTKBGjRpERUWxZcsWatasyQcffGCt4oSwSRoN1K5tQvn6Zvn6YZMf1aq5061bYRYscObKFU2W7xNCCFEwWS1Ru3jxIv3798fd3R0PDw/efvttmUwgCqykIe9n+fzRTsPx9TURHa1j9OhC1KrlTrt2bnzyiQvHj8sdEYQQoqCz2vIcGo2Gq1evUrZsWQCuXLmCTme14oSwaSnBISQAbnM+QXcyFoOPL0nvDaNtcBBtSeLSJQ0//6zjp5907Nql5cABV6ZPd6ViRROBgQYCAw3Ur28khxtyCCGEcEBWm0ywdetWJk6cSM2aNVFKcfDgQcLCwmjZsqU1isvAUQcbpnHkAZUFwcPi9/ffEBWlY8MGHVFROu7eNXeHlihhol07I+3bG2jZ0oCbW17VWKSRa8++SfzsmyPHL99mfd6+fZtDhw5hMpmoWbMmJUuWtFZRGThqINM48slaEDxO/FJSYPt2LRs26Pj5Zx3XrplHKxQurGjRwkD79gbatTNSqpT0keYFufbsm8TPvjly/PI0UVu+fDndu3dn7ty5Wb4+ePDg3CwuS44ayDSOfLIWBE8aP5MJ/vjDiY0bdWzcqOPECXM/qJOTol49c0tbYKCBypUlabMWufbsm8TPvjly/PL0FlIOuCybEDbByQlefNHEiy+m8sEHqZw5o2HDBnPStnevlj17dHz4IVStaiQw0NzaVquWCSerTRkSQghhbVbr+oyMjCQ4ODjDc4sXL6ZXr17WKC4DR8240zjyt4qCwBrxu3FDw6ZNWjZscObXX7UkJ5vHtZUpY7K0tDVpYsTVNVeLLXDk2rNvEj/75sjxy9MWtW+//ZbExESWLVvG5cuXLc8bjUZ+/PHHPEnUhChoSpdWvPaagddeM3D3Lvz6q3kywqZNWr77zoXvvnPB3V3Rpo25pe2llwwUK5bftRZCCPEwuZ6oVaxYkaNHj2Z63sXFhenTp+d2cUKIBxQpAh06GOjQwYDBAPv2afnpJ3MX6Zo1zqxZ44xOp2jcOL2L9LnnZMiCEELYIqt1fZ4+fZqKFSty4sQJtFotVatWRaPJm1XXHbVpNI0jN/8WBPkVP6XM9yBNG9d24ED6omwBAelJm5+fiTy6VO2OXHv2TeJn3xw5fnna9Znmr7/+4vXXX+eZZ57BZDKRkJDA7NmzCQgIsFaRQogcaDRQrZqJatVSGTYslStXNJYZpNu3azl0yJUZM1ypUMFkSdoaNDAi61QLIUT+sVqLWseOHQkPD8f3n3scHj58mIkTJxIREWGN4jJw1Iw7jSN/qygIbDF+CQkZF9m9c8fcpObpqWjb1py0tWploEiRfK5oPrPF2IlHJ/Gzb44cv5xa1Kw2cd/FxcWSpAHUqFHDWkUJIZ6ShwcEBxv4+utkjh9PZPnyJN54I5VChRQrVjjTr19hqlVzp3fvwixa5Mz165n7Rl0jV+LZohGlynri2aIRrpEr8+FIhBDCsVitRW3SpEno9Xq6deuGVqtl/fr1XLp0ib59+wJQr169bLc9ePAg4eHhLFy4kGPHjjFgwAAqVaoEQM+ePenQoUOOZTtqxp3Gkb9VFAT2FD+l4ODB9HFtx4+bx7VpNIq6dU0EBuoJDDTgd+gHPAb0y7R9wlcLSAkOyetqW409xU5kJvGzb44cv3y5hVSfPn2yL1Sj4fvvv8/ytfnz57N27VoKFy7MihUr+OGHH7hz5w79+mX+I5AdRw1kGkc+WQsCe47f2bPp49r27NFiMplb1o67BOCbejjT+w1+/sRF78zralqNPcdOSPzsnSPHL18mEyxcuBCAxMRETCYTHh4ej7RdhQoV+Oyzzxg5ciQAR44c4ezZs0RFRVGxYkXGjh2Lu7u7taothMiBl5di4EA9AwfquXUrbZFdHS9sOJbl+7UnY/O4hkII4Vis1qJ28eJFhg4dysWLF1FKUa5cOWbPnm3pwszJpUuXGDZsGCtWrGDVqlVUrVoVf39/vvzySxISEhg1alSO2xsMRnQ6bY7vEULkHpN/AE5HM7eoHSSA7lUP0rYttGsHLVtC0ey/OAohhHiA1VrUJkyYwFtvvUX79u0B+Omnnxg/frylpe1RtW3b1tIa17ZtW8LCwh66TVxc0uNX2I44cvNvQeCI8XP9z9Asx6itrzGSS2cUc+dqmDsXdDpF3bpGWrQw0rKl+V6kWjv6TuWIsStIJH72zZHjly+zPuPi4ixJGkCHDh34+++/H3s//fv359ChQwDs2rWL6tWr51odhRC5IyU4hISvFmDw80fpdBj8/En4agFvR73KiROJrFmTxLBhKQQEmNi7V8uMGa4EBhbB19edfv0K8f33zpw/L6vsCiHEg6zWoubi4sLRo0ctidWRI0coXLjwY+9n0qRJhIWF4ezsTKlSpR6pRU0IkfdSgkOynOHp4gKNGhlp1MjI6NGpxMXB9u06oqO1REfrWLfOmXXrnAHw8jLRooWBli2NNG1q4BGHtgohhMOy2hi1AwcOMGzYMIoXL45Sivj4eGbNmkXNmjWtUVwGjto0msaRm38LAolfOqXMM0mjo82J244d6YvtarWKOnVMtGxpoEULA3XqmPL9LgkSO/sm8bNvjhy/fFmeA0Cv13Pu3DlMJhNeXl64uLhYq6gMHDWQaRz5ZC0IJH7Z0+th/34tv/5qbm3bv9/JsgRI0aKKpk3NrW0tWxrw8sr7G8lL7OybxM++OXL88i1Ryy+OGsg0jnyyFgQSv0cXH5/eTfrrrzrOnUsfVluhQno3abNmBooXt359JHb2TeJn3xw5fpKoORhHPlkLAonfkzt3TsOvv5oTt23bdCQkmFvbnJwUtWunJ24vvmjE2Tn3y5fY2TeJn31z5Pjly4K3QgiR2ypVUlSqpOf11/UYDHDggJMlcfv9dy2//+7KJ5+Au7uiSRNzF2nLlgYqV1ZoZFKpEMIO5XqL2pgxY3J8fdq0ablZXJYcNeNO48jfKgoCiZ913LkDO3aYx7b9+quO06fTu0nLl0+blGDuJi1R4snKkNjZN4mffXPk+OVpi1r9+vVze5dCCPFQRYtC+/ZG2rc3AilcvJixm3TRIhcWLTLfUL5mzfTErV49I3k0z0kIIR5brreoXblyJcfXy5Url5vFZclRM+40jvytoiCQ+OU9oxEOHXL6p7VNy759WvR6c1+om5uiceO0blIj3t6mbLtJJXb2TeJn3xw5fnk6maB169ZoNBqy2q1GoyEqKio3i8uSowYyjSOfrAWBxC//JSbCrl1aS+J28mT6fazKljXRsqWRFi0MNG9upFQphWvkStxm/x+6k7EYfHxJGvJ+lov7Ctsm1559c+T4yaxPB+PIJ2tBIPGzPVeuaCxrt8XEaLl1K31824jnl/DxxV6Ztkn4aoEka3ZGrj375sjxy5dZn2fOnGHJkiUkJSWhlMJkMnHp0iUWL15srSKFEOKJlCun6NnTQM+eBkwmOHIkvZu0z/bpWW5j+ugTEtqEyG2uhBBWZbWbsg8dOhQPDw+OHz9OtWrVuHXrFt7e3tYqTgghcoWTEwQEmPjPf1JZteoe/k7HsnxfkQuxeHu706qVG6NHuxIZqePKFVkDRAiRu6zWomYymfjPf/6DwWDAz8+PHj160KNHD2sVJ4QQVmH08UV3/Gim52+UqkYjHyP792s5elTLggXm559/3kS9ekYaNDD/8/U14WS1r8RCCEdntUStcOHCpKamUqlSJY4ePUrdunVJSUmxVnFCCGEVSUPex2NAv0zPu380lNXB90hNNc8o3bNHy5495hmlERHORESYb41QrJjKkLjVqmWkUKG8PgohhL2y2mSCRYsWsWXLFsLDw+nevTsVK1bEZDKxIO1rpxU56mDDNI48oLIgkPjZH9fIlbjN+SR91ud7w7KdSKAUnD6tYc8enSV5O3s2vUnNxUUREGD6J3EzUL++8YkX4BWPR649++bI8cu3WZ+JiYm4u7tz5coVjh49SpMmTXBzc7NWcRaOGsg0jnyyFgQSP/v1pLG7dk3D3r1a9u41J26HDzthNKaPZ/PxMbe21a9v/r9iRbnllTXItWffHDl++ZKo7d69m9mzZ7Ns2TLOnDnDW2+9RXh4OHXq1LFGcRk4aiDTOPLJWhBI/OxXbsUuMRH++ENraXH77Tctd++mZ2bPPGOydJU2aGCkenUTOrkz81OTa8++OXL88iVRCw4OZsaMGfj4+ABw+vRpRo4cyapVq6xRXAaOGsg0jnyyFgQSP/tlrdgZDHDsWPo4tz17tFy7lt5d6uamqFs3PXGrU8eIu3uuV8PhybVn3xw5fvmyjlpKSoolSQOoUqUKBoPBWsUJIYTd0unMS4IEBJh4+209SsGFCxpL0rZ3r5aYGB0xMeaPbK1W4e+f3upWv76RMmUcbu1yIQRWTNQqV67MzJkz6dy5MwDr16+nUqVK1ipOCCEchkYDFSsqKlY00K2b+Qvu7duwb1/6OLcDB7QcPKjl66/N21SqlDFxy+mepUII+2G1rs/4+HjmzJnDvn370Ol01KtXj3fffZeiRbNv3sstjto0msaRm38LAomf/bKl2CUnw4ED6Ynb3r1a4uPTM7MSJUzUr58+QSEgwISraz5W2AbYUvzE43Pk+NndvT4PHjxIeHg4Cxcu5Pz584wePRqNRoO3tzcTJ07E6SGrRzpqINM48slaEEj87Jctx85kghMnnDIkbhcupH9WFiqkqF07PXGrV89IsWLm19JuOq89GYvRgW86b8vxEw/nyPHLlzFqT2r+/PmsXbuWwoULAzBt2jSGDBlCgwYNmDBhAlFRUbRt2zafaymEELbFyQmqVTNRrZqJ11/XA+abzaclbmn/du0yf+xrNApfXxPvll7KwJj0BX11x4/iMaAfCeCQyZoQ9sbmbmxSoUIFPvvsM8vjo0ePUr9+fQCaN2/Ozp0786tqQghhV8qVUwQFGZg2LYUtW5I4dSqR5cuTGDYshSZNjJw750STmI+z3Nb40SdcuyaD3ITIbzbXovbyyy9z6dIly2OlFJp/RsQWKVKEO3ce3uzp6emGTqe1Wh1tQU7NpML2Sfzslz3HrnRpqFwZunUzP9brQVf4GBgzv9f9Qiw1arhTtiy8+KL5X5065v/LlcNuJyrYc/xEwYyf1RK1iIgIZsyYQUJCApCecB0/fvyx9nP/eLS7d+/i4eHx0G3i4pIer7J2xpH76QsCiZ/9csTYeWZ30/nS1Wj/op6DB7WsW+fEunXpr5UubV5KpGZN4z/Lihh57jnbv5uCI8avIHHk+OXLGLXPP/+chQsXZlhL7Un4+fmxZ88eGjRoQExMDA0bNsylGgohhMj2pvNThvJ9cDIA169rOHzYiYMHtRw65MShQ1qionRERaX/CSlZMj15q1HD/P/zz9t+8iaErbNaolamTJmnTtIARo0axfjx4/nkk0+oXLkyL7/8ci7UTgghBJgnDCQAbnM+SZ/1+cBN5595RtGmjZE2bdL7SG/eNCdvhw5pOXjQ/P/WrTq2bk3/s+LpqahRw0jNmkZq1jRRo4aRSpUkeRPicVhteY6PPvqIa9eu0aRJE1zvW7wnKCjIGsVl4KhNo2kcufm3IJD42S+JXc7i4vgncdNaWuDOncs4Z61YMUVAQHqXac2a5uTtIasu5QqJn31z5PjlS9dnYmIiRYoU4cCBAxmez4tETQghRN7z9IQWLYy0aJHe8hYfb07e0rpMDx7Usm2bjm3b0rcrWtTc8pbWdVqzppHKlfMmeRPC1uXpgrfJyckUKlTI6uU4asadxpG/VRQEEj/7JbHLHXfuwOHD5i7TtNa3P/90Qqn0PtEiRdK6TU2W/194wYT2KSb0S/zsmyPHL19a1H7++Wc+//xzkpKSUEphMplITk5m165d1ipSCCGEHShaFBo3NtK4sREwL86bmAhHjphb3tImLezdq2X37vQ/U25uCn//+7tNTXh7m9DZ3EJTQuQeq53eM2fOZMqUKXzzzTf861//Yvv27cTFxVmrOCGEEHbM3R0aNjTSsGF68nb3Lhw9mt5leuiQE7//rmXv3vQ/XYULK/z80pYKMSdxVauacHZO33faLbI4GYunA98iSzgmqyVqHh4eNGzYkP3793Pnzh3effddunTpYq3ihBBCOJgiRaB+fRP165tIS96SkuDYMSfLuLeDB81dqL//nt4n6uqqqF7d3GUaalrGKwvlFlnCflktUStUqBBnz56lSpUq7N27l4YNGz7SXQWEEEKI7Li5Qd26JurWNVmeS06G48czrvN2+LAT+/drGUZ4lvsxTJnFmZqhVKyonmrcmxDWZrVEbciQIcyePZuZM2fy9ddfs3z5ckJC5NuLEEKI3FWoENSubaJ27fTkLSUFYmOd8H/5GJgyb1P04nEaNnTH1VVRpYoJX18TPj7mf1WrmvDykrFvwjbk2azP+Ph4ihUrlhdFOeyskDSOPPOlIJD42S+Jnf3xbNEoy1tk/fVMDd5r+TsnTjhx6pQTSUkZV+F1dla88EJ68paWyHl5mXBxyavai/s58vWXL7M+L1++zLhx47h8+TKLFy/m/fffZ+rUqZQvX95aRQohhBAZZHeLLLewocz95xZZJhNcuqTh5EknYmOdOHlSy8mTTpw44cTx4xn7RXU6ReXK5la3tNa3qlVNVK5s4r613YXINVZL1CZMmED//v0JDw+nVKlSdOzYkVGjRrF48WJrFSmEEEJkcP8tsnQnYzFkcYssJyeoUEFRoYKRl15Kn3WqFFy+rLEkbeZEzpzEnTyZMYHTahVeXhlb33x8zGu/5cHyocKBWS1Ri4uLo2nTpoSHh6PRaOjWrZskaUIIIfJcSnAIKcEhlC5dlLjH6DrTaKB8eUX58kZat06/24JS8NdfGk6cSE/gzD9r+fNPLT/9lL4PJydFpUoKHx+jpRXO19dElSom3Nxy8yiFo7LqrM+//voLzT933/3tt99wkY59IYQQdk6jgbJlFWXLGmnZMmMCd/265oHkzZzAbdzozMaN9+9DUaGC+qfr1GjpRn3hBRPu7vlwUMJmWS1RGzNmDAMGDODChQu8+uqrJCQkMGfOHGsVJ4QQQuQrjQbKlFGUKWOkefOMCdzNm/ePgUtP5H75Rccvv2T8U1yhwv2TGIyWn7NL4NIW9NWejMUoC/o6HKvO+tTr9Zw7dw6TyYSXl1eetag56qyQNI4886UgkPjZL4mdfbPF+N28qeHUKadM3ajXr2e+I/1zz2WcxODjY+TFUysoMyTzZImErxY4XLJmi/HLLfky6/PKlSuEhYWxe/dunJ2dad68OWPHjqVEiRLWKlIIIYSwK6VKKUqVMtKokTHD83FxcOKENkPr24kTTmzZomPLlvT3HWQWZbLYr9PHn5D0coiMg3MAVmtRe+211+jQoQNBQUEopVi1ahU7duxg/vz51iguA0fNuNM48reKgkDiZ78kdvbNEeIXH49l1mlsrBOff+2GVhkzvU+PDhf0lCljolIlExUrKipVSvvZRKVKilKlFBpNFoXYKEeIX3bypUUtMTGR3r17Wx6/8cYbREREWKs4IYQQwuEVKwb16pmoV898uwUV4wtZLOh71bMazfwNnD/vxL59WvbsyZyRFSmiMiRu6T+bKF9eZbixvcg/VkvUqlevzpo1a+jcuTMA0dHR+Pn5Was4IYQQosDJbkHf4tOHsir4HgB6PVy8qOHcOSfOnXPi/Hknzp0zPz571omjRzPf7FSrVZQvryyJm/mf+bGXl8xMzUtW6/ps1KgRcXFxuLq64uTkxL1799IL1Wg4fvy4NYoFpOtT2DaJn/2S2Nk3R42fa+RK3OZ8kj7r84EFfXOiFNy4obEk/lgSPwAAIABJREFUbuYkLu2fhhs3Mk9qAChVytyd+mAiV6mSiTJlrNOl6qjxg5y7PvPsXp95yVEDmcaRT9aCQOJnvyR29k3i9/ju3sWSvJ0/r7kviXPi4kUNBkPmjKxwYUWFCumJ2/1dqs8/rx77Vltpy49Y7izhgMuP5MsYtXv37jF37lx27dqF0WikYcOGvPfee7g94RSU4OBg3P9pay1fvjzTpk3LzeoKIYQQ4gFFioCfnwk/P1Om14xG8y22HuxOTft34kTmJE6jUZQrpzJ1p6Y9Ll484/tdI1dm6NrVHT+Kx4B+JIDDJWvZsVqL2pgxYyhcuDDdunUDYMWKFdy5c4eZM2c+9r5SUlLo3r07q1evfqT3O/o3JvlWaN8kfvZLYmffJH55RynzEiMZx8WZk7nz5524ciXrLtXixTMmbh+sqEvpq0cyvc/g509c9E5rH0aeyZcWtaNHj7J27VrL4wkTJtChQ4cn2ldsbCz37t2jX79+GAwGhg0bRq1atXKrqkIIIYTIRRoNlCgBJUqYqFMnc2tccjJcuJCeuKUndBpiY504eNA8wSGcrMeza0/GWrX+tsRqiZpSioSEBDw8PABISEhAq808s+RRFCpUiP79+xMaGsq5c+d4++232bhxIzpd1tX39HRDp3uysuxFTtm3sH0SP/slsbNvEj/b8fzz0KRJ5udNJrhyBU6fhoTefpS4dDjTezR+fgUmllZL1N544w1CQ0Np1aoVAFu2bOGdd955on15eXlRsWJFNBoNXl5eFC9enBs3blC2bNks3x8Xl/TE9bYH0nxv3yR+9ktiZ98kfvbD1RX8/EA3fihksfxIwqAhpDhQLPOl67NVq1bUqFGDffv2YTKZ+Oyzz6hateoT7WvlypWcPHmSSZMmce3aNRITEyldunQu11gIIYQQtiQlOIQEwG3OJ+mzPh9j+RFHYLXJBIGBgWzYsCFX9pWamsqYMWO4cuUKGo2G4cOHU6dOnWzf7+jfmORboX2T+NkviZ19k/jZN0eOX760qPn6+rJ69WoCAgIoVKiQ5fly5co99r5cXFz4v//7v9ysnhBCCCGEzbNaonbw4EEOHjyY4TmNRkNUVJS1ihRCCCGEcChWS9S2bNlirV0LIYQQQhQIVkvUxowZk+XzckcBIYQQQohHY7VErX79+pafDQYDUVFRVK5c2VrFCSGEEEI4HKslasHBwRkeh4SE0LNnT2sVJ4QQQgjhcLK+2ZYVnD59muvXr+dVcUIIIYQQds+qy3NoNBrAfDupEiVKMGzYMGsVJ4QQQgjhcKyWqMXGFpwbpgohhBBCWEOud30uWbLE8vOpU6cyvPbRRx/ldnFCCCGEEA4r1xO1H374wfLzyJEjM7z222+/5XZxQgghhBAOK9cTtftvHWql24gKIYQQQhQIVp31mTaZQAghhBBCPL5cT9QkORNCCCGEyB25Puvz1KlTtGnTBoBr165ZflZKcePGjdwuTgghhBDCYeV6ovbzzz/n9i6FEEIIIQqkXE/UnnvuudzepRBCCCFEgZRnt5ASQgghhBCPRxI1IYQQQggbJYmaEEIIIYSNkkRNCCGEEMJGWe2m7LnJZDIxadIkTpw4gYuLC1OmTKFixYr5XS0hhBBCCKuyixa1zZs3k5qayvLly3n//feZPn16fldJCCGEEMLq7CJR+/3332nWrBkAtWrV4siRI/lcIyGEEEII67OLrs/ExETc3d0tj7VaLQaDAZ0u6+qXLl00r6qWbwrCMToyiZ/9ktjZN4mffSuI8bOLFjV3d3fu3r1refz/7d17WJRl/sfxzwCCMKCi0lk8rXi8KNHc2hCzJLPDpdmiwBVmapqFpiJi5mmVMC29XDVsUzPTlVNmWnblbq5JaWtGl3k2MtN21woPGYxynPn90c9JFBhFmXlmeL/+Yp57Hu7vzbepT/czM4/Vaq02pAEAAHgKtwhqERERys3NlSTt3r1bYWFhLq4IAACg7plsNpvN1UU4cuFTn998841sNpvS0tLUtm1bV5cFAABQp9wiqAEAANRHbnHpEwAAoD4iqAEAABgUQQ0AAMCgCGoAAAAGRVADAAAwKIIaAACAQRHUAAAADIqgBgAAYFAENQAAAIMiqAEAABgUQQ0AAMCgCGoAAAAGRVADAAAwKIIaAACAQRHUAAAADIqgBgAAYFAENQAAAIMiqAEAABgUQQ0AAMCgCGoAAAAGRVADAAAwKIIaAACAQRHUAAAADIqgBgAAYFAENQAAAIPycXUBdaGgoNDVJdSp4OAAnTlzztVloJbon/uid+6N/rk3T+5fSEhQtWPsqLkhHx9vV5eAa0D/3Be9c2/0z73V1/4R1AAAAAyKoAYAAGBQBDUAAACDIqgBAAAYlEd+6hMA8JthL//rip/75uT76rASALXBjhoAAIBBEdQAAAAMiqAGAABgUAQ1AAAAgyKoAQAAGBRBDQAAwKD4eg44BV8RAADA1WNHDQAAwKDYUQMAuK2r2a1/f37/OqwEqBvsqAEAABiUU3fUrFarZs6cqcOHD8vX11epqalq2bKlffytt97Spk2bJEm9evVSYmKibDaboqKi1KpVK0nSHXfcoaSkJGeWDQAA4BJODWoff/yxSktLlZWVpd27d+vll1/W0qVLJUk//PCDNm7cqJycHHl5eSkuLk59+vSRv7+/OnfurNdff92ZpQIAALicUy995uXlqWfPnpJ+2xnbt2+ffeymm27S8uXL5e3tLZPJpPLycvn5+Wn//v366aeflJCQoKefflrfffedM0sGAABwGafuqBUVFSkwMND+2NvbW+Xl5fLx8VGDBg3UtGlT2Ww2zZs3T506dVLr1q118uRJjRw5Uv369dOXX36p5ORkrVu3rsZ5goMD5OPjXdfLcamQkCBXl1BnPHltF9SHNXoqT+6dJ6/tgvqwRk9WH/vn1KAWGBgoi8Vif2y1WuXj83sJJSUlmjJlisxms2bMmCFJ6tKli7y9fwtd3bt3188//yybzSaTyVTtPGfOnKujFRhDSEiQCgoKXV1GnfHktUme3z9P5um98+S1XVAf1uipPPn1V1MAdeqlz4iICOXm5kqSdu/erbCwMPuYzWbTs88+q/bt22vWrFn2cLZkyRKtWrVKknTo0CHdfPPNNYY0AAAAT+HUHbXo6Ght375dsbGxstlsSktL08qVKxUaGiqr1aovvvhCpaWl+vTTTyVJEyZM0MiRI5WcnKxt27bJ29tbc+bMcWbJAAAALuPUoObl5aVZs2ZVOta2bVv7z3v37q3yvDfeeKNO6wIAADAivvAWAADAoAhqAAAABkVQAwAAMCiCGgAAgEER1AAAAAyKoAYAAGBQBDUAAACDIqgBAAAYFEENAADAoAhqAAAABkVQAwAAMCin3usTAIxm2Mv/uuLnvj+/fx1WAgCXY0cNAADAoAhqAAAABnVVlz537NihkpISRUZGqkGDBrWa0Gq1aubMmTp8+LB8fX2Vmpqqli1b2sezs7OVmZkpHx8fjR49Wr1799bp06c1ceJEFRcX64YbbtCcOXPk7+9fq/kBAADcxRXvqKWlpWnz5s3Kzc1VYmJirSf8+OOPVVpaqqysLCUlJenll1+2jxUUFGj16tXKzMzUihUrtGDBApWWlio9PV2PPPKI1q5dq06dOikrK6vW8wMAALiLanfUMjIyNHjwYHl5/Zbljh8/rkWLFsnLy0v9+9f+DbV5eXnq2bOnJOmOO+7Qvn377GN79uxR165d5evrK19fX4WGhurQoUPKy8vTqFGjJElRUVFasGCBhg4dWu0cwcEB8vHxrnWNrvBo0oYrfu778/srJCSoDqu5/jz9Tdie3L+rWZvkfr2+2nrdqXeS+/Xjanl6/6723y3upDb/bnG3/l0P1Qa1Jk2aaNSoUYqJidEDDzyggQMH6tFHH1VFRYUSEhJqPWFRUZECAwPtj729vVVeXi4fHx8VFRUpKOj3JpjNZhUVFVU6bjabVVhYWOMcZ86cq3V97qKgoOa/AYzNk/vnyWsLCQny6PV5Ok/vnyev7QJPXWNNAbTaoNavXz9FR0crIyNDzzzzjEaMGKHNmzdfczGBgYGyWCz2x1arVT4+PlWOWSwWBQUF2Y83bNhQFotFjRo1uuY6gOvpzcn3uboEAIAHqvE9at99950iIyP16quv6tNPP9WECRN05MiRa5owIiJCubm5kqTdu3crLCzMPhYeHq68vDyVlJSosLBQR44cUVhYmCIiIrRt2zZJUm5urrp163ZNNQAAALiDanfUUlJS9Msvv6i4uFi33367JkyYoJ9++kmvvfaaJGnWrFm1mjA6Olrbt29XbGysbDab0tLStHLlSoWGhur+++9XQkKC4uPjZbPZNH78ePn5+Wn06NFKSUlRdna2goODNX/+/NqtFgAAwI1UG9QOHDig999/XxUVFRo4cKAmTJigG2+8UbNmzVJ+fn6tJ/Ty8ros5LVt29b+86BBgzRo0KBK482bN9eKFStqPScAAIA7qjaoRUZG6tFHH5XVatXAgQMrjbVr167OCwMAAKjvarz0+eyzz8rb21sBAQHOrAkAAABycGeCi78qAwAAAM7FvT4BAAAMiqAGAABgUA5vyv7rr7/q/fff1y+//CKbzWY/fi33+wQAAIBjDoPa888/r6CgILVr104mk8kZNQEAAEBXENROnjyplStXOqMWAAAAXMThe9Q6duyoQ4cOOaMWAAAAXMThjlp+fr4ee+wxNWvWTH5+frLZbDKZTNqyZYsz6gMAAKi3HAa1JUuWOKMOAAAAXKLaoLZ161b17t1bu3btqnL81ltvrbOiAAAAUENQ27t3r3r37q2dO3dWOT5gwIA6KwoAAAA1BLWxY8dKkubMmXPdJisuLlZycrJOnTols9msuXPnqmnTppWeM3fuXH311VcqLy/X4MGDNWjQIP3yyy/q27evwsLCJEl9+vTRk08+ed3qAgAAMCKH71G7njIyMhQWFqYxY8Zo06ZNSk9P19SpU+3j//73v3X8+HFlZWWptLRUDz/8sPr27asDBw7okUce0bRp05xZLgAAgEs59RZSeXl56tmzpyQpKipKn3/+eaXxrl27Ki0tzf64oqJCPj4+2rdvn/bv368nnnhCY8eO1c8//+zMsgEAAFziinfUzp49q8aNG1/xL87JydGqVasqHWvWrJmCgoIkSWazWYWFhZXG/fz85Ofnp7KyMk2ePFmDBw+W2WxWmzZt1KVLF/3pT3/Sxo0blZqaqkWLFlU7d3BwgHx8vK+4VncUEhLk6hJwDTy5f568Nsnz1+fpPLl/nry2C+rDGi/lMKgdPHhQ48ePV3FxsbKysvTEE09o4cKF6ty5c43nxcTEKCYmptKxxMREWSwWSZLFYlGjRo0uO+/s2bMaO3asevTooVGjRkmS7rrrLvn7+0uSoqOjawxpknTmzDlHy3J7BQWFjp8EQwoJCfLo/nny2jy9d57O0/vnyWu7wFPXWFMAdXjpMzU1Va+99pqaNGmiG2+8UTNnztSMGTNqVUhERIS2bdsmScrNzVW3bt0qjRcXF2vo0KF6/PHH9dxzz9mPT506VZs3b5Ykff755w5DIgAAgCdwGNTOnz+vtm3b2h/fc889Ki0trdVkcXFxys/PV1xcnLKyspSYmChJmjdvnvbs2aPMzEz98MMPysnJUUJCghISEvTDDz8oKSlJGRkZSkhIUGZmpl588cVazQ8AAOBOHF76bNKkiQ4dOiSTySRJ2rhx41W9V+1i/v7+VV62nDRpkiQpPDxcQ4cOrfLc1atX12pOd/Hm5PtcXQIAADAYh0Ft5syZSklJUX5+vrp3766WLVvqlVdecUZtAAAA9ZrDoBYaGqrFixcrICBAVqtVp06dUsuWLZ1RGwADYLcXAFzH4XvU3n77bT399NMKCAjQ2bNn9cwzzygrK8sZtQEAANRrDoNadna2/v73v0v67Ubs7777rtasWVPnhQEAANR3DoNaWVmZfH197Y8bNGhQpwUBAADgNw7fo3bhBuj9+vWTJP3jH//QfffxnhUAAIC65jCoJScn66OPPtKuXbvk4+OjIUOGqE+fPs6oDQAAoF67ont9tm3bVs2bN5fNZpMk7dq1S3feeWedFgYAAFDfOQxqf/nLX7R161a1aNHCfsxkMuntt9+u08IAAADqO4dBbfv27froo4/UsGFDZ9QDAACA/+fwU58tWrSwX/IEAACA8zjcUWvcuLEefvhhde3atdLXdMyZM6dOCwMAAKjvHAa1nj17qmfPns6oBQAAABdxGNQee+wx/ec//9G3336ryMhInThxotIHCwAAAFA3HAa1Dz/8UEuXLlVxcbEyMzMVGxurSZMmqX///lc9WXFxsZKTk3Xq1CmZzWbNnTtXTZs2rfSc0aNH68yZM2rQoIH8/Py0fPlyHTt2TJMnT5bJZFK7du00Y8YMeXk5fHsdAACAW3OYdpYtW6aMjAyZzWY1a9ZM69ev1xtvvFGryTIyMhQWFqa1a9dqwIABSk9Pv+w5x44dU0ZGhlavXq3ly5dL+u39cOPGjdPatWtls9m0ZcuWWs0PAADgThzuqHl5eSkwMND++IYbbqj1blZeXp5GjBghSYqKirosqJ08eVK//vqrnnnmGf36668aOXKkevfurf3796tHjx7287Zv367o6Ohq5wkODpCPj3etanQXISFBri4B14D+uS965948uX+evLYL6sMaL+UwqLVr105r1qxReXm5Dh48qLVr16pDhw4Of3FOTo5WrVpV6VizZs0UFPTbH9lsNquwsLDSeFlZmYYNG6YhQ4bo7NmziouLU3h4uGw2m0wmU7XnXerMmXMO63NnISFBKiio+W8A46J/7oveuTdP758nr+0CT11jTQHUYVCbPn26li5dKj8/P02ZMkV33XWXUlJSHE4aExOjmJiYSscSExNlsVgkSRaLRY0aNao03rx5c8XGxsrHx0fNmjVTx44ddfTo0Uo7eFWdBwAA4IkcXsOcPXu2kpKStG7dOq1fv14pKSmVLoVejYiICG3btk2SlJubq27dulUa37Fjh55//nlJvwWy/Px8tWnTRp06ddLOnTvt53Xv3r1W8wMAALgTh0Htm2++se+CXau4uDjl5+crLi5OWVlZSkxMlCTNmzdPe/bsUa9evdSqVSsNGjRIw4cP14QJE9S0aVOlpKRo8eLFGjx4sMrKytS3b9/rUg8AAICRXdGHCXr37q3WrVvLz8/Pfrw2N2X39/fXokWLLjs+adIk+88vvvjiZeOtW7fWmjVrrno+AAAAd+YwqCUnJzujDgAAAFzC4aXPHj16yNvbW0eOHNEdd9whk8lk/6oMAAAA1B2HQW3VqlVauHCh3nrrLVksFk2fPl0rVqxwRm0AAAD1msOgtn79eq1YsUL+/v4KDg7WO++8o3Xr1jmjNgAAgHrNYVDz8vKSr6+v/bGfn5+8vT37W/8BAACMwOGHCXr06KG5c+fq/Pnz+vjjj5WVlaW77rrLGbUBAADUa9XuqB07dkzSb1+d0bJlS7Vv317vvfeeevXqdUV3JgAAAMC1qXZHbdy4cVq/fr0SExOVnp6u2NhYZ9YFAABQ71Ub1Ewmk+Li4nT48GENGTLksvHafOEtAAAArly1Qe3tt9/WwYMH9eKLL9pv9QQAAADnqTaoPfnkk1q3bp26d+/OF9wCAAC4QLVB7dy5c5o4caI+/fRTvfDCC5eNz5kzp04LAwAAqO+qDWpvvvmmdu7cqby8PHbUAAAAXKDaoHbzzTdrwIAB6tChgzp06HBdJisuLlZycrJOnTols9msuXPnqmnTpvbx3NxcLVu2TJJks9mUl5enDz74QCUlJRo1apRatWolSYqLi9NDDz10XWoCAAAwqmqD2qhRo/S3v/1Nzz77rEwmk/24zWaTyWTSli1brnqyjIwMhYWFacyYMdq0aZPS09M1depU+3hUVJSioqIkScuXL1dERITatm2rnJwcPfXUUxo2bNhVzwkAAOCuqg1qs2fPliStXr36uk2Wl5enESNGSPotlKWnp1f5vB9//FEbNmyw31N03759Onr0qLZs2aKWLVtqypQpCgwMvG51AQAAGFG1QW3Hjh01nnjrrbfWOJ6Tk6NVq1ZVOtasWTMFBQVJksxmswoLC6s8d+XKlRo6dKj9HqPh4eGKiYlRly5dtHTpUr322ms13h0hODhAPj6efT/SkJAgV5eAa0D/3Be9c2+e3D9PXtsF9WGNl6o2qO3cuVOSdPz4cR07dky9evWSt7e3PvvsM/3hD3/QgAEDavzFMTExiomJqXQsMTFRFotFkmSxWNSoUaPLzrNarfrkk080fvx4+7Ho6Gj7c6Ojo+27fdU5c+ZcjePuLiQkSAUFVYdcGB/9c1/0zr15ev88eW0XeOoaawqg1Qa1C1+/kZCQoI0bN9rf9H/27Fk999xztSokIiJC27ZtU3h4uHJzc9WtW7fLnvPNN9+odevWatiwof3Y8OHDNW3aNIWHh+vzzz9X586dazU/AACAO6k2qF3w888/q0mTJvbH/v7+KigoqNVkcXFxSklJUVxcnBo0aKD58+dLkubNm6cHH3xQ4eHhOnr0qFq0aFHpvJkzZ2r27Nlq0KCBmjdv7nBHDQAAwBM4DGr33nuvnnrqKT3wwAOyWq366KOP1K9fv1pN5u/vr0WLFl12fNKkSfaf+/Xrd9nv79y5szIzM2s1JwAAgLtyGNReeOEFbd68WV988YVMJpOGDRum+++/3xm1AQAA1GsOg5ok9e3bV3379q3rWgAAAHARL1cXAAAAgKoR1AAAAAyKoAYAAGBQBDUAAACDIqgBAAAYFEENAADAoK7o6zkAAIDzvTn5PleXABdjRw0AAMCgCGoAAAAGRVADAAAwKIIaAACAQRHUAAAADMolQe2f//ynkpKSqhzLzs7WwIEDNWjQIG3dulWSdPr0aQ0bNkzx8fEaN26czp8/78xyAQAAXMLpQS01NVXz58+X1Wq9bKygoECrV69WZmamVqxYoQULFqi0tFTp6el65JFHtHbtWnXq1ElZWVnOLhsAAMDpnP49ahEREerTp0+VYWvPnj3q2rWrfH195evrq9DQUB06dEh5eXkaNWqUJCkqKkoLFizQ0KFDq50jODhAPj7edbUEQwgJCXJ1CbgG9M990Tv3Rv/cW33sX50FtZycHK1atarSsbS0ND300EPauXNnlecUFRUpKOj3JpjNZhUVFVU6bjabVVhYWOPcZ86cu8bqjS0kJEgFBTX/DWBc9M990Tv3Rv/cn6f2r6YAWmdBLSYmRjExMVd1TmBgoCwWi/2xxWJRUFCQ/XjDhg1lsVjUqFGj610uAACA4RjqU5/h4eHKy8tTSUmJCgsLdeTIEYWFhSkiIkLbtm2TJOXm5qpbt24urhQAAKDuGeJenytXrlRoaKjuv/9+JSQkKD4+XjabTePHj5efn59Gjx6tlJQUZWdnKzg4WPPnz3d1yQAAAHXOZLPZbK4u4nrz1GvYF/A+C/dG/9wXvXNv9M9Yhr38r6t6/vvz+3ts/2p6j5qhLn0CAADgdwQ1AAAAgyKoAQAAGBRBDQAAwKAIagAAAAZFUAMAADAoghoAAIBBEdQAAAAMyhB3JgAAAPXLm5Pvc3UJboEdNQAAAIMiqAEAABgUQQ0AAMCgCGoAAAAGRVADAAAwKIIaAACAQZlsNpvN1UUAAADgcuyoAQAAGBRBDQAAwKAIagAAAAZFUAMAADAoghoAAIBBEdQAAAAMiqAGAABgUAQ1gysrK1NSUpJiY2MVHx+vI0eO6NixY4qLi1N8fLxmzJghq9Xq6jJRjdLSUiUlJWnQoEEaNmyYvv/+e+3evVsxMTGKjY3VkiVLXF0iqvD1118rISFBkqp9vS1ZskR//vOfFRsbqz179riyXFzi4v5dkJaWpoyMDPvj7OxsDRw4UIMGDdLWrVudXSKqcXHvDh48qPj4eCUkJGj48OE6efKkpPrXOx9XF4Cabdu2TeXl5crMzNT27du1cOFClZWVady4cfrjH/+o6dOna8uWLYqOjnZ1qahCdna2AgIClJ2dre+++06zZ8/WyZMntXjxYrVo0UIjR47UgQMH1KlTJ1eXiv+3bNkybdy4Uf7+/pKkOXPmXPZ6u+WWW/TFF18oJydHJ06c0JgxY7Ru3ToXVw7p8v6dPn1akyZN0vfff6/hw4dLkgoKCrR69WqtW7dOJSUlio+P1z333CNfX19Xll7vXdq7l156SdOmTVPHjh2VmZmpZcuWacSIEfWud+yoGVzr1q1VUVEhq9WqoqIi+fj4aP/+/erRo4ckKSoqSjt27HBxlajOt99+q6ioKElSmzZttHfvXpWWlio0NFQmk0mRkZH0z2BCQ0O1ePFi++OqXm95eXmKjIyUyWTSLbfcooqKCp0+fdpVJeMil/bPYrFozJgx6t+/v/3Ynj171LVrV/n6+iooKEihoaE6dOiQK8rFRS7t3YIFC9SxY0dJUkVFhfz8/Opl7whqBhcQEKD//ve/6tevn6ZNm6aEhATZbDaZTCZJktlsVmFhoYurRHU6duyorVu3ymazaffu3SosLFRAQIB9nP4ZT9++feXj8/vFhqpeb0VFRQoMDLQ/hz4ax6X9a9GihW6//fZKzykqKlJQUJD9sdlsVlFRkdNqRNUu7d0NN9wgSfrqq6+0Zs0aDR06tF72jkufBvfWW28pMjJSSUlJOnHihJ588kmVlZXZxy0Wixo1auTCClGTxx9/XEeOHFF8fLwiIiLUoUMHnT9/3j5O/4zPy+v3/5+90K/AwEBZLJZKxy/+jweMjf65jw8//FBLly7VG2+8oaZNm9bL3rGjZnCNGjWy/0PYuHFjlZeXq1OnTtq5c6ckKTc3V927d3dliajB3r17dffddysjI0MPPvigWrVqpQYNGuj48eOy2Wz67LPP6J/BVfV6i4iI0GeffSar1aqi6VpNAAADYUlEQVT//e9/slqtatq0qYsrxZUKDw9XXl6eSkpKVFhYqCNHjigsLMzVZeESGzZs0Jo1a7R69Wq1aNFCUv3sHTtqBjd06FBNmTJF8fHxKisr0/jx49WlSxdNmzZNCxYsUJs2bdS3b19Xl4lqtGzZUn/961/1+uuvKygoSC+99JJOnDihiRMnqqKiQpGRkZddloGxpKSkXPZ68/b2Vvfu3TV48GBZrVZNnz7d1WXiKoSEhCghIUHx8fGy2WwaP368/Pz8XF0WLlJRUaGXXnpJN998s8aMGSNJuvPOOzV27Nh61zuTzWazuboIAAAAXI5LnwAAAAZFUAMAADAoghoAAIBBEdQAAAAMiqAGAABgUAQ1ALjIokWL9OWXX1Y5duE2RIsXL650qxsAqCsENQC4yK5du1RRUVHl2IYNG5xcDYD6ji+8BVBv/fjjj5o4caLOnTsnLy8v3Xvvvdq3b5+mTp2qJUuWKDU1VY0bN1Z+fr4WLlyoAQMG6PDhw/bzKyoqNH78eN12222aNGmScnNztWjRIpWXl+u2227T7NmzFRwc7MIVAnB37KgBqLfeeecd3XvvvXr33XeVnJwsf39/denSRampqWrfvr0kqX379tq8ebM6duxY6VybzaapU6fqpptu0qRJk3T69GnNnz9fK1as0HvvvafIyEi9+uqrrlgWAA/CjhqAeuvuu+/WmDFjdPDgQfXq1UtPPPGEPvnkk0rPCQ8Pr/LczMxMFRYWasuWLZKkr7/+WidOnNCQIUMkSVarVY0bN67T+gF4PoIagHqrW7du2rRpkz755BN9+OGHWr9+/WXPadiwYZXndu3aVZ06dVJqaqoWLVqkiooKRURE6PXXX5cklZSUyGKx1Gn9ADwflz4B1Fvz5s3Thg0b9Nhjj2n69Ok6cOCAvL29q/0wwcU6dOigp59+Wvn5+dq6datuv/127d69W0ePHpUkpaena968eXW9BAAejh01APVWQkKCkpKStH79enl7e2vGjBk6ceKEZsyYoblz5zo839fXVzNnztTkyZP1wQcfKC0tTePGjZPVatWNN96oV155xQmrAODJTDabzebqIgAAAHA5Ln0CAAAYFEENAADAoAhqAAAABkVQAwAAMCiCGgAAgEER1AAAAAyKoAYAAGBQ/wf8a5mMZdZlsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, dyna_res, 'ro', label='dynamic')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(bottom=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - dyna_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125);\n",
    "fig.suptitle('Analytical option values vs. Monte Carlo estimators (dynamic simulation)')\n",
    "plt.savefig('./images/stoch_16.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 American Options\n",
    "#### ([Back to Top](#Table-of-Contents))\n",
    "\n",
    "The valuation of American options is more involved compared to European options. In this case, an **optimal\n",
    "stopping** problem has to be solved to come up with a fair value of the option. The Equation below formulates the\n",
    "valuation of an American option as such a problem. The problem formulation is already based on a discrete\n",
    "time grid for use with numerical simulation. In a sense, it is therefore more correct to speak of an option\n",
    "value given **Bermudan** exercise. For the time interval converging to zero length, the value of the Bermudan\n",
    "option converges to the one of the American option.\n",
    "\n",
    "$$V_{0}=\\sup_{\\tau\\in\\{0,\\Delta t,2\\Delta t,\\dots,T\\}}e^{-rT}\\mathbb{E}_{0}^{Q}[h_{\\tau}(S_{\\tau})]$$\n",
    "\n",
    "The algorithm described in the following is called **Least-Squares Monte Carlo** (LSM) and is from the paper by Longstaff and Schwartz (2001). It can be shown that the value of an American (Bermudan) option at any given date $t$ is given as \n",
    "\n",
    "$$V_t(s)=max\\{h_t(s),C_t(s)\\}$$, where \n",
    "\n",
    "$$C_{t}(s)=\\mathbb{E}_{t}^{Q}[e^{-r\\Delta t}V_{t+\\Delta t}(S_{t+\\Delta t})|S_{t}=s]$$ \n",
    "\n",
    "is the so-called **continuation value** of the option given an index level of $S_t=s$ \n",
    "\n",
    "Consider now that we have simulated $I$ paths of the index level over $M$ time intervals of equal size $\\Delta t$.\n",
    "\n",
    "Define $Y_{t,i}\\equiv e^{-r\\Delta t}V_{t+\\Delta t,i}$ to be the simulated continuation value for path $i$ at time $t$. We cannot use this number directly because it would imply perfect foresight. However, we can use the cross section of all such simulated continuation values to estimate the (expected) continuation value by least-squares regression. \n",
    "\n",
    "Given a set of basis functions $b_d,d=1,\\dots,D$, the continuation value is then given by the regression estimate $\\hat{C}_{t,i}=\\sum_{d=1}^{D}\\alpha_{d,t}^{*}\\cdot b_{d}(S_{t,i})$, where the optimal regression parameters $\\alpha^*$ are the solution of the least-squares problem stated in the equation below:\n",
    "\n",
    "$$\\min_{\\alpha_{1,t},\\dots,\\alpha_{D,t}}\\frac{1}{I}\\sum_{i=1}^{I}(Y_{t,i}-\\sum_{d=1}^{D}\\alpha_{d,t}\\cdot b_{d}(S_{t,i}))^{2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "033296d5-230b-4b35-ae3f-a2a7ed8c8937"
   },
   "outputs": [],
   "source": [
    "# The function gbm_mcs_amer() implements the LSM algorithm for both American call and put options\n",
    "def gbm_mcs_amer(K, option='call'):\n",
    "    ''' Valuation of American option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation by LSM algorithm\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    df = math.exp(-r * dt)\n",
    "    # simulation of index levels\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * math.sqrt(dt) * sn[t])\n",
    "    # case based calculation of payoff\n",
    "    if option == 'call':\n",
    "        h = np.maximum(S - K, 0)\n",
    "    else:\n",
    "        h = np.maximum(K - S, 0)\n",
    "    # LSM algorithm\n",
    "    V = np.copy(h)\n",
    "    for t in range(M - 1, 0, -1):\n",
    "        reg = np.polyfit(S[t], V[t + 1] * df, 7)\n",
    "        C = np.polyval(reg, S[t])\n",
    "        V[t] = np.where(C > h[t], V[t + 1] * df, h[t])\n",
    "    # MCS estimator\n",
    "    C0 = df * np.mean(V[1])\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "18dba6e2-2a7f-4474-bbee-227f354fcbc3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.721705606305352"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "a82c68fc-9820-43a7-8302-3ae0f5a47650"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.609997625418051"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='put')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The European value of an option represents a lower bound to the American option’s value. The difference is generally called the **early exercise premium**. What follows compares European and American option values for the same range of strikes as before to estimate the early exercise premium, this time with puts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "euro_res = []\n",
    "amer_res = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_list = np.arange(80., 120.1, 5.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "for K in k_list:\n",
    "    euro_res.append(gbm_mcs_dyna(K, 'put'))\n",
    "    amer_res.append(gbm_mcs_amer(K, 'put'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "2c4a0f35-5a41-416b-aa39-53d78d1cc366"
   },
   "outputs": [],
   "source": [
    "euro_res = np.array(euro_res)\n",
    "amer_res = np.array(amer_res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure below shows that for the range of strikes chosen the early exercise premium can rise to up to 10%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "uuid": "6304932d-114f-43b1-ae59-4b0ad2de33fc"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10, 6))\n",
    "ax1.plot(k_list, euro_res, 'b', label='European put')\n",
    "ax1.plot(k_list, amer_res, 'ro', label='American put')\n",
    "ax1.set_ylabel('call option value')\n",
    "ax1.legend(loc=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (amer_res - euro_res) / euro_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('early exercise premium in %')\n",
    "ax2.set_xlim(left=75, right=125);\n",
    "fig.suptitle('European vs. American Monte Carlo estimators')\n",
    "plt.savefig('./images/stoch_17.png');"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}