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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "import matplotlib.pylab as plt\n",
      "from scipy.stats import norm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Week 7"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This weeks takes a first look at the pricing of derivatives using Monte Carlo methods. An example of a derivative is a European Call Option. This is a contract which gives the holder of the contract the right but not the obligation to purchase the underlying (e.g. a stock or an index) at a set price $K$ (called the strike) at the time of maturity $T$ of the contract. \n",
      "\n",
      "At maturity the derivative results in a payoff, which is a general function of the underyling. E.g. for a European Call of a stock the payoff function is the difference of the underlying price and the strike, giving $S(T) - K$. However, you would not exercise the option if the stock price is lower than the strike. Thefore the payoff is given by $\\max\\big(S(T) - K, 0\\big)$.\n",
      "\n",
      "The question we now ask is: given the payoff of a derivative how do we determine the price of this derivative at an earlier time $t$? For this we have to make some assumptions regarding the statistical model of the underlying."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_priceEuropeanCallMC and related files"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now consider the Black-Scholes model. The underlying is a stock and this stock is modelled using geometric Brownian motion. The price of the derivative is given by the expectation value of the payoff function, $e^{-rT}\\mathbb{E}\\big[\\textrm{payoff}\\big]$, where the averageing is over all possible paths generated from the geometric Brownian motion model. A discount factor $e^{-rT}$ is included to account for the risk premium.\n",
      "\n",
      "In the Monte Carlo approach we sample over many paths to determine the price of the derivative. The Black-Scholes model has the advantage that it can be solved analytically, so we can compare the MC approach to the exact result. The exact price $C$ of a European Call Option in the Black-Scholes model is given by:\n",
      "\n",
      "$$C = S_0 \\Phi(d_+) - e^{-rT}K\\Phi(d_-)$$\n",
      "\n",
      "where\n",
      "\n",
      "$$d_{\\pm} = \\frac{1}{\\sigma \\sqrt{T}} \\log\\left(\\frac{S_0}{e^{-rT}K}\\right) \\pm \\frac{1}{2}\\sigma \\sqrt{T}$$\n",
      "\n",
      "Here $\\Phi$ is the CDF of the normal distribution. The remaining parameter are explained in in the python function below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCall(S0, K, r, T, sigma, *args):\n",
      "    \"\"\"\n",
      "    Price of a European call option in the Black-Scholes model\n",
      "    \n",
      "    INPUT:\n",
      "       S0 : Initial value of the underlying asset\n",
      "        K : Strike \n",
      "        r : Risk-free interest rate \n",
      "        T : Time to expiry \n",
      "    sigma : Volatility \n",
      "    *args : extra arguments can be passed, but are not used\n",
      "\n",
      "    OUTPUT:\n",
      "    price : Price of the option in the Black-Scholes model  \n",
      "    \"\"\"\n",
      "    \n",
      "    discountedStrike = np.exp(-r * T) * K\n",
      "    totalVolatility = sigma * np.sqrt(T)\n",
      "    \n",
      "    d_minus = np.log(S0 / discountedStrike) / totalVolatility - .5 * totalVolatility\n",
      "    d_plus = d_minus + totalVolatility\n",
      "    \n",
      "    # The extra zero in the return is the variance in price, which is of course zero. This way the\n",
      "    # function behaves similar to the Monte Carlo methods defined below which have non-zero variance\n",
      "    return S0 * norm.cdf(d_plus) - discountedStrike * norm.cdf(d_minus), 0."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "priceEuropeanCall(100, 90, .05, 2., .4)[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "30.761890179053708"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To illustrate the pricing scheme we consider the Call Option price as a function of time to maturity T, while keeping stock price and all other parameters fixed. We consider this for three strike prices: in the money ($S(T) > K$), at the money ($S(T) = K$) and out of the money ($S(T) < K$)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def example(pricingMethod, *args):\n",
      "    S0 = 100\n",
      "    K = np.array([75, 90, 100, 110, 125])\n",
      "    sigma = .4\n",
      "    r = .05\n",
      "    # function does not evaluate at T = 0, so we get as close as possible\n",
      "    T = np.linspace(.5, 1e-15, 75) \n",
      "    price = dict((k, np.array([pricingMethod(100, k, .05, t, sigma, *args)[0] for t in T])) for k in K)\n",
      "\n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    for k in K:\n",
      "        ax.plot(T, price[k], label='K='+str(k))\n",
      "    ax.set_xlabel('Time to maturity')\n",
      "    ax.set_ylabel('C')\n",
      "    ax.set_title('Price of a Call Option over time, keeping underlying fixed')\n",
      "    ax.invert_xaxis()\n",
      "    ax.set_ylim(0, 50)\n",
      "    plt.legend(loc='best')\n",
      "    plt.show()\n",
      "\n",
      "example(priceEuropeanCall)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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BY6x9aeSqBE3SxH/HN3vbyxtp7LaXKpVKHDZSKBSorKy86eXai/cZMMbaF6KW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\npJsERbpF110qRbSbmxgS0a6uiHFzQ7S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rs/nPXKFQoKKiAgDg7e0NpVKJo0ePAgA2bdqE\nhISEZtWvsrISHh4e8PLyQkFBAfbu3WtzmQAQFBSEixcvQq/X49tvv7UrnCzn4eLigvHjx+Pxxx83\n22/BmL04DFi7ZvxhlEgkNvtNpzEdlslk2Lp1K5YsWYJ+/fqhf//+SEtLs5r/jBkz8K9//QsDBw7E\n1atXkZycjH/+85+Ij4/HmTNn8NJLLzVar4aW37dvX/Tv3x/du3fHrFmzMHz4cPHxhQsX4p577hF3\nIK9atQp/+ctfMGzYMISGhja6HOOwab3T09MBADNnzoRUKsW4ceNs1pmxxvChpYx1EmvWrEFlZaXN\nnd6M3QjvM2CsE5gyZQrS09ORkpLS1lVhHRS3DBhjjPE+A8YYYxwGjDHGwGHAGGMMHAaMMcbAYcAY\nYwwcBowxxgD8f6dhwwmry1hIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa442ba8>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that as the option contract reaches maturity its price starts to converge towards the payoff, $\\max(S(T)-K, 0)$. All contracts that are out or at of the money ($K \\leq S$ ) become worthless, while the options that are in the money ($K > S$) converge towards the difference $(S(T) - K)$.\n",
      "\n",
      "Next we implement a Monte Carlo Scheme to evaluate the same price."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCallMC(S0,K,r,T,sigma,M):\n",
      "    \"\"\"\n",
      "    Price of a European call option in the Black-Scholes model\n",
      "    \n",
      "    INPUT:\n",
      "       S0 : Initial value of the underlying asset\n",
      "        K : Strike \n",
      "        r : Risk-free interest rate \n",
      "        T : Time to expiry \n",
      "    sigma : Volatility \n",
      "        M : Number of simulations\n",
      " \n",
      "\n",
      "    OUTPUT:\n",
      "     price_MC : MC estimate of the price of the option in the Black-Scholes model  \n",
      "     stdev_MC : MC estimate of the standard deviation  \n",
      "    \"\"\"  \n",
      "    \n",
      "    # generate M samples from N(0,1)\n",
      "    X = np.random.randn(M)\n",
      "    \n",
      "    \n",
      "    # simulate M trajectories in one step\n",
      "    ST = S0 * np.exp((r - 0.5 * sigma**2) * T + sigma * np.sqrt(T) * X)\n",
      "    # define payoff\n",
      "    payoff = np.where(ST < K, 0, ST - K) # acts as max(ST-K, 0) \n",
      "    \n",
      "    # MC estimate\n",
      "    discountFactor = np.exp(-r*T)\n",
      "    \n",
      "    price_MC = discountFactor*mean(payoff)\n",
      "    stdev_MC = discountFactor*std(payoff)/sqrt(M)\n",
      "    return price_MC, stdev_MC"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As a comparison with the exact case:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "price_exact = priceEuropeanCall(100, 75, .05, .5, .4)[0]\n",
      "print \"Exact price:\", price_exact\n",
      "for M in [1e2, 1e4, 1e6]:\n",
      "    price_mc, std_mc = priceEuropeanCallMC(100, 75,.05, .5,.4, M)\n",
      "    print \"M =\", M\n",
      "    print \"Estimated price:\", price_mc\n",
      "    print \"Absolute error in price:\", np.abs(price_mc - price_exact)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exact price: 28.4830082974\n",
        "M ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 100.0\n",
        "Estimated price: 25.1554729591\n",
        "Absolute error in price: 3.32753533837\n",
        "M = 10000.0\n",
        "Estimated price: 28.4783359869\n",
        "Absolute error in price: 0.00467231049649\n",
        "M ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1000000.0\n",
        "Estimated price: 28.5066855456\n",
        "Absolute error in price: 0.0236772481509\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The variance of the Monte Carlo method is nicely visualized looking at the same example as before."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "example(priceEuropeanCall)\n",
      "example(priceEuropeanCallMC, 1e3)\n",
      "example(priceEuropeanCallMC, 1e5)  \n",
      "## Warning: this example gets really slow for increased M, \n",
      "## as it is not optimized for evaluating for multiple maturities"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BY6x9aeSqBE3SxH/HN3vbyxtp7LaXKpVKHDZSKBSorKy86eXai/cZMMbaF6KW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\nYwwcBowxxgD8f6dhwwmry1hIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa4d5940>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GjLHKhUg1rxLKHvbywYMHGDNmjMp3q7BhL3PPy55fkUNicjBgjLH/lHXYy8IU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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9e140b8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Nvv76a2zfvh3Z2dnS7SaT6awDZJctW4YlS5ac87mPHDmCOXPmSP+3XvaysLAQ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\nj1+d6wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa9ce358>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "The Greeks"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The European Call Option depends on multiple variables such as the strike, underlying price, volatility and interest rate. To characterize the sensitivity of the Call on these variables we look at the derivative of the Call option with respect to these variables. These sensitivities are called collectively The Greeks.\n",
      "\n",
      "Here we look at vega, which is the sensitivity of the Call on the volatility: $\\frac{\\partial C}{\\partial \\sigma}$. In the Black-Scholes model it has an exact expression given by: $\\textrm{vega} = S_0\\phi(d_+)\\sqrt{T}$, where this time $\\phi$ is the PDF of a standard normal distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def vegaEuropeanCall(S0,K,r,T,sigma):\n",
      "    \"\"\"\n",
      "    Vega of a European call option\n",
      "    \n",
      "    INPUT:\n",
      "       S0 : Initial value of the underlying asset\n",
      "        K : Strike \n",
      "        r : Risk-free interest rate \n",
      "        T : Time to expiry \n",
      "    sigma : Volatility \n",
      "\n",
      "    OUTPUT:\n",
      "     vega : Vega of the option in the Black-Scholes model  \n",
      "    \"\"\"\n",
      "    discountedStrike = np.exp(-r * T) * K\n",
      "    totalVolatility = sigma * np.sqrt(T)\n",
      "    d_plus = np.log(S0 / discountedStrike) / totalVolatility + .5 * totalVolatility\n",
      "    return S0 * np.sqrt(T) * norm.pdf(d_plus)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course, we can also determine the sensitivity numerically."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def numericalDerivative(f, x0, h):\n",
      "    \"\"\"\n",
      "    Numerical estimate of the derivative of f at x0\n",
      "\n",
      "    INPUT:\n",
      "             f : Handle to the function whose derivative is being calculated\n",
      "            x0 : Point at which the derivative is calculated\n",
      "             h : Parameter for divided differences (1e-5 - 1e-6)\n",
      "\n",
      "    OUTPUT:\n",
      "    derivative : Value of the derivative of f at x0  \n",
      "   \"\"\"      \n",
      "    \n",
      "    if x0 == 0:\n",
      "        derivative = (f(h) - f(-h))/(2 * h)\n",
      "    else:\n",
      "        derivative = (f(x0 * (1 + h))-f(x0 * (1 - h)))/(2 * x0 * h);\n",
      "    return derivative "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's compare these two methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def comparison():\n",
      "    \n",
      "    S0    = 100  # initial price\n",
      "    K     = 90   # strike\n",
      "    r     = 0.05 # interest rate\n",
      "    T     = 2    # maturity \n",
      "    sigma = 0.4  # volatility\n",
      "\n",
      "    ## Numerical estimate of vega\n",
      "    \n",
      "    # pricing function\n",
      "    def fPrice(sigma):\n",
      "        return priceEuropeanCall(S0,K,r,T,sigma)[0]\n",
      "    # good balance between rounding and truncation errors in the numerical derivative\n",
      "    h = 1e-5;\n",
      "\n",
      "    numericalVega = numericalDerivative(fPrice,sigma,h)\n",
      "\n",
      "    ## Vega of a European call option\n",
      "    vega = vegaEuropeanCall(S0,K,r,T,sigma)\n",
      "    return numericalVega, vega\n",
      "print comparison()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(45.797511901035641, 45.797511899711402)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "vega plays an important role in obtaining an estimate for the volatility."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Implied Volatility"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The volatility $\\sigma$ is an input into the pricing methods of the Black-Scholes formulae. One can use historical data to measure this volatiltiy, but it turns out that this leads to a poor estimate of the price of options. The main reason for this is that the Black-Scholes model does not adequately model the financial markets. \n",
      "\n",
      "Instead, the volatility is obtained by looking at the price of the derivatives on the market and obtain an implied volatility such that the pricing scheme reproduces the market price. We therefore need to invert the Black-Scholes formula (read from the market) to obtain the volatility. There is, however, no exact expression for the inverse of the BS formula, so we need to resort to a numerical scheme.\n",
      "\n",
      "With the use of a pricing model such as Black-Scholes we can use the Newton-Raphson method to find an estimate for the implied volatility. The idea is simple: we have a function available for the price, which depends on the volatiltiy. We call this `fprice(sigma)`. Furthermore we have a price for the option which is taken from the market, which wel call `market_price`. We need to find a `sigma_implied` such that this `market_price` is produced by `fprice(sigma_implied)`. In other words, we are looking for a solution of `fprice(sigma) - market_price = 0`. The Newton-Raphson method is method which finds a root of a function and makes use of the derivative of the function `fprice`, which corresponds to the Greek vega. It is implemented below"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def impliedVolatility(fPrice, fVega, price):\n",
      "    \"\"\"\n",
      "    Implied volatility of a derivative\n",
      "\n",
      "    INPUT:\n",
      "    fPrice : Handle to the function that gives the price of the derivative\n",
      "     fVega : Handle to the function that gives the vega of the derivative\n",
      "     price : The price of the derivative\n",
      "\n",
      "    OUTPUT:\n",
      "     sigma : Implied volatility         \n",
      "    \"\"\"\n",
      "\n",
      "    TOLABS  = 1e-6\n",
      "    MAXITER = 100\n",
      "    \n",
      "    sigma  = 0.3          # intial estimate   \n",
      "    dSigma = 10 * TOLABS  # enter loop for the first time\n",
      "    nIter  = 0\n",
      "    while ((nIter < MAXITER) & (abs(dSigma) > TOLABS)):\n",
      "        nIter = nIter + 1\n",
      "        # Newton-Raphson method\n",
      "        dSigma = (fPrice(sigma)-price)/fVega(sigma)\n",
      "        sigma = sigma - dSigma\n",
      "    \n",
      "    if (nIter == MAXITER):\n",
      "        warning('Newton-Raphson not converged')\n",
      "    return sigma\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def impliedVol(price):\n",
      "    S0 = 100\n",
      "    K = 90\n",
      "    r = 0.05\n",
      "    T = 2\n",
      "    def fPrice(sigma):\n",
      "        return priceEuropeanCall(S0,K,r,T,sigma)[0]\n",
      "    def fVega(sigma):\n",
      "        return vegaEuropeanCall(S0,K,r,T,sigma)\n",
      "    impliedSigma  = impliedVolatility(fPrice,fVega,price)\n",
      "    impliedPrice = priceEuropeanCall(S0,K,r,T,impliedSigma)[0]  # should be equal to price\n",
      "    return impliedSigma, impliedPrice, impliedPrice - price\n",
      "\n",
      "for p in [19.8701, 26.24, 21]:\n",
      "    imp_vol, imp_price, error = impliedVol(p)\n",
      "    print \"Implied volatility:\", imp_vol\n",
      "    print \"Price from implied volatility\", imp_price\n",
      "    print \"Absolute error in pricing:\", np.abs(error)\n",
      "    print"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Implied volatility: 0.137398425806\n",
        "Price from implied volatility 19.8701\n",
        "Absolute error in pricing: 7.1054273576e-15\n",
        "\n",
        "Implied volatility: 0.299996208706\n",
        "Price from implied volatility 26.24\n",
        "Absolute error in pricing: 3.5527136788e-15\n",
        "\n",
        "Implied volatility: 0.172202727906\n",
        "Price from implied volatility 21.0\n",
        "Absolute error in pricing: 1.84741111298e-13\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Variance Reduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The probabilistic nature of Monte Carlo methods is the source of the relatively large variance of the price estimate. The most straightforward way to reduce the variance in the price estimate of the Monte Carlo approach is to increase the number of simulations $M$ of the MC calculation. This can be computationally expensive, since the variance is proportional to only $1/\\sqrt(M)$.\n",
      "\n",
      "Variance reduction are methods that can be used to circumvent or reduce this large increase in computational cost, while still reducing the variance of the price estimate. These reduction methods can be quite powerful, but are not universal as they depend on properties of the sampling distribution and the target price estimate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Antithetic variates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first method of variance reduction are so-called *antithetic variates*. This makes use of symmetry properties of the sampling distribution. The idea is that each drawn sample is re-used to generate another sample. The estimate of the price is then appropriately averaged over these two sample points. This technique can be applied for instance if the underlying sampling distribution is symmetric (such as a normal distribution) or is computed from a symmetric distribution (such as the lognormal distribution)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCallMC_antithetic(S0, K, r, T, sigma, M):\n",
      "    \"\"\"\n",
      "    Price of a European call option in the Black-Scholes model with antithetic variates\n",
      "\n",
      "    INPUT:\n",
      "        S0 : Initial value of the underlying asset\n",
      "         K : Strike \n",
      "         r : Risk-free interest rate \n",
      "         T : Time to expiry \n",
      "     sigma : Volatility \n",
      "         M : Number of simulations\n",
      " \n",
      "\n",
      "    OUTPUT:\n",
      "    price_MC : MC estimate of the price of the option in the Black-Scholes model  \n",
      "    stdev_MC : MC estimate of the standard deviation            \n",
      "    \"\"\"\n",
      "    ## Generate M samples from N(0,1)\n",
      "    X = np.random.randn(M) \n",
      "    \n",
      "    ## Simulate M trajectories in one step\n",
      "    ST_plus  = S0*np.exp((r-0.5*sigma**2)*T + sigma*np.sqrt(T)*X);\n",
      "    ST_minus = S0*np.exp((r-0.5*sigma**2)*T - sigma*np.sqrt(T)*X);\n",
      "    \n",
      "    ## Compute payoffs\n",
      "    \n",
      "    payoff_plus  = np.where(ST_plus < K, 0, ST_plus -K)\n",
      "    payoff_minus = np.where(ST_minus < K, 0, ST_minus -K)\n",
      "    \n",
      "    # average payoff\n",
      "    payoff       = 0.5*(payoff_plus+payoff_minus)\n",
      "    \n",
      "    ## MC estimate of the price and the error of the option\n",
      "    discountFactor = np.exp(-r*T)\n",
      "    price_MC = discountFactor*np.mean(payoff)\n",
      "    stdev_MC = discountFactor*np.std(payoff)/np.sqrt(M)\n",
      "    return price_MC, stdev_MC\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We define a simple script to compare the different methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def estimatePrice(method):\n",
      "    S0 = 100\n",
      "    K = 90\n",
      "    r = 0.05\n",
      "    T = 2\n",
      "    sigma = 0.2\n",
      "    M = 1e4 \n",
      "    price_method, stdev_method = method(S0, K, r, T, sigma, M)\n",
      "    price_exact = priceEuropeanCall(S0, K, r, T, sigma)[0]\n",
      "    error = (price_method - price_exact) / price_exact  * 100\n",
      "    return price_method, stdev_method, error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For instance, the MC method gives:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Price estimate, std answer, true error:\", estimatePrice(priceEuropeanCallMC)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Price estimate, std answer, true error: (21.969736663526227, 0.25035997164594082, -0.28884969147827361)\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As for the antithetic variaties approach:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Price estimate, std answer, true error:\", estimatePrice(priceEuropeanCallMC_antithetic)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Price estimate, std answer, true error: (22.178128255956839, 0.10295867437147282, 0.65694978323176312)\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Importance Sampling"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In importance sampling we average the price by making use of a different distribution from which samples are drawn, which then typically has a lower variance. Because a different distribution is chosen, we also need to redefine the object over which is averaged."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCallMC_importanceSampling(S0,K,r,T,sigma,M):\n",
      "    \"\"\"\n",
      "    Price of a European call option in the Black-Scholes model with importance sampling\n",
      "\n",
      "    INPUT:\n",
      "       S0 : Initial value of the underlying asset\n",
      "        K : Strike \n",
      "        r : Risk-free interest rate \n",
      "        T : Time to expiry \n",
      "    sigma : Volatility\n",
      "        M : Number of simulations\n",
      " \n",
      "\n",
      "    OUTPUT:\n",
      "     price_MC : MC estimate of the price of the option in the Black-Scholes model  \n",
      "     stdev_MC : MC estimate of the standard deviation  \n",
      "    \"\"\"\n",
      "    \n",
      "    ## Generate M samples from N(0,1)\n",
      "    X = np.random.randn(M)\n",
      "    \n",
      "    ## Simulate M trajectories in one step\n",
      "    \n",
      "    mu = np.log( K / S0) / T\n",
      "    ST = S0 * np.exp((mu - 0.5 * sigma**2) * T + sigma * np.sqrt(T) * X)\n",
      "    correctionFactor = norm.pdf(X + (mu - r) * np.sqrt(T) / sigma) / norm.pdf(X)\n",
      "    \n",
      "    ## Compute the payoffs\n",
      "    payoff  = np.where(ST < K, 0, ST - K)\n",
      "    correctedPayoff = payoff * correctionFactor\n",
      "    \n",
      "    ## MC estimate of the price and the error of the option\n",
      "    discountFactor = exp(-r * T)\n",
      "    \n",
      "    price_MC = discountFactor * np.mean(correctedPayoff)\n",
      "    stdev_MC = discountFactor * np.std(correctedPayoff) / np.sqrt(M)\n",
      "    return price_MC, stdev_MC\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Price estimate, std answer, error:\", estimatePrice(priceEuropeanCallMC_importanceSampling)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Price estimate, std answer, error: (22.252117395735443, 0.66676848771762853, 0.99275454733303992)\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that if $\\log( K / S0) / T - r$ is approximately  zero, then there is no noticable gain."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Stratified sampling"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In stratified sampling we partition the source distribution into equal-sized 'bins', i.e. each bin contributes an equal amount of probability to the overall distribution. We then sample from each bin individually, thereby reducing the overall variance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCallMC_stratifiedSampling(S0,K,r,T,sigma,M,nStrata):\n",
      "    \"\"\"\n",
      "    Price of a European call option in the Black-Scholes model with stratified sampling\n",
      "\n",
      "    INPUT:\n",
      "       S0 : Initial value of the underlying asset\n",
      "        K : Strike \n",
      "        r : Risk-free interest rate \n",
      "        T : Time to expiry \n",
      "    sigma : Volatility \n",
      "        M : Number of simulations\n",
      "  nStrata : Number of strata per simulation \n",
      "\n",
      "    OUTPUT:\n",
      "     price_MC : MC estimate of the price of the option in the Black-Scholes model  \n",
      "     stdev_MC : MC estimate of the standard deviation  \n",
      "    \"\"\"\n",
      "    ## Generate M x nStrata samples from U(0,1)\n",
      "    U = np.random.rand(M,nStrata)\n",
      "    # delimit the strata\n",
      "    strataBorders, strataSize = np.linspace(0, 1, nStrata + 1, retstep=True)\n",
      "    \n",
      "    # stratify U[0,1]\n",
      "    V = np.tile(strataBorders[:-1], (M, 1)) + U * strataSize\n",
      "    \n",
      "    # stratified N(0,1)\n",
      "    X = norm.ppf(V) # this is the inverse CDF, i.e. norminv in Matlab\n",
      "    \n",
      "    ## Simulate M trajectories in one step\n",
      "    ST  = S0 * np.exp((r-0.5*sigma**2) * T + sigma * np.sqrt(T) * X)\n",
      "    \n",
      "    ## Compute the payoffs\n",
      "    \n",
      "    payoff  = np.where(ST < K, 0, ST - K)\n",
      "    \n",
      "    payoff  = np.mean(payoff, axis=1)  # average payoff, using one sample per strata. \n",
      "    \n",
      "    ## MC estimate of the price and the error of the option\n",
      "    discountFactor = exp(-r*T)\n",
      "    \n",
      "    price_MC = discountFactor * np.mean(payoff)\n",
      "    stdev_MC = discountFactor * np.std(payoff) / np.sqrt(M)\n",
      "    return price_MC, stdev_MC\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The stratified sampling method takes an extra parameter `nStrata` to specify the number of bins."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def priceEuropeanCallMC_stratifiedSampling_fixed_nStrata(S0,K,r,T,sigma,M):\n",
      "    nStrata = 5\n",
      "    M_ = np.int(np.round(M / nStrata))\n",
      "    return priceEuropeanCallMC_stratifiedSampling(S0,K,r,T,sigma,M_,nStrata)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Price estimate, std answer, error:\", estimatePrice(priceEuropeanCallMC_stratifiedSampling_fixed_nStrata)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Price estimate, std answer, error: (22.119720908938604, 0.099798431114983113, 0.3918640497588658)\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we compare all the different methods:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "methodlist = [priceEuropeanCall, priceEuropeanCallMC, priceEuropeanCallMC_antithetic,\n",
      "              priceEuropeanCallMC_importanceSampling, priceEuropeanCallMC_stratifiedSampling_fixed_nStrata]\n",
      "M = 1e2\n",
      "for method in methodlist:\n",
      "    print \"Method:\", method.__name__\n",
      "    example(method, 1e2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method: priceEuropeanCall\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BY6x9aeSqBE3SxH/HN3vbyxtp7LaXKpVKHDZSKBSorKy86eXai/cZMMbaF6KW\nKU1kvO3lH3/8gQULFrT4y2rstpeWjxkfb81bYnIYMMaYwc3e9rIxjd32Mi4uDlqtFpcvXzZ73LKF\n4kgcBowxZuJmbntZV1cHtVoNvV4PjUYDtVot7sxt7LaXHh4emDp1Kl566SVUV1fj6NGj2LlzJ+bM\nmdN6L5zaqXZcNcbYTWiv3+2oqCg6cOCAOJyenk7h4eH0/PPP2z2PUaNGkUQiIalUShKJhCQSCR06\ndEh8/O2336agoCDy8vKihx9+mDQajfhYSUkJTZ48mTw8PCgyMpI2b97c6LIaWo/NXb98aCljrFXx\nd7tl8OUoGGOMtTgOA8YYYxwGjDHGOAwYY4yBw4Axxhg4DBhjjIHDgDHGGDgMGGOMgcOAMcYYOAwY\nYwyA4297efbsWYwfPx4BAQGQSq1/evm2l4wx1g44+raXcrkcM2bMwIYNG2w+t61ve8k3t2GMMQMi\nwocffogXXngB33//fZNve2m87LWrq6vVY3FxcYiLizO7TLVRVVUVvvnmG5w7dw7u7u4YNmwY7r//\nfmzatKnB2162NA4DxhgzcORtLxtz6dIlvu0lY4yZkrTQDyAlJDRtegff9rIx7eG2lxwGjLF2pak/\n4i3FeNvLlStXYsGCBQ1u23cEvu0lY4y1I4687WVj2sNtL7llwBhjJoy3vRw1ahSefvppvP3221Cp\nVHY9t66uDjqdzuy2ly4uLuL+BrVaDY1GAwCora0FALi4uJjd9vLjjz/GyZMnsXPnTqSlpTnmRdrA\nLQPGGLMQHh6OlJQUbN26FcuWLbP7eWPHjoW7uzt++uknLFy4EO7u7uJ5ChkZGXB3d0fv3r0hkUjg\n5uaGHj16iM9dt24dampqEBgYiNmzZ+ODDz4we9zR+LaXjLFWxd/tlsG3vWSMMdbiOAwYY4xxGDDG\nGOMwYIwxBg4DxhhjcGAYqNVqDB48GP369UPPnj2xdOlSAMJlWseOHYu4uDiMGzfO4ad5M8YYuzGH\nHlpaXV0Nd3d3aLVaDB8+HGvWrMGOHTvg7++PpKQkrF69GqWlpTbP4OPDzxjrnPi73TI61KGl7u7u\nAACNRgOdTgelUokdO3YgMTERAJCYmIht27Y5sgqMMcbs4NAw0Ov16NevH4KCgjB69Gj06tULBQUF\nCAoKAiBcB6SgoMCRVWCMMWYHh4aBVCrFqVOnkJOTg8OHD+PgwYNmj5veWYgxxtqSo297mZycjEGD\nBsHb2xvf/+UnAAAgAElEQVTh4eFYsmQJdDqd+HhCQgLc3NzEC+C15qUogFa6UJ23tzfuu+8+/Prr\nrwgKCkJ+fj6Cg4ORl5eHwMDABp+3YsUKsT8hIQEJbXRpW8ZY52d528tnnnkGe/bswZAhQ+yeR79+\n/TBjxgwsWbLE6o9uTU0N1q5di8GDB6OwsBCTJk3CmjVrsGTJEnH577//Ph5++OEm1Ts1NbVFboLj\nsDAoLi6Gs7MzfHx8UFNTgx9++AHLly/HpEmTkJycjCVLliA5ORmTJ09ucB6mYcAYY47myNtePvbY\nY2J/aGgoZs2aZbW1pDk7fi3/KL/88stNngfgwM1EeXl5GDNmDPr164fBgwdj4sSJuOuuu/Dcc8/h\nhx9+QFxcHFJSUvDcc885qgqMMdYk69atw/Lly5GSkmIWBD4+PlAqlTbLm2++2axlHTp0yOp+BUuX\nLkVAQACGDx+OQ4cO3dRraSqHtQz69OmDkydPWo339fXF/v37HbVYxlgHlypJbZH5JFBCk6Zvzdte\nfvLJJzh58iQ++eQTcdzq1avRq1cvyOVybN68GRMnTsSpU6cQExPTostuCN/chjHWrjT1R7yltNZt\nL7dt24bnn38eBw4cgK+vrzj+jjvuEPvnzp2LzZs3Y8+ePXjyyScdUg9LfDkKxhgzcPRtL7/77jss\nXLgQu3btQq9evRzxEpqtXbcMRo0CvLyaVry9ATc3gI9YZYw1h6Nue5mSkoJZs2Zh+/btGDRokNnz\nysvL8dNPP2HUqFFwdnbGl19+iSNHjuC9995zxEu0qV3f6Sw1lVBRAVRUAOXlQGUlzIaN/ZbTaDQN\nB4XpsELR8GNeXoCHByDlthNjLaq9Xo4iOjoaGzZswJgxYwAIt6kcOXIk5syZg9dee82ueSQkJODw\n4cNmrzE1NRUjR47EmDFjcPToUbi4uIjTjxw5Ert370ZRURHuu+8+XLx4EU5OTujRowdWrlyJu+66\nq8FltfTlKNp1GDS3anV1QihYBoitEDGdxviYcVxNDeDpaTsoGgsRy8c8PTlUGDNqr2HQ0XAYtCKt\nFlCpGm+FWAaIreCprhZaGfaESGPholAATk5tukoYu2nt4bvdGXAYdEA6nRAqTQ0Ry+BRqQB39+a3\nUExDxbld7y1inVln+m63JQ6DW5hebx0q9uxDsQyeykrA1bXpIWKryGRtvVZYR8Pf7ZbBYcBuGhFQ\nVdVwqDS0D8XWNM7OTT/iy1ZxdeUjwG4V/N1uGRwGrN0gAtRq2yFiGSC2duibDmu1to/ysjXc2D4V\n3q/S/vF3u2VwGLBOSaOxDozGjgizNY2xuLk1HCgNdW1Nx4cWOwZ/t1tGS4cB70Zk7YJcDvj5CeVm\nmG4Ca6hlYhyfm2seKqbTVlbWHwVmbHGYtj4aChbLYhzv6ck77Y2USiXfx6QFKJXKFp0ftwwYa4Dx\nKDDTADHtWo5v7DGVCnBxsR0Ynp72jTcOe3pyuLCG8WYixtoxIqGlYRoUtopp+FiOM32sqkoIF9OA\nMA0K0357i4cHB0xnwGHA2C3EGC6WQWHsVlXVD5uOsxw2HVdVJYSBMRiMXWO50bCHh3AeTEPDHDSt\ng8OAMXZTiIDa2vpwMAaEMTCM/baGLUt1tXm3qko4yssYDu7uDRc3N+t+025DxdW1vnsrB0+Lh8Gf\nf/6JgoICDB8+3Gz80aNHERISgtjY2ObV1N6KcRgw1mkQCUeMVVebB4VlqamxPWzatVXUavNhJyfz\ncLDsNy0uLvXdG/XL5fXDpsU43vRxuVworX1EWosfTbR48WK88cYbVuO9vLywePFi7Ny5s8kLY4zd\nmiSS+h/JFj4IxgqRcLFKtbo+JIz9puNqa83H1dbWj6utFXb+W46zVTQa62HjOI1GaKVYhoRpWFgO\n2+q39byGHmuuBsOgoKAAffv2tRrft29fpKenN3+JjDHmQBJJ/Q+ml1fb1sUYTKYBUVsrjLMMEstx\nlqFi7FZVAaWlth+rrW1+XRsMg8bu+alWq5u/RMYYu0WYBlNrLrM5GtyaNWjQIHz00UdW49evX4+B\nAwc2b2mMMcbapQZ3IOfn52PKlCmQy+Xij/+vv/6K2tpafPvttwgJCXFsxXgHMmOMNZlDDi0lIhw8\neBBnz56FRCJBr169xFvCORqHAWOMNR2fZ8AYY6zZv518TUbGGGMcBowxxjgMGGOMgcOAMcYYOAwY\nY4yBw4Axxhg4DBhjjIHDgDHGGDgMGGOMgcOAMcYYOAwYY4yBw4AxxhgcHAbZ2dkYPXo0evXqhd69\ne+Pdd98FAJSUlGDs2LGIi4vDuHHjGr2RDmOMMcdz6FVL8/PzkZ+fj379+kGlUmHgwIHYtm0bNm7c\nCH9/fyQlJWH16tUoLS3FqlWrzCvGVy1ljLEma5dXLQ0ODka/fv0AAJ6enujRowdyc3OxY8cOJCYm\nAgASExOxbds2R1aDMcbYDbTa/QwyMjIwatQonD17FhERESgtLQUg3EDH19dXHBYrxi0DxhhrsnbZ\nMjBSqVSYNm0a1q5dC4VCYfaYRCKBpLl3cGaMMdYinB29gLq6OkybNg1z5szB5MmTAQBBQUHIz89H\ncHAw8vLyEBgYaPO5K1asEPsTEhKQkJDg6OoyxliHkpqaitTU1Juej0M3ExEREhMT4efnh3feeUcc\nn5SUBD8/PyxZsgSrVq1CWVkZ70BmjLEW0C7vgXz06FGMHDkSffv2FTcFvfHGG7jjjjswffp0ZGVl\nISoqClu2bIGPj495xTgMGGOsydplGNwMDgPGGGu6dr0DmTHGWPvGYcAYY4zDgDHGGIcBY4wxcBgw\nxhhDK5x0djO6vtsVAR4BCHA3FI+Gu+4y97auLmOMdVjt+tDSP4r/QFFVEYqri1FUXYSiqiKha9pv\n6EolUquACHQPtAqOQA9hnIfMgy+DwRjrdG7p8wyICFV1VWIwFFYVmoVFYXWh1WMEMguHQI9AMTwC\nPQKF8SaPc8uDMdYR3NJh0BxVmiohGIyBYegvrCq0Gl9YVQhnqbNVcBhDw2y8IURkTjKH1Z0xxhrC\nYeBARASVRmUWFAWqArPwMB1/veY6FHKFWVgEeQSZD3vWD3u7ePMmK8ZYi+AwaEf0pEdJTYnNwDCO\nK6gqEIdrdbVWoSF2Pc2HAzwC4Cxt1/v9GWNtiMOgA6upqxFbFYVVhWZBUVhdaDa+pKYEPq4+YkAE\neQYJXdN+QzfQIxAuzi5t/fIYY62Iw+AWodPrcL3mOgpUBSioKrDumvQXVRXBQ+6BII8gBHsGWwVH\nsGewWXhwcDDW8XEYMCt60qO0ptRmaOSr8uu7hpaHh9xDDIhgz2CrfmPhTVWMtV8cBuymGIPDMiTy\nVfnIr6rvL6gqwPXq61C6KW0GhWVRuip55zhjrYjDgLUanV6H4upiISgMJU+VhwJVAfJUeWbDNdoa\nMRhCPEPMu4r64SDPIMid5G390hjr8DgMWLtUU1djFhj5qnzkVeaZD6vyUFhVCG8XbzEkQjwNRWHd\n9ZR7tvXLYqzd4jBgHZqe9CiuLkZeZR7yVHnWXZN+Z6kzQhWhYjiEeoYKXcO4UIUwrJAreBMVu+Vw\nGLBbAhGhvLbcZmhcU13DtcpryKvMQ25lLiSQiCFhGhSWhVsarDPhMGDMBBGhUlMphETlNeSp8pBb\nkYs8lTBsWowtDWPpougidL26iMMhihDep8E6BA4DxprB2NIwBoMxMHIrcnFNJQxfq7yGfFU+fFx9\nxJAQA0PRRRzu4tUFfm5+vGmKtSkOA8YcSE96FFUVIbcyVwwIY39uZa7YX11XLQZGmFeYEBKGoAjz\nCkOYVxhCPEP4QobMYTgMGGsHquuqca3yGnIqcuqDoiIXOZXCcE5FDgqrCuHn7ieGhTEkTEsXRRe4\nydza+uWwDojDgLEOQqfXoaCqANnl2fVhUZGD7Aph2BgknnJPhHmFIdw7HGEKQ9crDOFe4WJocGAw\nSxwGjHUiRITi6mJkV2QLQVGeLQaGcZwxMExDItwrHOHe4YjwjkC4Vzi6eHXhHd+3GA4Dxm4xxv0Y\n2RXZyC7PNu8a+vNV+fB39xcDIsIror7fUALcA3indyfCYcAYs6LVa5GvykdWeZYYFFnlWcJwRTYy\nyzKh0qjMAiLSO9IsLCK8I+Dq7NrWL4XZicOAMdYsVZoqMRiMYZFZnonMskxklWchtzIXSlclIn0i\nxbCI9I5EpE9918fVp61fBjPgMGCMOYROrxNbF8aQyCzPNOt3kjiJ4RDlEyV2o3yiEOkTyedftKLO\nGQbduwNBQTcurtyEZaytEBFK1aXILMtERlkGMsoyxLDIKMtAZlkmNDqNGA6mJdonGlE+UfB18+Ww\naCGdMwzOngUKChovhYVCGJiGQ3Cwede0uPGheIy1tnJ1uRgOGWUZSC9NR0a50E0vSwcRCeGgjEa0\nj6Eo67t8/Sj7dc4wsKdqREBZme2gyM+37nd1NQ+LhvoDAwE5H5LHWGsoU5eJwZBemi4ERln9sIfc\nAzHKGET7RJt1Y5QxCPcO5zvvmbh1w6ApTIPDGA55eeaBYSxFRYC3t3VY2Cp+foBU2rJ1ZYwBEDZD\nFVQV4GrpVTEwrpZeFUtBVQG6KLqI4WAsscpYxChjoHRTtvVLaFUcBi1NrweuXxeCwRgYxgAxjjMG\nR2Wl0JIwhkNIiHW/scubqRhrUbXaWmSVZwlhUZaOKyVXcLVMCIorJVfgLHW2CohY31jEKmMR5hUG\nJ6lTW7+EFsVh0JZqa61bFnl55oFh7Hdzsw6IkBDr4uMD8A41xm4KEeF6zXUxGK6UXhH6S6/gSskV\nFFcXI9InUgyKWGWsGBQxypgOebkPDoOOgAgoLTUPB2NoWBaNxjooQkOt+3kTFWPNVlNXg4yyDDEc\nrpQK5XLJZWSWZcLP3Q+xylh09e1qFhSxvrHwdfNt6+rb1C7D4OGHH8bu3bsRGBiI33//HQBQUlKC\nBx98EJmZmYiKisKWLVvg42N9wkqnDIOmqK62HRLXrpkPV1YK+zSM4WDaNe3n0GCsSXR6HXIqcqyC\nwtgvlUitWhLGFkZbbn5ql2Fw5MgReHp6Yu7cuWIYJCUlwd/fH0lJSVi9ejVKS0uxatUq64rd6mFg\nr9paoYVhDAnTbm6u7dAIDQW6dKnvNx3n7c2bpxi7AePmpyslJpudDEGRXpaOwqpChHuFiwFhek5F\ntDLaodeDapdhAAAZGRmYOHGiGAbdu3fHoUOHEBQUhPz8fCQkJODixYvWFeMwaFlqtXnrwlhyc837\ntVrzsDDtmgYIn+jHWIPUWjUyyzLFI54yyjLMzquoqauxunig8e55xuLv7t+s1kVzfztb/eDcgoIC\nBAUFAQCCgoJQUFDQ2lW4Nbm6AtHRQmlMZaUQGMaQyM0FMjOBtLT6cXl5gEJRHxC2SlgY4OvLrQx2\nS3J1dkU3/27o5t/N5uMqjQrZ5dniBQOzyrNwPPd4/e1XK3NRWlMKb1dv+Lv7w9/dH35uflC4KOAp\n84SnXCjuMne4OLvA1dlVLM3VpmdqSCSSRptKK1asEPsTEhKQkJDg+Erd6hQKocTFNTyNXg8UFwvh\nYFp++qm+PydHaI2EhgrBYAwIY9fYHxwMOPMJQ+zW4in3RI+AHugR0KPBaXR6HUrVpSiuLhaLSqOC\nSqNClaYKKo1K2FR18goyTmVARzpo9dpm16nVv4XGzUPBwcHIy8tDYGBgg9OahgFrR6RS4byKwECg\nf/+Gp6uuNg+HnBzg8mUgNbV++Pp1YT7GgAgLA8LDzYdDQwEZ3zOY3VqcpE5iq6BRY80Hm7svotXD\nYNKkSUhOTsaSJUuQnJyMyZMnt3YVWGtxdwduu00oDamrEzY7GcMhO1sIj+PHhf7sbOH6U35+9SER\nHl5fjMOhodzCYOwmOHQH8kMPPYRDhw6huLgYQUFBeOWVV3D//fdj+vTpyMrK4kNLmX20WuGIqezs\n+sAwdo2lqEhoYZgGRUSEeTcwkPdhsE6v3R5N1FwcBqxJ6uqEndvGcMjKMg+LrCxApTIPCssSHg54\neLT1K2HspnAYMHYj1dXmQZGZWT9sHOfhAURGCuFgqxsQwK0L1q5xGDB2s4iE/RPGcMjMFIppf01N\nfTAYS1RUfTckBHDqXBc+Yx1LpwyDgKNHESiTIUguR6BcjiCZTOjK5fXjDV03/gKy1qBS1QeDZcnI\nEI6OCgszDwjT0qULhwVzqE4ZBvm1tSjQaFCo0aCgrk7oajQorKsz6xZoNJBLpQiyCI4gQ3AEWQwr\nnJz4FnvMMdRqYXNTerp5SKSnC93iYiEsoqOFcDDtRkcL513wZ5PdhE4ZBvZWjYhQodOZBYcxJAps\nDOuARsMi2GSct7MzBwdrOWq1sNnJGBDGkDD2q1RCiyImRggH025MjHBCIGONuKXDoKmqDMHRUFiY\nDtfq9Qg0CYhgQ0gEmwSJsd+LWxzsZqlUQjhcvSqEg2n36lVhB7cxGGJigNjY+m6XLnxlWsZh4Cg1\nOh3yLUIi31CMgZFveExLZBYWpgFiWoLkcrjzdmPWVETCTZSMwXD1KnDlilCuXhXulREZKQRD165C\n19gfFQW4uLT1K2CtgMOgHTC2OIxBkWcSFpbjXKRSq5AIlssRYjEcIJfDiVsbzB7V1UIrwhgQly/X\n92dlCUc6de1aX267rT40+Cq0nQaHQQdCRCjXapFvIzCM44z9JVot/JydhaBwcRHDwqrr4gIPbm2w\nhtTVCYFw+bJQ/vxTCIk//xQ2SwUF1QeEscTFCZug5PK2rj1rAg6DTkqr16Owrs4sJPJqa+v7TbrO\nEglCDAFhGhKm40JcXODLO8WZKa1WOALq0iUhHIzl0iVhfHi4EAzG0q2bULp04SOf2iEOg1uc8Ygq\nY1Dk2QgPY6nW6cRWhTEsQi2CI9TFBQEyGaT8Zb+1aTTCpqdLl4Tyxx/13cpKoQXRrRvQvXt9Ny6O\nL+vRhjgMmN2MO8XzNBpcswgK0+FyrRaBMhlCXFwQaggI0+AI5dC4tZWX14fExYtC+eMPoVURGCgE\nQ/fuQI8e9YUv5+FwHAasxWn0euRbBMS12lpcs+g3hkaoSUCEyuXo4uJiNo43T90idDrhZLsLF4SA\nuHChvkilQij07CmUXr2EbkgIh0QL4TBgbUaj1wthYQiHa7W1yDUZzjV0a3Q6sUXRxSQkuliM8+T7\nEnROxms/nT8vlAsXgHPnhH6NRgiF3r2FgDB2DbfIZfbjMGDtXrVOJ7Yocg2Bcc00MAzj5BIJuhhC\nooshJCyHA/mQ286luFgIhnPngLNnhe7vvws3LOrdG+jTx7zr6dnWNW63OAxYp0BEKNVqxWDINQaH\nxXCpVosguRxd5HKEmYRFmGlXLocrH27bcREJd8E7e1YIht9/B86cETY9hYYCffsKJT4e6NdPOLGO\n/yBwGLBbi3HTlGlY5BgCI8fQf622FgonJ7OAMC3GcV68Wapj0WqFndRnzgjl9Gng1Cnh6Ka+fYVg\n6N9fKL163XLnSXAYMGaBiFBcVyeGQ45JaOTU1iLbMOwkkVgFRZiLC8JN+vmChR1AcXF9MPz2m1DS\n04VDXgcMAAYOFErfvoCbW1vX1mE4DBhrBuPZ4KYBYdpvHAYghkO4sbi6mg0ruIXR/lRXC62HkyeF\n8uuvwuGvt90G3H57fenTB5DJ2rq2LaJThkFech5kfjI4+zrXd5UySJz4HxprPcYT+rLVarOQyK6t\nRbZaLfbLJRJEuLqahUWEoT/CEBxyvqpo21OrhYD45Rfg55+Fkp4utBgGD64v0dEdch9EpwyDc7PO\nQVuiRd31OtRdr4O2RAttuRbOXs5w9nOGzFcmhISfEBamwSHzlZlN4+TFl5dmjkNEKNFqzcIhu7YW\nWYbhLLUaeRoNfGUyRBjCwbRrDIwAmYw/p21BpRLC4fjx+lJXB9x5JzB0qNAdNKhDbF7qlGFgq2qk\nI2jLDAFRUgftdS3qSgxhYdlvMo1erTdvYRjCQwwTX5l1K8RPBic3PhqFtQwdEfI1GmSp1cgyBIRp\nN1OtRo1ebxUWkS4uiHR1FVsd3LpoJdnZQFoacOyYUM6dEzYnjRghlOHDAV/ftq6llVsmDJpLX6tH\nXal1SBhbHcaWh9hveEziLLFqfZgN+9p4zMeZN2WxZlFptcg2BEOWSTdLrUamoXXhL5Mh0tVVKIag\nMB3mk/YcpLpaaDEcOSKU48eBiAggIQEYPRoYNQrw92/rWnIYOAIRQVelMwsN08BoqDWirRA2ZTU1\nRKTuUt5EwBqlNRxSm6lWI9MQFsaSYQgON6kUUa6uiDIERJRF4UNpW4hWKxyxlJoKHDwI/PijcHOh\nMWOAceOEcGiDC/ZxGLQjpCPzVkhDIWIxTES2g6OxYd6hzkwQEYrq6sRwMHZNi9wkLIwl2qSfj4pq\nJq1WOFpp/37ghx+E/oEDhWCYMEE4Oa4V/uxxGHQCuhpdg0HR0LBxh7rd4WHod3LnfSG3IiLC9bo6\npJsERbpF110qRbSbmxgS0a6uiHFzQ7ShpeHC+yzso1IBhw8D+/YBe/YANTVCKEyYAIwd67BWA4fB\nLcpsh7od4WEcBtCk8JD5G/aFSLkV0pkREQrr6pBeUyOGw1W1WhzOqa1FoFwuBISrK6Ld3BBjCIsY\nV1cEy+W8qbMhly4Bu3cL5cQJ4K67gKlTgb/8BVAqW2wxHAasSXTVQiukrtiOADFMo1Pp4OzThAAx\nDDu5ciuks9Dq9cjVaHDVEA5i19BfqdOJLQnTkIg1tCzc+FpRgpISYNcu4JtvgJQU4fDVWbOEcLjJ\ni/BxGDCH02v1No+4utGwRCZpMCxk/rYDxNmbL//QEam0WqEloVbjSk0NrtbU4KqhP1Othp9Mhlg3\nN6EYQqKrYdi3k5wB3GQqlRAM/+//AUePCi2FuXOFlkMzwpPDgLVLRASdqr4VYm+A6Gv0cFY2si/E\nxgmHMj8ZpC68Pbu90hEht7YWV2pqhGIIiSs1NbhcUwOpRCIEg6sruhpCwliCbpXNT4WFwBdfAJs2\nCf2LFgELFgB+fnbPgsOAdSp6jd72uSCN7Uwv0ULqKm38HBCTEw6Njzl7876QtmbcsX1FrcZlQzj8\nWV0tDtfodOjq5obb3N2FrklQhHTWoPj1V+C994Dt24Fp04CnnhIumXEDHAbslkdE0FXqbhwcFiGj\nqzLfF2LvGepOHnyJk9ZSZgiKP6ur68PCUKpNgiLOEBTGfv/OcHmPwkJg/Xrg/feBkSOB118HYmIa\nnJzDgLFm0tfpoS21PifE6twQi+tkkY4avR6W2aVNTMbxJU5aVrlWiz+rq8Vw+NPQqrhUUwM9kRgM\ncRbdDnc+RVUV8PbbwL//DcybByxbZvNyGBwGjLUyXY2uPiBMrpNlNs40QAyBI5FIxNAwBoU9XW6J\nNN31ujpcMgTFJUNAGIe9nZ3NwqGbuzvi3N0R4+oKWXs+lyI/H1ixQjgS6f33gQceMHuYw4CxDoCI\noK/RW4dHSX1gGIfFFkqpFnWldSANCTvVfWVwVjrXB4XlOKWh32S8VN6Of9zagN6wM9sYDn+YBEVO\nbS0iXF3FgBBLe9uRffIkMH68cMZzfLw4usOFwXfffYfFixdDp9NhwYIFWLJkiXnFOAwYM6OvNYRI\nqVYICEO/OK5ECA1tiVYMEGO/RC4RwsEYFD7O9YFhOc6063PrtUhq9XpcranBH9XV+MPYNZQ6IsQZ\ngsHYkuhm2Efh0RbnUHz+ObB8uXD5bW9vAB0sDHQ6Hbp164b9+/ejS5cuuP3227F582b06NGjvmIc\nBqLU1FQkJCS0dTXaBV4X9exdF+IFFw0hIgZFqRbaMotxZebjtOVaoUXiYxIO3k5mw87eJsX4uGHY\nyUvol8oc2zJprc9FSV2d2IowDYkrajX8ZTKxNXGbyeanKEdvdnr8caCoCPjqK0AiafZvZ5vsQTlx\n4gS6du2KqKgoAMCMGTOwfft2szBg9fgHsB6vi3r2rguJRAJnT2c4ezoD4U1fjl6jh7bcJCTKtVbD\nNX/WmI3XVejqh8u1kMqlYjA4exlCwrSrcBL6FTb6PQ3F0G8rWFrrc+Erk2GotzeGGv6FG+mIkKVW\n4w/j/omaGnxXUoJLNTW4ZtjsZDwc9jbDSXYxhgsDut5si+Kdd4R7K6xdCyxe3OzZtEkY5ObmIjy8\n/lMZFhaG48ePt0VVGGM3IJVLIQ+QQx4gb9bziQj6aj20FYaQqBACQlepE4d1FULLpTarFrpKHbSV\nhscrddCpdPXjVDpInCT1AeHpBCcPJ+QV5uHMz2fg5CEMS92lcHJ3gtTD0HWTQuomhZNbfb/U1aTr\nKoXUpb5I5BKhK5PYtYnMSSJBtJsbot3ccI/FY8bNTsbDYc9XV2PX9eu4qlYj29CiiHZzE+94F264\niVGoXI4AuRwBMhncGwsMV1ehVWC8XWcztUkY3ErbHxm71UkkEvFHGiE3Ny8igr5WD32VXggJlQ66\nKh183vdB6AOhwvgqHXTVOuir9cI1uIrqoKvRQV+jF4uuRge9Wl9favTQ1+pBtYb5a4R+0pIQCHIJ\npHJDOMgkkDhLIJUZhp0kgBMgcRb6JU4SQArhREaTboREgggJcJfU+BvoBpK4QU161Oh0qKEq1Ogr\nodbrUaTTI5v00BBBo9cDAORSKZwlgBQSOEmEYvpLKon5AlhQeFMrt9WlpaXR+PHjxeHXX3+dVq1a\nZTZNbGwsAeDChQsXLk0osbGxzfpdbpMdyFqtFt26dcOBAwcQGhqKO+64w2oHMmOMsdbTJpuJnJ2d\n8Z///Afjx4+HTqfDI488wkHAGGNtqN2edMYYY6z1tPlpid999x26d++O2267DatXr7Z6PDU1Fd7e\n3ujfvz/69++PV199tQ1q6Xg3Wg9GP//8M5ydnfHNN9+0Yu1a143Wxfbt2xEfH4/+/ftj4MCBSElJ\naYNato4brYvPPvsM8fHx6Nu3L4YNG4YzZ860QS1bx43WxcWLFzF06FC4urrirbfeaoMath57fi+e\nehlH42wAAAg+SURBVOop3HbbbYiPj8dvv/1245k2ey9wC9BqtRQbG0vp6emk0WgoPj6ezp8/bzbN\nwYMHaeLEiW1Uw9Zhz3owTjd69Gi67777aOvWrW1QU8ezZ12oVCqx/8yZM83eYdbe2bMujh07RmVl\nZUREtHfvXho8eHBbVNXh7FkXhYWF9PPPP9OyZctozZo1bVRTx7NnXezevZvuvfdeIiL66aef7Ppc\ntGnLwPTkM5lMJp58Zok6+ZYse9fDe++9h7/+9a8ICAhog1q2DnvWhYfJjcRVKhX8/f1bu5qtwp51\nMXToUHgbToAaPHgwcnJy2qKqDmfPuggICMCgQYMg6+R3TLNnXezYsQOJiYkAhM9FWVkZCgoKGp1v\nm4aBrZPPcnNzzaaRSCQ4duwY4uPjMWHCBJw/f761q+lw9qyH3NxcbN++HY8//jiAznuuhj3rAgC2\nbduGHj164N5778W7777bmlVsNfauC6MNGzZgwoQJrVG1VtfUddGZ2ft7YTnNjf4otOkFve35QRsw\nYACys7Ph7u6OvXv3YvLkybh06VIr1K712LMeFi9ejFWrVonXHemsrSV7Q27y5MmYPHkyjhw5gjlz\n5uCPP/5wcM1aX1MC/+DBg/jkk0/w448/OrBGbaez/vlpDnvXheVvxI2e16Zh0KVLF2RnZ4vD2dnZ\nCAsLM5tGoVCI/ffeey8WLVqEkpIS+Nq4qUNHZc96+PXXXzFjxgwAQHFxMfbu3QuZTIZJkya1al0d\nzZ51YWrEiBHQarW4fv06/Jpwn9iOwN51cebMGTz66KP47rvvoFQqW7OKraapn4vOzJ51YTlNTk4O\nunTp0viMW3zvRhPU1dVRTEwMpaenU21trc0dIfn5+aTX64mI6Pjx4xQZGdkGNXUse9aDqXnz5tHX\nX3/dijVsPfasi8uXL4ufiV9//ZViYmLaoqoOZ8+6yMzMpNjYWEpLS2ujWraOpnxHli9f3ql3INuz\nLkx3IKelpdm1A7lNWwYNnXz24YcfAgD+9re/YevWrfjvf/8LZ2dnuLu744svvmjLKjuEPevhVmHP\nuvj666/xv//9DzKZDJ6enp3yMwHYty5eeeUVlJaWivuSZDIZTpw40ZbVdgh71kV+fj5uv/12VFRU\nQCqVYu3atTh//jw8PT3buPYty551MWHCBOzZswddu3aFh4cHNm7ceMP58klnjDHG2v6kM8YYY22P\nw4AxxhiHAWOMMQ4Dxhhj4DBgjDEGDgPGGGPgMGDtzPXr18XLlYeEhCAsLAz9+/eHQqHAk08+2eLL\n2759Oy5cuNDi823Mv//9b9TU1DT5eTt37hQvV7xt27ZWrzfr3Pg8A9Zuvfzyy1AoFHj66acdtox5\n8+Zh4sSJmDZtmsOWYSk6Ohq//PJLky6fodPp4OTkJA63Rb1Z58YtA9auGf+rpKamYuLEiQCAFStW\nIDExESNHjkRUVBS++eYbPPvss+jbty/uvfdeaLVaAML1nBISEjBo0CDcc889yM/PN5v3sWPHsHPn\nTvzzn/9E//79cfXqVZw6dQpDhgxBfHw8pk6dirKyMqs6zZs3D4sWLcLQoUMRGxuL1NRUJCYmomfP\nnpg/f7443aJFi3D77bejd+/eWLFiBQDg3XffxbVr1zB69GjcddddAGB2huzWrVvFecybNw+PPfYY\nhgwZgqSkJCQnJ+Pvf/870tLSxHoPGDAAV69excCBA8V5/Pnnn2bDjNmDw4B1SOnp6Th48CB27NiB\n2bNnY+zYsThz5gzc3Nywe/du1NXV4e9//zu+/vpr/PLLL5g/fz6WLVtmNo8777wTkyZNwpo1a/Db\nb78hJiYGc+fOxb/+9S+cPn0affr0wcsvv2y1bIlEgrKyMqSlpeGdd97BpEmTkJSUhHPnzuH333/H\n6dOnAQCvvfYafv75Z5w+fRqHDh3C2bNn8dRTTyE0NBSpqak4cOCAOD/TeZu6du0a0tLSzO7cNXTo\nULHeJ0+eRExMDLy9vcXlbty4EQ8//HDLrGh2y+AwYB2ORCLBvffeCycnJ/Tu3Rt6vR7jx48HAPTp\n0wcZGRm4dOkSzp07h7vvvhv9+/fHa6+91uD1742tj/LycpSXl2PEiBEAgMTERBw+fNjmc4ytlN69\neyM4OBi9evWCRCJBr169kJGRAQD48ssvMXDgQAwYMADnzp1r8r04JBIJHnjggQYvPWy6hXfBggXY\nuHEj9Ho9tmzZgpkzZzZpWYy16YXqGGsuuVwOAJBKpWZ3tpJKpdBqtSAi9OrVC8eOHbvhvOz5sW1s\n+S4uLmbL1+l0SE9Px1tvvYVffvkF3t7emD9/PtRq9Q2Xb7lj2d3d3a56T5s2DS+//DLGjBmDQYMG\nddpLWTPH4ZYB63DsOeahW7duKCoqwk8//QQAqKurs/nPXKFQoKKiAgDg7e0NpVKJo0ePAgA2bdqE\nhISEZtWvsrISHh4e8PLyQkFBAfbu3WtzmQAQFBSEixcvQq/X49tvv7UrnCzn4eLigvHjx+Pxxx83\n22/BmL04DFi7ZvxhlEgkNvtNpzEdlslk2Lp1K5YsWYJ+/fqhf//+SEtLs5r/jBkz8K9//QsDBw7E\n1atXkZycjH/+85+Ij4/HmTNn8NJLLzVar4aW37dvX/Tv3x/du3fHrFmzMHz4cPHxhQsX4p577hF3\nIK9atQp/+ctfMGzYMISGhja6HOOwab3T09MBADNnzoRUKsW4ceNs1pmxxvChpYx1EmvWrEFlZaXN\nnd6M3QjvM2CsE5gyZQrS09ORkpLS1lVhHRS3DBhjjPE+A8YYYxwGjDHGwGHAGGMMHAaMMcbAYcAY\nYwwcBowxxgD8f6dhwwmry1hIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa70dba8>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method: priceEuropeanCallMC\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XvSwNZcteZmdnS7bFGBgYICsrq9z1qgr3GXA4nMoFkWZ+aiJe9vLRo0cYN26c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\nSgEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa4e8550>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method: priceEuropeanCallMC_antithetic\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rXYg08yqi7GEv79+/j9GjR2t8s/Ib9vLtednzS3JITA4GjDH2r3cd9jI/+Q17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\n1tfT07m5XdZbdERRU12FssmmBamptNNCfYOZ5yksIYH+rK8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NDQ3NsSSJRIKk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\nwP8DbpcvCuVbztgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa72aef0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method: priceEuropeanCallMC_importanceSampling\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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X1FLmWMQig6ws2yoDOYAsQwgmlb00sxEXC0zZy+XLl2Pu3LlYt26dWd/v0qWL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XP4JCwMs9zdGY+vlcuRLpEgQyJBukSCUpkM6s57JAC4HA4WenlhPsv1mHCqqQlLc3LwU2QkBjEU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\n+R4Z76EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa4e0630>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method: priceEuropeanCallMC_stratifiedSampling_fixed_nStrata\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LkXIeJZQz7eWTJ08wZswYpR9WUdNe5l2Xs748p8TkYMAYY/8q67SXRSlq2ktH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\nYW5ujHB3Z3dzMy+VljLey4t7R41iXmAgNkVhj9FIisFAclMTPzQ2snD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GA1qtlhdffJH9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\nUFFRUVFBdQYqKioqKsD/A6VZF2LQx5NWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa72f9e8>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The breakdown of importance_sampling for certain strikes is huge (but note that for certain K's it does actually reduce the variance)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}