{ "cells": [ { "cell_type": "markdown", "metadata": { "_cell_guid": "83708667-4fdc-1563-7b3a-06b6575d2865" }, "source": [ "# Derivatives Hedging\n", "\n", "In this case study we implement Reinforcement learning-based hedging strategy\n", "adopting the ideas presented in the paper ‘_Deep Hedging_’ (https://arxiv.org/abs/\n", "1802.03042) by _Hans Bühler, Lukas Gonon, Josef Teichmann, Ben Wood_. \n", "\n", "We will\n", "build an optimal hedging strategy for call options by minimizing the risk adjusted\n", "PnL of a hedging. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Content" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* [1. Problem Definition](#0)\n", "* [2. Getting Started - Load Libraries and Dataset](#1)\n", " * [2.1. Load Libraries](#1.1) \n", " * [2.2. Generating the Data](#1.2)\n", "* [3. Exploratory Data Analysis](#2)\n", " * [3.1 Plot Paths](#2.1) \n", "* [4.Evaluate Algorithms and Models](#4) \n", " * [4.1. Agent Script](#4.1)\n", " * [4.3. Training Data](#4.2) \n", "* [5.Testing Data](#5) \n", " * [5.1. Helper Functions For comparison against Black Scholes](#5.1) \n", " * [5.2. Comparison between Black Scholes and RL](#5.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='0'></a>\n", "# 1. Problem Definition" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "In the Reinforcement Learning based framework for this case study, the algorithm decides the best hedging strategy for call options from the market prices of the underlying asset based on direct policy search reinforcement learning. \n", "\n", "The key components of the Reinforcement Learning framework used for this case study are described below:\n", "\n", "* Agent: Trader or a trading agent\n", "* Action: Hedging strategy (i.e. δ1, δ2 . . , δT)\n", "* Reward function: CVaR is used as the reward function for this case study. This is a convex function and is minimized during the model training.\n", "\n", "* State: State is the representation of the current market state and relevant product state variables. The state represent the model inputs which are Stock Price Path\n", "(i.e. S1, S2 . . , ST), strike and risk aversion parameter(α)\n", "\n", "* Environment: Stock exchange or the stock market.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='1'></a>\n", "# 2. Getting Started- Loading the data and python packages" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='1.1'></a>\n", "## 2.1. Loading the python packages" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "_cell_guid": "5d8fee34-f454-2642-8b06-ed719f0317e1" }, "outputs": [], "source": [ "# Load libraries\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import datetime as dt\n", "import random\n", "import scipy.stats as stats\n", "import seaborn as sns\n", "from IPython.core.debugger import set_trace\n", "\n", "#Import Model Packages for reinforcement learning\n", "from keras import layers, models, optimizers\n", "from keras import backend as K\n", "import tensorflow as tf\n", "from collections import namedtuple, deque" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "#Diable the warnings\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='1.2'></a>\n", "## 2.2. Generating the Data " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function below generates the monte-carlo paths for the stock price and get the option price on each of the monte-carlo path.\n", "\n", "### Black-Sholes Simulation\n", "Simulate $N_{MC}$ stock price sample paths with $T$ steps by the classical Black-Sholes formula.\n", "\n", "$$dS_t=\\mu S_tdt+\\sigma S_tdW_t\\quad\\quad S_{t+1}=S_te^{\\left(\\mu-\\frac{1}{2}\\sigma^2\\right)\\Delta t+\\sigma\\sqrt{\\Delta t}Z}$$\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "def monte_carlo_paths(S_0, time_to_expiry, sigma, drift, seed, n_sims, n_timesteps):\n", " \"\"\"\n", " Create random paths of a underlying following a browian geometric motion\n", " \n", " input:\n", " \n", " S_0 = Spot at t_0\n", " time_to_experiy = end of the timeseries (last observed time)\n", " sigma = the volatiltiy (sigma in the geometric brownian motion)\n", " drift = drift of the process\n", " n_sims = number of paths to generate\n", " n_timesteps = numbers of aquidistant time steps \n", " \n", " return:\n", " \n", " a (n_timesteps x n_sims x 1) matrix\n", " \"\"\"\n", " if seed > 0:\n", " np.random.seed(seed)\n", " stdnorm_random_variates = np.random.randn(n_sims, n_timesteps)\n", " S = S_0\n", " dt = time_to_expiry / stdnorm_random_variates.shape[1]\n", " r = drift\n", " # See Advanced Monte Carlo methods for barrier and related exotic options by Emmanuel Gobet\n", " S_T = S * np.cumprod(np.exp((r-sigma**2/2)*dt+sigma*np.sqrt(dt)*stdnorm_random_variates), axis=1)\n", " return np.reshape(np.transpose(np.c_[np.ones(n_sims)*S_0, S_T]), (n_timesteps+1, n_sims, 1))" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "S_0 = 100\n", "K = 100\n", "r = 0\n", "vol = 0.2\n", "T = 1/12\n", "timesteps = 30\n", "seed = 42\n", "n_sims = 50000" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "# Train the model on the path of the risk neutral measure\n", "paths_train = monte_carlo_paths(S_0, T, vol, r, seed, n_sims, timesteps)" ] }, { "cell_type": "markdown", "metadata": { "_cell_guid": "df6a4523-b385-69ee-c933-592826d81431" }, "source": [ "<a id='2'></a>\n", "# 3. Exploratory Data Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='2.1'></a>\n", "## 3.1. Plot Paths" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "_cell_guid": "52f85dc2-0f91-3c50-400e-ddc38bea966b" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Plot Paths for one simulation\n", "plt.figure(figsize=(10,6))\n", "plt.plot(paths_train[1:31,1])\n", "plt.xlabel('Time Steps')\n", "plt.title('Stock Price Sample Paths')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='4'></a>\n", "# 4. Evaluate Algorithms and Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The approach used in the case study is Policy Gradient which is a type of Direct Policy Search (or policy-based) algorithm. In this approach we use LSTM model to map the state to action. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='4.1'></a>\n", "## 4.1. Policy Gradient script\n", "In this step we implement in the RL “Agent” class. Agent holds the variables and member functions that perform the training. An\n", "object of the “Agent” class is created using the training phase and is used for training\n", "the model. After sufficient number of iterations policy\n", "gradient model is generated.\n", "The “class” consists of two modules:\n", "\n", "* Constructor\n", "* Function execute_graph_batchwise" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "from IPython.core.debugger import set_trace\n", "\n", "class Agent(object):\n", " def __init__(self, time_steps, batch_size, features, nodes = [62,46,46,1], name='model'):\n", " tf.reset_default_graph()\n", " self.batch_size = batch_size #NUmber of options in a batch\n", " self.S_t_input = tf.placeholder(tf.float32, [time_steps, batch_size, features]) #Spot\n", " self.K = tf.placeholder(tf.float32, batch_size) #Strike \n", " self.alpha = tf.placeholder(tf.float32) #alpha for cVaR\n", "\n", " S_T = self.S_t_input[-1,:,0] #Spot at time T\n", " dS = self.S_t_input[1:, :, 0] - self.S_t_input[0:-1, :, 0] # Change in the Spot price\n", " #dS = tf.reshape(dS, (time_steps, batch_size))\n", "\n", " #Prepare S_t for the use in the RNN remove the last time step (at T the portfolio is zero)\n", " S_t = tf.unstack(self.S_t_input[:-1, :,:], axis=0)\n", "\n", " # Build the lstm\n", " lstm = tf.contrib.rnn.MultiRNNCell([tf.contrib.rnn.LSTMCell(n) for n in nodes])\n", "\n", " #So the state is a convenient tensor that holds the last actual RNN state, ignoring the zeros. \n", " #The strategy tensor holds the outputs of all cells, so it doesn't ignore the zeros. \n", " self.strategy, state = tf.nn.static_rnn(lstm, S_t, initial_state=lstm.zero_state(batch_size, tf.float32), \\\n", " dtype=tf.float32)\n", "\n", " self.strategy = tf.reshape(self.strategy, (time_steps-1, batch_size))\n", " self.option = tf.maximum(S_T-self.K, 0)\n", "\n", " self.Hedging_PnL = - self.option + tf.reduce_sum(dS*self.strategy, axis=0)\n", " self.Hedging_PnL_Paths = - self.option + dS*self.strategy\n", " # Calculate the CVaR for a given confidence level alpha\n", " # Take the 1-alpha largest losses (top 1-alpha negative PnLs) and calculate the mean\n", " CVaR, idx = tf.nn.top_k(-self.Hedging_PnL, tf.cast((1-self.alpha)*batch_size, tf.int32))\n", " CVaR = tf.reduce_mean(CVaR)\n", " self.train = tf.train.AdamOptimizer().minimize(CVaR)\n", " self.saver = tf.train.Saver()\n", " self.modelname = name\n", " \n", " def _execute_graph_batchwise(self, paths, strikes, riskaversion, sess, epochs=1, train_flag=False):\n", " sample_size = paths.shape[1]\n", " batch_size=self.batch_size\n", " idx = np.arange(sample_size)\n", " start = dt.datetime.now()\n", " for epoch in range(epochs):\n", " # Save the hedging Pnl for each batch \n", " pnls = []\n", " strategies = [] \n", " if train_flag:\n", " np.random.shuffle(idx)\n", " for i in range(int(sample_size/batch_size)):\n", " indices = idx[i*batch_size : (i+1)*batch_size]\n", " batch = paths[:,indices,:]\n", " if train_flag:#runs the train, hedging PnL and strategy using the inputs \n", " _, pnl, strategy = sess.run([self.train, self.Hedging_PnL, self.strategy], {self.S_t_input: batch,\n", " self.K : strikes[indices],\n", " self.alpha: riskaversion})\n", " else:\n", " pnl, strategy = sess.run([self.Hedging_PnL, self.strategy], {self.S_t_input: batch,\n", " self.K : strikes[indices],\n", " self.alpha: riskaversion})\n", " pnls.append(pnl)\n", " strategies.append(strategy)\n", " #Calculate the option prive given the risk aversion level alpha\n", " #set_trace()\n", " CVaR = np.mean(-np.sort(np.concatenate(pnls))[:int((1-riskaversion)*sample_size)])\n", " #set_trace()\n", " if train_flag:\n", " if epoch % 10 == 0:\n", " print('Time elapsed:', dt.datetime.now()-start)\n", " print('Epoch', epoch, 'CVaR', CVaR)\n", " #Saving the model\n", " self.saver.save(sess, \"model.ckpt\")\n", " self.saver.save(sess, \"model.ckpt\")\n", " return CVaR, np.concatenate(pnls), np.concatenate(strategies,axis=1)\n", " \n", " def training(self, paths, strikes, riskaversion, epochs, session, init=True):\n", " if init:\n", " sess.run(tf.global_variables_initializer())\n", " self._execute_graph_batchwise(paths, strikes, riskaversion, session, epochs, train_flag=True)\n", " \n", " def predict(self, paths, strikes, riskaversion, session):\n", " return self._execute_graph_batchwise(paths, strikes, riskaversion,session, 1, train_flag=False)\n", "\n", " def restore(self, session, checkpoint):\n", " self.saver.restore(session, checkpoint)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='4.2'></a>\n", "## 4.2. Training the data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will proceed to train the data, based on our policy based model. This will provide us with the strategy, based on the simulated price of the stock prices at the end of the day. \n", "\n", "Steps: \n", "* Define the risk aversion parameter for cVaR, number of features, strike and define the batch size with which the neural network will be trained.\n", "* Instantiate the Policy Gradient Agent which has the RNN based policy with the loss function or the reward function based on the cVaR reward\n", "* The Training data is the Monte-Carlo path generated in the previous step. \n", "* We can start to iterate through the batches and the strategy is based on the policy that is the output of the LSTM based network. \n", "* The trained model is saved\n" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "batch_size = 1000 \n", "features = 1 \n", "K = 100\n", "alpha = 0.50 #risk aversion parameter for cVaR\n", "epoch = 100 #It is set to 100, but should ideally be a high number \n", "model_1 = Agent(paths_train.shape[0], batch_size, features, name='rnn_final')" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time elapsed: 0:00:11.029064\n", "Epoch 0 CVaR 3.7888103\n", "Time elapsed: 0:02:01.549036\n", "Epoch 10 CVaR 2.7065594\n", "Time elapsed: 0:03:55.465211\n", "Epoch 20 CVaR 2.6054726\n", "Time elapsed: 0:05:48.695138\n", "Epoch 30 CVaR 2.6241252\n", "Time elapsed: 0:07:42.143004\n", "Epoch 40 CVaR 2.5914657\n", "Time elapsed: 0:09:40.278260\n", "Epoch 50 CVaR 2.594914\n", "Time elapsed: 0:11:42.008070\n", "Epoch 60 CVaR 2.6521277\n", "Time elapsed: 0:13:49.944725\n", "Epoch 70 CVaR 2.5898495\n", "Time elapsed: 0:15:55.188680\n", "Epoch 80 CVaR 2.5970662\n", "Time elapsed: 0:17:58.187328\n", "Epoch 90 CVaR 2.6028452\n", "Training finished, Time elapsed: 0:19:49.353047\n" ] } ], "source": [ "# Training the model takes about a few minutes\n", "start = dt.datetime.now()\n", "with tf.Session() as sess:\n", " # Train Model\n", " model_1.training(paths_train, np.ones(paths_train.shape[1])*K, alpha, epoch, sess)\n", "print('Training finished, Time elapsed:', dt.datetime.now()-start)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5'></a>\n", "# 5. Testing the Data \n", "In the testing step, we will com‐\n", "pare the effectiveness of the hedging strategy and compare it to the delta hedging\n", "strategy based on the Black Scholes model. We first define the helper functions fol‐\n", "lowed by the results comparison." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.1'></a>\n", "## 5.1. Helper Functions for Comparison against Black Scholes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.1.1'></a>\n", "### 5.1.1 Black Scholes Price and Delta" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "def BS_d1(S, dt, r, sigma, K):\n", " return (np.log(S/K) + (r+sigma**2/2)*dt) / (sigma*np.sqrt(dt))\n", "\n", "def BlackScholes_price(S, T, r, sigma, K, t=0):\n", " dt = T-t\n", " Phi = stats.norm(loc=0, scale=1).cdf\n", " d1 = BS_d1(S, dt, r, sigma, K)\n", " d2 = d1 - sigma*np.sqrt(dt)\n", " return S*Phi(d1) - K*np.exp(-r*dt)*Phi(d2)\n", "\n", "def BS_delta(S, T, r, sigma, K, t=0):\n", " dt = T-t\n", " d1 = BS_d1(S, dt, r, sigma, K)\n", " Phi = stats.norm(loc=0, scale=1).cdf\n", " return Phi(d1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.1.2'></a>\n", "### 5.1.2 Test Results and Plotting" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "def test_hedging_strategy(deltas, paths, K, price, alpha, output=True):\n", " S_returns = paths[1:,:,0]-paths[:-1,:,0]\n", " hedge_pnl = np.sum(deltas * S_returns, axis=0)\n", " option_payoff = np.maximum(paths[-1,:,0] - K, 0)\n", " replication_portfolio_pnls = -option_payoff + hedge_pnl + price\n", " mean_pnl = np.mean(replication_portfolio_pnls)\n", " cvar_pnl = -np.mean(np.sort(replication_portfolio_pnls)[:int((1-alpha)*replication_portfolio_pnls.shape[0])])\n", " if output:\n", " plt.hist(replication_portfolio_pnls)\n", " print('BS price at t0:', price)\n", " print('Mean Hedging PnL:', mean_pnl)\n", " print('CVaR Hedging PnL:', cvar_pnl)\n", " return (mean_pnl, cvar_pnl, hedge_pnl, replication_portfolio_pnls, deltas)\n", "\n", "def plot_deltas(paths, deltas_bs, deltas_rnn, times=[0, 1, 5, 10, 15, 29]):\n", " fig = plt.figure(figsize=(10,6))\n", " for i, t in enumerate(times):\n", " plt.subplot(2,3,i+1)\n", " xs = paths[t,:,0]\n", " ys_bs = deltas_bs[t,:]\n", " ys_rnn = deltas_rnn[t,:]\n", " df = pd.DataFrame([xs, ys_bs, ys_rnn]).T\n", " #df = df.groupby(0, as_index=False).agg({1:np.mean,\n", " # 2: np.mean})\n", " plt.plot(df[0], df[1], df[0], df[2], linestyle='', marker='x' )\n", " plt.legend(['BS delta', 'RNN Delta'])\n", " plt.title('Delta at Time %i' % t)\n", " plt.xlabel('Spot')\n", " plt.ylabel('$\\Delta$')\n", " plt.tight_layout()\n", " \n", "def plot_strategy_pnl(portfolio_pnl_bs, portfolio_pnl_rnn):\n", " fig = plt.figure(figsize=(10,6))\n", " sns.boxplot(x=['Black-Scholes', 'RNN-LSTM-v1 '], y=[portfolio_pnl_bs, portfolio_pnl_rnn])\n", " plt.title('Compare PnL Replication Strategy')\n", " plt.ylabel('PnL')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.1.3'></a>\n", "### 5.1.3 Hedging Error for Black Scholes Replication\n", "Function for Black Scholes Hedge Replication" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "def black_scholes_hedge_strategy(S_0, K, r, vol, T, paths, alpha, output):\n", " bs_price = BlackScholes_price(S_0, T, r, vol, K, 0)\n", " times = np.zeros(paths.shape[0])\n", " times[1:] = T / (paths.shape[0]-1)\n", " times = np.cumsum(times) \n", " bs_deltas = np.zeros((paths.shape[0]-1, paths.shape[1]))\n", " for i in range(paths.shape[0]-1):\n", " t = times[i]\n", " bs_deltas[i,:] = BS_delta(paths[i,:,0], T, r, vol, K, t)\n", " return test_hedging_strategy(bs_deltas, paths, K, bs_price, alpha, output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.2'></a>\n", "## 5.2. Comparison between Black Scholes and Reinforcement Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.2.1'></a>\n", "### 5.2.1. Test at 99% CVaR" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we compare the average PnL and the CVaR of the trading strategies assuming we can charge the Black Scholes price for the option.\n", "\n", "For the first test set (strike 100, same drift, same vol) the results looks quite good." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "S_0 = 100\n", "K = 100\n", "r = 0\n", "vol = 0.2\n", "T = 1/12\n", "timesteps = 30\n", "seed_test = 21122017\n", "n_sims_test = 10000" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [], "source": [ "# Monte Carlo Path for the test set\n", "alpha = 0.99\n", "paths_test = monte_carlo_paths(S_0, T, vol, r, seed_test, n_sims_test, timesteps)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO:tensorflow:Restoring parameters from model.ckpt\n" ] } ], "source": [ "with tf.Session() as sess:\n", " model_1.restore(sess, 'model.ckpt')\n", " #Using the model_1 trained in the section above\n", " test1_results = model_1.predict(paths_test, np.ones(paths_test.shape[1])*K, alpha, sess)" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BS price at t0: 2.3029744678024286\n", "Mean Hedging PnL: -0.0010458505607415178\n", "CVaR Hedging PnL: 1.2447953011695538\n", "BS price at t0: 2.302974467802428\n", "Mean Hedging PnL: -0.0019250998451393934\n", "CVaR Hedging PnL: 1.3832611348053374\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_,_,_,portfolio_pnl_bs, deltas_bs = black_scholes_hedge_strategy(S_0,K, r, vol, T, paths_test, alpha, True)\n", "plt.figure()\n", "_,_,_,portfolio_pnl_rnn, deltas_rnn = test_hedging_strategy(test1_results[2], paths_test, K, 2.302974467802428, alpha, True)\n", "plot_deltas(paths_test, deltas_bs, deltas_rnn)\n", "plot_strategy_pnl(portfolio_pnl_bs, portfolio_pnl_rnn)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.2.2'></a>\n", "### 5.2.2. Changing Moneyness" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO:tensorflow:Restoring parameters from model.ckpt\n" ] } ], "source": [ "with tf.Session() as sess:\n", " model_1.restore(sess, 'model.ckpt')\n", " #Using the model_1 trained in the section above\n", " test_results_Moneyness = model_1.predict(paths_test, np.ones(paths_test.shape[1])*(K-10), alpha, sess)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BS price at t0: 10.07339936955367\n", "Mean Hedging PnL: 0.0007508571761945107\n", "CVaR Hedging PnL: 0.6977526775080665\n", "BS price at t0: 10.073\n", "Mean Hedging PnL: -0.038571546628968216\n", "CVaR Hedging PnL: 3.4732447615593975\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_,_,_,portfolio_pnl_bs, deltas_bs = black_scholes_hedge_strategy(S_0,K-10, r, vol, T, paths_test, alpha, True)\n", "plt.figure()\n", "_,_,_,portfolio_pnl_rnn, deltas_rnn = test_hedging_strategy(test_results_Moneyness[2], paths_test, K-10, 10.073, alpha, True)\n", "plot_deltas(paths_test, deltas_bs, deltas_rnn)\n", "plot_strategy_pnl(portfolio_pnl_bs, portfolio_pnl_rnn)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<a id='5.2.3'></a>\n", "### 5.2.3. Changing Drift" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "# Test set 2: Assume the drift of the underlying is 4% per month under the real world measure \n", "paths_test_drift = monte_carlo_paths(S_0, T, vol, 0.48+r, seed_test, n_sims_test, timesteps)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO:tensorflow:Restoring parameters from model.ckpt\n" ] } ], "source": [ "with tf.Session() as sess:\n", " model_1.restore(sess, 'model.ckpt')\n", " #Using the model_1 trained in the section above\n", " test_results_drift = model_1.predict(paths_test_drift, np.ones(paths_test_drift.shape[1])*K, alpha, sess)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BS price at t0: 2.3029744678024286\n", "Mean Hedging PnL: -0.01723902964827388\n", "CVaR Hedging PnL: 1.2141220199385756\n", "BS price at t0: 2.3029\n", "Mean Hedging PnL: -0.037668804359885316\n", "CVaR Hedging PnL: 1.357201635552361\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_,_,_,portfolio_pnl_bs, deltas_bs = black_scholes_hedge_strategy(S_0,K,r, vol, T, paths_test_drift, alpha, True)\n", "plt.figure()\n", "_,_,_,portfolio_pnl_rnn, deltas_rnn = test_hedging_strategy(test_results_drift[2], paths_test_drift, K, 2.3029, alpha, True)\n", "plot_deltas(paths_test_drift, deltas_bs, deltas_rnn)\n", "plot_strategy_pnl(portfolio_pnl_bs, portfolio_pnl_rnn)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <a id='5.2.4'></a>\n", "### 5.3.4. Shifted Volatility" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [], "source": [ "# Test set 3: Assume the volatility is not constant and the realized volatility is 5% higher \n", "# than the implied (historical observed) one\n", "paths_test_vol = monte_carlo_paths(S_0, T, vol+0.05, r, seed_test, n_sims_test, timesteps)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO:tensorflow:Restoring parameters from model.ckpt\n" ] } ], "source": [ "with tf.Session() as sess:\n", " model_1.restore(sess, 'model.ckpt')\n", " #Using the model_1 trained in the section above\n", " test_results_vol = model_1.predict(paths_test_vol, np.ones(paths_test_vol.shape[1])*K, alpha, sess)" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BS price at t0: 2.3029744678024286\n", "Mean Hedging PnL: -0.5787493248269506\n", "CVaR Hedging PnL: 2.5583922824407566\n", "BS price at t0: 2.309\n", "Mean Hedging PnL: -0.5735181045192523\n", "CVaR Hedging PnL: 2.835487824499669\n" ] }, { "data": { "image/png": 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7u4BdI/VOknTKeCewJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTSwqAJE8n+VaSA0mmWu38JPuTPNG+z2v1JPl4kukkB5O8YzkGIElanOXYA/i1qtpYVZNt/mbg/qraANzf5gGuAja0z3bgjmXYtiRpkU7FIaAtwO42vRu4ZqD+6ZrzAHBukotOwfYlSUNYagAU8MUkjyTZ3mpvrapnAdr3ha2+GnhmYN2ZVnuVJNuTTCWZmp2dXWL3JEknsuBL4Rfwzqo6kuRCYH+Sb5+kbeap1esKVTuBnQCTk5OvWy5JWh5L2gOoqiPt+3ngC8Am4Lnjh3ba9/Ot+QywdmD1NcCRpWxfkrR4iw6AJD+V5C3Hp4ErgEeBvcC21mwbcHeb3gtc364GuhR48fihIknSylvKIaC3Al9Icvx3/rKq/nuSh4E9SW4AvgNc29rvA64GpoGXgPcvYduSpCVadABU1ZPAr85T/7/A5fPUC7hxsduT5rPu5nvH3QXptOWdwJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdWqpzwKSpFNunPd7PH3be8a27VPNPQBJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSp1b8RrAkm4H/BKwC/ryqblvpPmj5+WIW6fSzonsASVYBnwCuAi4Grkty8Ur2QZI0Z6UPAW0Cpqvqyar6f8BdwJYV7oMkiZU/BLQaeGZgfga4ZIX7cEbzUIykYa10AGSeWr2qQbId2N5mf5Dk8VPeq8W5APjbcXdimZ1pYzrTxgNn3pje8OPJx0Ze5Y0wpn80TKOVDoAZYO3A/BrgyGCDqtoJ7FzJTi1Gkqmqmhx3P5bTmTamM208cOaN6UwbD5xeY1rpcwAPAxuSrE/yJmArsHeF+yBJYoX3AKrqWJKbgPuYuwx0V1UdWsk+SJLmrPh9AFW1D9i30ts9Bd7wh6kW4Uwb05k2HjjzxnSmjQdOozGlqhZuJUk64/goCEnqlAGwDJL82ySV5IJx92Wpknw0ycEkB5J8McnPjbtPS5Hkj5N8u43pC0nOHXeflirJtUkOJflhktPiapP5JNmc5PEk00luHnd/lirJriTPJ3l03H0ZlgGwREnWAr8OfGfcfVkmf1xVv1JVG4F7gH8/7g4t0X7gl6vqV4D/Cdwy5v4sh0eBfwl8ddwdWawz9LEwnwI2j7sTozAAlu524Pd5zQ1tp6uq+v7A7E9xmo+rqr5YVcfa7APM3XtyWquqw1X1Rr1Bclhn3GNhquqrwNFx92MUK34V0JkkyXuB71bVN5P5bnI+PSXZAVwPvAj82pi7s5z+NfC5cXdCgI+FeUMwABaQ5G+AfzjPog8DHwKuWNkeLd3JxlRVd1fVh4EPJ7kFuAm4dUU7OKKFxtPafBg4BnxmJfu2WMOM6TS34GNhdOoZAAuoqnfPV0/yT4H1wPG//tcAX0+yqar+zwp2cWQnGtM8/hK4lzd4ACw0niTbgN8ALq/T5LrnEf6NTlcLPhZGp54BsEhV9S3gwuPzSZ4GJqtq3A+BWpIkG6rqiTb7XuDb4+zPUrUXEH0Q+BdV9dK4+6Mf+dFjYYDvMvdYmN8ab5f640lgvdZtSR5NcpC5w1sfGHeHlug/A28B9rdLW//LuDu0VEnel2QG+OfAvUnuG3efRtVOzB9/LMxhYM/p/liYJJ8F/gfwT5LMJLlh3H1aiHcCS1Kn3AOQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkder/AzaCgvCLzT+4AAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_,_,_,portfolio_pnl_bs, deltas_bs = black_scholes_hedge_strategy(S_0,K, r, vol, T, paths_test_vol, alpha, True)\n", "plt.figure()\n", "_,_,_,portfolio_pnl_rnn, deltas_rnn = test_hedging_strategy(test_results_vol[2], paths_test_vol, K, 2.309, alpha, True)\n", "plot_deltas(paths_test, deltas_bs, deltas_rnn)\n", "plot_strategy_pnl(portfolio_pnl_bs, portfolio_pnl_rnn)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(30, 10000)" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deltas_rnn.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**\n", "\n", "The Policy Gradient based model is able to learn a hedging strategy for a particular option without any assumption of the underlying stochastic process.\n", "\n", "We compare the effectiveness of the hedging strategy and compare it to the delta hedging strategy using the Black Scholes Delta. The RL based hedging strategy quite well even when the few input parameters such as risk aversion and drifts were modified. However, RL method wasn’t able to generalize the strategy for options at different moneyness levels. It demonstrates the fact that RL is a data intensive approach, and it is important to train the model with different cases, which becomes more important if model is intended to be used across wide variety of derivatives. As compared to Black Scholes model, there is a significant scope of improvement of the RL based models by training them using a wide variety of instruments with different hyperparameters. It would be interesting to analyze the comparison of the RL based model vs the traditional hedging models for exotic derivatives given the trade-off between these approaches.\n", "\n", "\n" ] } ], "metadata": { "_change_revision": 206, "_is_fork": false, "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }