{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Deep Hedging\n", "\n", "The lecture is devoted to pricing and hedging from a machine learning perspective. First we develop some basic tools from mathematical finance and learn to understand pricing and hedging as questions from convex analysis. Then we consider several machine learning views on it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic principles of pricing and hedging" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We shall first go through basic principles of modeling in mathematical Finance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To model financial market we shall consider a probability space $ (\\Omega,\\mathcal{F},P) $ together with a filtration $ (\\mathcal{F}_t) $.\n", "\n", "We shall denote by $ S^i $ the price of asset $i$ and by $ H^i $ the holdings in asset $i$ (can be any real number here, no market frictions assumed). $ H^i_t $ is fully determined at time $ t- 1 $ with all the information available there.\n", "\n", "First we learn to write portfolio values, i.e. $ V_t = \\sum_{i=0}^d H^i_tS^i_t $ as P & L processes in case the portfolio is self-financing. Self-financing means that\n", "$$\n", "\\sum_{i=0}^d H^i_{t+1}S^i_t = \\sum_{i=0}^d H^i_tS^i_t \\, ,\n", "$$\n", "which in turn leads to\n", "$$\n", "V_{t+1} - V_t = \\sum_{i=0}^d H^i_{t+1} (S^i_{t+1} - S^i_{t}) \\, .\n", "$$\n", "This means that the change in value of the portfolio comes from the change in value of the prices and nothing else." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This formula allows for a simplification. If we divide everything by the value of $S^0$, the price of the $0$-th asset, then in the above sum one term vanishes. We denote $ X^i_t = S^i_t/S^0_t $\n", "When discounted, e.g. by $S^0$, this means\n", "$$\n", "\\frac{V_t}{S^0_t} - \\frac{V_0}{S^0_0} = (H \\bullet X)_t = \\sum_{s \\leq t} \\sum_{i=1}^d H^i_{t+1} (X^i_{s+1} - X^i_{s})\\, .\n", "$$\n", "Notice that the inner sum only starts at $1$ because $ X^0_t = 1 $.\n", "\n", "The right hand side is a P & L process. The argument can be turned around: given a portfolio value which is given by a constant plus a P & L process, then we can of course construct a self-financing portfolio.\n", "\n", "We can ask whether arbitrages are possible and under which conditions (for which price) payoffs can be dominated (super-hedged) by self-financing portfolios." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A model is free of arbitrage if there is no self-financing portfolio which starts at zero and has a positive outcome\n", "\n", "This leads us the valuation problem: what is the value of a payoff $f$ at time $T$? We can answer that by constructing appropriate (super-)hedging portfolios. Superhedging just means \"dominating\".\n", "\n", "Let us consider this question in a one period case, i.e. $T=1$. The states of the world are denoted by $\\omega$, hence we are interested in the question to find the smallest $ x $ such that for all $ \\omega $\n", "$$\n", "f(\\omega) \\leq x + \\sum_{i=1}^d H_0^i (X^i_1(\\omega)-X^i_0(\\omega)) \\, .\n", "$$\n", "This is equivalent to characterize the cone $ C:= \\{ (H \\bullet X)_1 - g \\text{ for all possible strategies } H \\text{ and } g \\geq 0\\} $.\n", "\n", "This is a geometric question: the solution is $ C = \\{ e \\text{ such that } E_Q[e] \\leq 0 \\text{ for all equivalent martingale measures } $Q$\\} $. This yields the beautiful formula\n", "$$\n", "\\sup_{Q \\in \\mathcal{M}} E_Q[f] = \\inf \\{x \\text{ such that there is a strategy } H \\text{ with } f \\leq x + (H \\bullet X)_1 \\} \\, .\n", "$$\n", "The set $\\mathcal{M} $ is the set of equivalent martingale measures. A super-hedging portfolio is a self-financing portfolio (i.e. the value process is the initial value of the portfolio plus the P&L process -- all in discounted terms) dominating a certain payoff.\n", "\n", "We have seen in one step bi- and tri-nomial models that pricing and hedging are in a fundamental duality relationship given a certain payoff: the largest arbitrage free price equals the smallest price of a super-hedging portfolio. Superhedging prices can be calculated by backwards induction.\n", "\n", "### This yields the following pricing formula: if a payoff's contract is liquidly traded at price $ \\pi_t(f) $ at intermediate times $ t $, then there exists an equivalent martingale measure for the given market constituted by $X^1,\\dots,X^d$ such that\n", "$$\n", "E_Q\\big[ \\frac{f}{S^0_T} | \\mathcal{F}_t \\big] = \\frac{\\pi_t(f)}{S^0_t} .\n", "$$\n", "Let us consider these principles in the following modeling situations. Furthermore models are free of arbitrage if and only if there exists an equivalent pricing measure, which associates in particular to P & L processes the value $0$. Whence prices of payoffs can be calculated by taking expectations (i.e. a Monte Carlo evaluation is possible) with respect to this equivalent pricing measure.\n", "\n", "First we draw the tree in undiscounted terms in the format time / numeraire / stock price. For simplicity we take the numeraire equal to $1$ but one can easily adapt that. Next the draw the tree in discounted terms in the format time / price. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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ylEJeXh6WLVtmmBunMucfOnQo9uzZg8zMTOzbtw/BwcFISUnBI488AgDodHlF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\natUSADJr1qwKff7NN9+UQYMGlXtcXFy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"text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from itertools import product\n", "\n", "\n", "# EUROPEAN\n", "S0 = 100.\n", "u = 1.2\n", "d = 0.9\n", "payoffE = lambda S: np.maximum(S-S0,0.)\n", "\n", "timesteps = 2\n", "bin = set((0,1))\n", "trajectories = set(product(bin, repeat = timesteps))\n", "\n", "\n", "import pygraphviz as PG\n", "from IPython.display import Image\n", "binomialtreeforward = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforward.node_attr.update(color='red')\n", "binomialtreeforwarddiscounted = PG.AGraph(directed=True, strict=True)\n", "binomialtreeforwarddiscounted.edge_attr.update(len='2.0',color='blue')\n", "binomialtreeforwarddiscounted.node_attr.update(color='red')\n", "binomialtreebackward = PG.AGraph(directed=True, strict=True)\n", "binomialtreebackward.edge_attr.update(len='2.0',color='blue')\n", "binomialtreebackward.node_attr.update(color='red')\n", "process = {(omega,0):S0 for omega in trajectories}\n", "numeraire = {(omega,0):1. for omega in trajectories}\n", "discountedprocess = {(omega,0):S0 for omega in trajectories}\n", "\n", "#construct process by forward steps\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " process.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " #shelper = process[(omega,time-1)]*u**(omega[time-1])*d**(1.-omega[time-1])\n", " numeraire.update({(omega,time):1.0})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforward.add_edge('%d / %d / %d'% (time-1,numeraire[(omega,time-1)],process[(omega,time-1)]),\n", " '%d / %d / %d'% (time,numeraire[(omega,time)],process[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "Image(binomialtreeforward.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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7/pYtWzB16lRkZWVh7ty5mDt3Lr755hu89957WLdunfXH1IQII0rattXm+PaK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\n8tkaIvR7rV0L/PUXX8vK4nb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"text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "for time in range(0,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time)]/numeraire[(omega,time)]\n", " discountedprocess.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforwarddiscounted.add_edge('%d / %d'% (time-1,discountedprocess[(omega,time-1)]),'%d / %d'% (time,discountedprocess[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "\n", "Image(binomialtreeforwarddiscounted.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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KhFKYzooj5Iuby6VLLIo8fjw7YCoUxUStkjsrc+cCkZHAtGl6S2J9HnyQivKLL4CrV/WW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\n8tkaIvR7rV0L/PUXX8vK4nb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"text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "for time in range(0,timesteps+1):\n", " for omega in trajectories:\n", " shelper = process[(omega,time)]/numeraire[(omega,time)]\n", " discountedprocess.update({(omega,time):shelper})\n", " \n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreeforwarddiscounted.add_edge('%d / %d'% (time-1,discountedprocess[(omega,time-1)]),'%d / %d'% (time,discountedprocess[(omega,time)]))\n", "\n", "#for time in range(1,timesteps+1):\n", "# for omega in trajectories:\n", "# binomialtreeforward.add_edge('%d, %d'% (time-1,numeraire[(omega,time-1)]),'%d, %d'% (time,numeraire[(omega,time)]))\n", "\n", "\n", "Image(binomialtreeforwarddiscounted.draw(format='png',prog='dot')) " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def condprob(omega,time): \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " return (discountedprocess[(omega,time)]-discountedprocess[(omegahelperd,time+1)])/(discountedprocess[(omegahelperu,time+1)]-discountedprocess[(omegahelperd,time+1)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous function calculates the conditional probabilities which make the process at each node a martingale. Finally the price of a Eurpean Call payoff is calculated in a backwards manner. The tree is drawn in the format time / stock price / derivative price." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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dYTLJV9pkKtsI8+WXwPjxNfxBubmSgQJAerpcFhWV7ZKsquwC9PKvMlWVP+XL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\nwoDU7t3cdt111KS0NBpOEogSBO9TVUW7Yc8eatbBg2zVSku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"text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "processbackward = {(omega,timesteps):(payoffE(process[(omega,timesteps)])/numeraire[(omega,timesteps)]) for omega in trajectories}\n", "#backwardssteps: European\n", "for time in reversed(range(0,timesteps)):\n", " for omega in trajectories:\n", " shelper=0 \n", " omegahelperu = list(omega)\n", " omegahelperd = list(omega)\n", " omegahelperu[time]=1\n", " omegahelperd[time]=0\n", " omegahelperu = tuple(omegahelperu)\n", " omegahelperd = tuple(omegahelperd)\n", " shelper = processbackward[(omegahelperu,time+1)]*condprob(omega,time)+processbackward[(omegahelperd,time+1)]*(1-condprob(omega,time))\n", " processbackward.update({(omega,time):shelper})\n", "\n", "for time in range(1,timesteps+1):\n", " for omega in trajectories:\n", " binomialtreebackward.add_edge('%d / %f / %f'% (time-1,discountedprocess[(omega,time-1)],processbackward[(omega,time-1)]),'%d / %f / %f'% (time,discountedprocess[(omega,time)],processbackward[(omega,time)]))\n", "\n", "Image(binomialtreebackward.draw(format='png',prog='dot')) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deep Hedging" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the sequel we construct deep hedges in a high dimensional frictionless market. In principle also transaction costs can be easily added, however, one should change the loss function appropriately.\n", "\n", "The code is based on great work of my master student Michael Giegrich, whose work is based on the paper [Deep Hedging](https://arxiv.org/abs/1802.03042) by Hans Bühler, Lukas Gonon, Josef Teichmann and Ben Wood.\n", "\n", "First a parameter class is defined and several functions needed in the sequel. Then - in tensorflow - a feedforward network with two hidden layers is defined for every time step $ i $ and for every asset $ S^i $ where we need a hedging strategy: Input is the price at time $ i $ _and_ the strategy at time $ i - 1 $, which is due to transaction costs on the one hand or can be seen as way to account for memory effects on the other hand. Be aware that the $L^2$ distance to measure the quality of the hedge is not appropriate in case of transaction costs.\n", "\n", "The loss function is given by\n", "$$\n", "E_Q\\Big[{\\big( Y - (\\delta \\bullet S) - p \\big)}^2\\Big]\n", "$$\n", "where $ Y $ denotes a payoff, $ \\delta $ the strategies to be learnt and $ p $ the price to be learned. $Q$ is an a priori chosen martingale measure.\n", "\n", "For reasons of illustration we actually use correlated Black-Scholes models to generate prices and we use call options on a certain amount of most relevant assets. This allows to easily write down a Black-Scholes hedge." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us recall briefly the Black-Scholes theory: we consider $ d = 1 $, a bank account process $ S^0 = 1 $, and\n", "$$\n", "S_t = S_0 \\exp(\\sigma W_t + \\mu t)\n", "$$\n", "for $ t \\in [0,T] $. $ W $ denotes a Wiener process. $ \\sigma > 0 $ is called the volatility and $ \\mu $ the drift.\n", "\n", "We ask whether we can write a given payoff profile $ f(S_T) $ as a premium plus a hedging portfolio\n", "$$\n", "f(S_T) = x + (H \\bullet S)_T \\,\n", "$$\n", "This formula holds with respect to the physical measure but also any other equivalent measure (if it holds true!), hence we can solve it with respect to martingale measure $ Q \\sim P $.\n", "\n", "The idea to construct the hedging strategy $ H $ comes from Ito's formula. Consider a $C^2$ function $ v $ on $ [0,T] \\times \\mathbb{R}_{> 0} $ with $ v(0,S) = f(S) $, then Ito's formula yields\n", "$$\n", "v(T-t,S_t) = v(T,S_0) = ( \\partial_S v(T-.,S) \\bullet S)_t + ( (- \\partial_t + \\frac{\\sigma^2 S^2}{2} \\partial^2_S)v(T-.,S) \\bullet S)_t \\, .\n", "$$\n", "If we $ v $ satisfies the Black-Scholes PDE\n", "$$\n", "\\partial_t v(t,S) = \\frac{\\sigma^2 S^2}{2} \\partial^2_Sv(t,S)\n", "$$\n", "for $ t in [0,T] $ and $ S > 0 $, we obtain the hedging strategy as so called Delta $ H_t = \\partial v(T-t,S_t) $ and the premium $ x = v(T,S_0) $.\n", "\n", "This PDE can be solved explicitly by calculating\n", "$$\n", "v(T-t,S_t) = E\\big[f(\\exp(\\sigma W_T - \\frac{\\sigma^2T}{2}))|S_t\\big] \\,\n", "$$\n", "which yields for $ f(S):=(S-K)_+ $ the famous Black-Scholes formula\n", "$$\n", "v(u,S) = E((S\\exp(\\sigma W_u - \\sigma^2/2) - K)_+)= S \\Phi(\\frac{\\log(\\frac{S}{K}) + \\frac{\\sigma^2u}{2}}{\\sigma \\sqrt{u}}) - K \\Phi\\Big(\\frac{\\log(\\frac{S}{K} \\Big) -\\frac{\\sigma^2u}{2}}{\\sigma \\sqrt{u}} \\Big) \\, .\n", "$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib64/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] } ], "source": [ "# by Michael Giegrich and Josef Teichmann\n", "\n", "import os\n", "import time\n", "os.environ['TF_CPP_MIN_LOG_LEVEL']='2'\n", "import tensorflow as tf\n", "import numpy as np \n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as ss\n", "\n", "# Set Parameters\n", "np.random.seed(2)\n", "tf.set_random_seed(2)\n", "global_step = tf.Variable(0, trainable=False)\n", "t0 = time.time()\n", "epsilon = 0.\n", "class parameters():\n", " def __init__(self):\n", " self.NUM_EPOCHS = 40\n", " self.TIME_STEPS = 30\n", " self.NUM_ASSETS = 1#50\n", " self.NUM_RELAVENT = 1 \n", " self.NUM_SAMPLES = 500000\n", " self.BATCH_SIZE = 258\n", " self.NUM_BATCHES = self.NUM_SAMPLES // self.BATCH_SIZE\n", " self.hidden_dim1 = 2*self.NUM_ASSETS\n", " self.hidden_dim2 = 2*self.NUM_ASSETS\n", " self.LEARNING_RATE = 0.0005\n", " self.NUM_TEST = 10000\n", " self.training = 1\n", " self.decay = 0.999\n", " self.minimal_loss = 100.0 #Determines if model is saved\n", " self.NUM_VALIDATION = 10000\n", " self.L1_LAMBDA = 0.001 #Parameter for L1-Penalty\n", " self.correlated = True\n", " self.corr = 1\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#############################################\n", "# Generates Model Hedge And Price For Calls #\n", "#############################################\n", "def delta_BS(S, sigma = 0.2, K = 100., r = 0., T =30./365.):\n", " delta_hedge = []\n", " time_steps = int(T*365)\n", " for i in range(time_steps-1):\n", " i_ratio = float(i)/365.\n", " delta = (ss.norm.cdf((np.log(S[:,i]/K) +(r+sigma**2/2)*(T-i_ratio))/(sigma*np.sqrt(T-i_ratio))))\n", " delta_hedge.append(delta)\n", " delta_hedge = np.stack(delta_hedge, axis=1)\n", " return delta_hedge\n", "def d1(S0, K, r, sigma, T):\n", " return (np.log(S0/K) + (r + sigma**2 / 2) * T)/(sigma * np.sqrt(T)) \n", "def d2(S0, K, r, sigma, T):\n", " return (np.log(S0 / K) + (r -sigma**2 / 2) * T) / (sigma * np.sqrt(T)) \n", "def BlackScholes(S0, sigma = 0.2, K = 100., r = 0., T =30./365.):\n", " return (S0 * ss.norm.cdf(d1(S0, K, r, sigma, T)) - K * np.exp(-r * T)* ss.norm.cdf(d2(S0, K, r, sigma, T)))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "import math as m\n", "\n", "####################\n", "# Generate Samples #\n", "####################\n", "def SampleGenerator(NumOfAssets ,corr, NumOfRelevant = 5,InitPrice = 100, rf_rate = 0., dt = 1./365.,TimeSteps = 30, sigma = 0.2, K = 100.):\n", " S0 = np.ones(NumOfAssets)*InitPrice\n", " features = np.zeros((TimeSteps, NumOfAssets))\n", " L = np.linalg.cholesky(corr)\n", " features[0, 0:NumOfAssets] = 0.\n", " features[1, 0:NumOfAssets] = S0\n", " for i in range(2, TimeSteps):\n", " W = m.sqrt(dt)*np.dot(L,np.random.randn(NumOfAssets))\n", " features[i, 0:NumOfAssets] =(features[i-1, 0:NumOfAssets]*np.exp((rf_rate*np.ones(NumOfAssets)-0.5*sigma*sigma)*dt+sigma*W)) \n", " FinalPrices = features[TimeSteps-1, 0:NumOfRelevant]\n", " value = np.maximum(FinalPrices - K, 0) \n", " value = np.sum(value)\n", " return features, value\n", "\n", "###############################\n", "# Generate Correlation Matrix #\n", "###############################\n", "def corr(NumOfAssets):\n", " dim = NumOfAssets\n", " A = np.random.normal(3, 8,size=(dim,dim))\n", " cov = np.dot(A,np.transpose(A))\n", " D = np.identity(dim)/np.sqrt(np.diag(cov))\n", " corr = np.dot(D,np.dot(cov,D))\n", " return corr \n", "\n", "#################\n", "# Generate Data #\n", "#################\n", "def DataGenerator(NumOfSamples, TimeSteps = 30,NumOfAssets = 50, corr = 1, correlated = False,NumOfRelevant = 5):\n", " if not(correlated): \n", " corr = np.eye(NumOfAssets)\n", " features = np.zeros((NumOfSamples, TimeSteps, NumOfAssets))\n", " labels = np.zeros((NumOfSamples))\n", " for i in range(1, NumOfSamples+1):\n", " features[i-1, :, :], labels[i-1] = SampleGenerator(\n", " NumOfAssets, TimeSteps=TimeSteps, corr=corr, \n", " NumOfRelevant = NumOfRelevant)\n", " labels = labels.reshape((NumOfSamples, 1))\n", " return features, labels" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "##########################\n", "# Generate Price Tensors #\n", "##########################\n", "def price(FLAGS):\n", " price = (BlackScholes(100, T = float(FLAGS.TIME_STEPS)/365.)*np.ones((FLAGS.BATCH_SIZE))*FLAGS.NUM_RELAVENT)\n", " q = tf.constant(price, dtype = tf.float32)\n", " return q\n", "def price_test(FLAGS):\n", " price = (BlackScholes(100, T = float(FLAGS.TIME_STEPS)/365.)*np.ones((FLAGS.NUM_TEST))*FLAGS.NUM_RELAVENT)\n", " q = tf.constant(price, dtype = tf.float32)\n", " return q\n", "def price_valid(FLAGS):\n", " price = (BlackScholes(100, T = float(FLAGS.TIME_STEPS)/365.)*np.ones((FLAGS.NUM_VALIDATION))*FLAGS.NUM_RELAVENT)\n", " q = tf.constant(price, dtype = tf.float32)\n", " return q\n", "\n", "###############################\n", "# Functions for Data-Pipeline #\n", "###############################\n", "def generate_data(FLAGS):\n", " X, Y = DataGenerator(FLAGS.NUM_SAMPLES,TimeSteps = FLAGS.TIME_STEPS, corr = FLAGS.corr,correlated = FLAGS.correlated, NumOfAssets = FLAGS.NUM_ASSETS,NumOfRelevant = FLAGS.NUM_RELAVENT)\n", " return X, Y\n", "def generate_test_data(FLAGS):\n", " X, Y = DataGenerator(FLAGS.NUM_TEST,TimeSteps = FLAGS.TIME_STEPS, corr = FLAGS.corr,correlated = FLAGS.correlated, NumOfAssets = FLAGS.NUM_ASSETS,NumOfRelevant = FLAGS.NUM_RELAVENT)\n", " return X, Y\n", "def generate_validation_data(FLAGS):\n", " X, Y = DataGenerator(FLAGS.NUM_VALIDATION,TimeSteps = FLAGS.TIME_STEPS, corr = FLAGS.corr,correlated = FLAGS.correlated, NumOfAssets = FLAGS.NUM_ASSETS,NumOfRelevant = FLAGS.NUM_RELAVENT)\n", " return X, Y \n", "def generate_batch(FLAGS, raw_data):\n", " raw_X, raw_y = raw_data\n", " # Create Batches from Raw Data\n", " num_batches = FLAGS.NUM_SAMPLES // FLAGS.BATCH_SIZE \n", " data_X = np.zeros([FLAGS.BATCH_SIZE, FLAGS.NUM_ASSETS,FLAGS.TIME_STEPS], dtype=np.float32)\n", " data_y = np.zeros([FLAGS.BATCH_SIZE], dtype=np.float32)\n", " for i in range(num_batches):\n", " data_X = (raw_X[FLAGS.BATCH_SIZE * i:FLAGS.BATCH_SIZE * (i+1), :, :])\n", " data_y = raw_y[FLAGS.BATCH_SIZE * i:FLAGS.BATCH_SIZE * (i+1)]\n", " yield (data_X, data_y)\n", "def generate_epochs(FLAGS):\n", " for i in range(FLAGS.NUM_EPOCHS):\n", " yield generate_batch(FLAGS, FLAGS.data)\n", "\n", "#######################\n", "# Batch Normalization #\n", "#######################\n", "def batch_norm(FLAGS, x, name):\n", " with tf.variable_scope(name, reuse=tf.AUTO_REUSE):\n", " if FLAGS.training==2:\n", " FLAGS.decay = 0\n", " elif FLAGS.training==3:\n", " FLAGS.decay = FLAGS.NUM_SAMPLES/(FLAGS.NUM_SAMPLES\n", " +FLAGS.NUM_TEST)\n", " param_shape = [x.get_shape()[-1]]\n", " batch_mean, batch_var = tf.nn.moments(x, [0], name='moments')\n", " pop_mean = tf.get_variable('moving_mean', param_shape,tf.float32, initializer=tf.constant_initializer(0.0),trainable=False)\n", " pop_var = tf.get_variable('moving_variance', param_shape,tf.float32, initializer=tf.constant_initializer(1.0),trainable=False)\n", " train_mean_op = tf.assign(pop_mean, pop_mean * FLAGS.decay + batch_mean * (1 - FLAGS.decay))\n", " train_var_op = tf.assign(pop_var, pop_var * FLAGS.decay + batch_var * (1 - FLAGS.decay))\n", " if FLAGS.training==1:\n", " with tf.control_dependencies([train_mean_op, train_var_op]):\n", " return tf.nn.batch_normalization(x, batch_mean, batch_var, 0, 1, 1e-3)\n", " elif FLAGS.training==2:\n", " with tf.control_dependencies([train_mean_op, train_var_op]):\n", " return tf.nn.batch_normalization(x, batch_mean, batch_var, 0, 1, 1e-3)\n", " elif FLAGS.training==3:\n", " with tf.control_dependencies([train_mean_op, train_var_op]):\n", " return tf.nn.batch_normalization(x, pop_mean,pop_var, 0, 1, 1e-3)\n", "\n", "###################\n", "# Define RNN Cell #\n", "###################\n", "def rnn_cell(FLAGS, rnn_input, state, name):\n", " with tf.variable_scope('rnn_cell'+ str(name), reuse=True):\n", " input_ = tf.concat( [rnn_input, state], axis = 1)\n", " W1 = tf.get_variable('W1',[FLAGS.NUM_ASSETS*2, FLAGS.hidden_dim1],initializer=tf.random_normal_initializer(stddev=0.1))\n", " b1 = tf.get_variable('b1', [FLAGS.hidden_dim1],initializer=tf.constant_initializer(0.0))\n", " W2 = tf.get_variable('W2',[FLAGS.hidden_dim1, FLAGS.hidden_dim2],initializer=tf.random_normal_initializer(stddev=0.1))\n", " b2 = tf.get_variable('b2', [FLAGS.hidden_dim2],initializer=tf.constant_initializer(0.0))\n", " W3 = tf.get_variable('W3',[FLAGS.hidden_dim2, FLAGS.NUM_ASSETS], initializer=tf.random_normal_initializer(stddev=0.1))\n", " b3 = tf.get_variable('b3', [FLAGS.NUM_ASSETS],initializer=tf.constant_initializer(0.0))\n", " input_ = batch_norm(FLAGS, input_, 'Layer_0')\n", " out1 = tf.matmul(input_, W1) + b1\n", " hidden_out1 = tf.nn.relu(out1)\n", " out2 = batch_norm(FLAGS, hidden_out1, 'Layer_1')\n", " out2 = tf.matmul(out2, W2) + b2\n", " hidden_out2 = tf.nn.relu(out2)\n", " output =tf.matmul(hidden_out2, W3) + b3\n", " return output, W3, b3, W2, b2, W1, b1\n", "\n", "#########################\n", "# Define Loss Functions #\n", "#########################\n", "def QuadraticHedgingLossRegularized(FLAGS, outputs,W3, b3,\n", " W2, b2, W1, b1, y, X, q):\n", " PriceChanges = X[:, 1:, :] - X[:, :-1, :]\n", " PortfolioValue = tf.reduce_sum(tf.reduce_sum(tf.multiply(PriceChanges, outputs), axis=1),axis=1)\n", " one = tf.ones(tf.squeeze(y).shape, dtype = tf.float32)\n", " penalization = (tf.reduce_sum(tf.abs(W3), [0,1,2])+tf.reduce_sum(tf.abs(b3),[0,1])+tf.reduce_sum(tf.abs(W2),[0,1,2])+tf.reduce_sum(tf.abs(b2),[0,1])+tf.reduce_sum(tf.abs(W1),[0,1,2])+tf.reduce_sum(tf.abs(b1),[0,1]))\n", " loss = tf.reduce_mean(tf.square(PortfolioValue - tf.squeeze(y)+ q*one)) + FLAGS.L1_LAMBDA*penalization\n", " return loss\n", "def QuadraticHedgingLoss(FLAGS, outputs, y, X, q):\n", " PriceChanges = X[:, 1:, :] - X[:, :-1, :]\n", " PriceChanges = PriceChanges[:,1:,:] # normalize first entry to one\n", " helper0 = 0.05*X[:,1:2,:] # normalize first entry to one\n", " PriceChanges = tf.concat([helper0,PriceChanges],axis=1) # normalize first entry to one\n", " Prices = X[:,1:,:]\n", " #print(Prices.shape)\n", " StrategyChangeshelper = outputs[:,1:,:]-outputs[:,:-1,:]\n", " StrategyChangeshelper = StrategyChangeshelper[:,1:,:]\n", " #print(StrategyChangeshelper.shape)\n", " helper1=outputs[:,1:2,:]\n", " helper2=outputs[:,FLAGS.TIME_STEPS-2:FLAGS.TIME_STEPS-1,:]\n", " x = tf.zeros(helper1.shape,dtype=tf.float32)\n", " StrategyChanges=tf.concat([helper1, StrategyChangeshelper, helper2],axis=1)\n", " #print(StrategyChanges.shape)\n", " PortfolioValue = tf.reduce_sum(\n", " tf.reduce_sum(tf.multiply(PriceChanges,outputs),axis=1),axis=1)\n", " TransactionCost = tf.reduce_sum(\n", " tf.reduce_sum(tf.multiply(tf.abs(Prices),tf.abs(StrategyChanges)),axis=1),axis=1)\n", " one = tf.ones(tf.squeeze(y).shape, dtype = tf.float32)\n", " loss = tf.reduce_mean(tf.square(PortfolioValue - epsilon*TransactionCost - tf.squeeze(y) + 0.0*q*one))\n", " return loss\n", "# Calculate Portfolio Losses\n", "def HedgingLossNP(outputs, y, X, p):\n", " PriceChanges = X[:, 1:, :] - X[:, :-1, :]\n", " PriceChanges[:,0,:] = 0.05*PriceChanges[:,0,:] # normalize first entry to one\n", " Prices = X[:,1:,:]\n", " StrategyChangeshelper = outputs[:,1:,:]-outputs[:,:-1,:]\n", " StrategyChangeshelper = StrategyChangeshelper[:,1:,:]\n", " helper1=outputs[:,1:2,:]\n", " helper2=outputs[:,FLAGS.TIME_STEPS-2:FLAGS.TIME_STEPS-1,:]\n", " x = np.zeros(helper1.shape)\n", " StrategyChanges=np.concatenate([helper1, StrategyChangeshelper, helper2],axis=1)\n", " TransactionCost = np.sum(np.sum(np.abs(Prices)*np.abs(StrategyChanges),axis=1),axis=1)\n", " PortfolioValue = np.sum(np.sum(PriceChanges*outputs,axis=1),axis=1)\n", " one = np.ones(np.squeeze(y).shape, dtype = np.float32)\n", " loss = PortfolioValue + 0.0*p*one-np.squeeze(y)-epsilon*TransactionCost\n", " return loss \n", "\n", "def HedgingLossNPcum(outputs, y, X, p):\n", " PriceChanges = X[:, 1:, :] - X[:, :-1, :]\n", " PriceChanges[:,0,:] = 0.05*PriceChanges[:,0,:] # normalize first entry to one\n", " Prices = X[:,1:,:]\n", " StrategyChangeshelper = outputs[:,1:,:]-outputs[:,:-1,:]\n", " StrategyChangeshelper = StrategyChangeshelper[:,1:,:]\n", " helper1=outputs[:,1:2,:]\n", " helper2=outputs[:,FLAGS.TIME_STEPS-2:FLAGS.TIME_STEPS-1,:]\n", " x = np.zeros(helper1.shape)\n", " StrategyChanges=np.concatenate([helper1, StrategyChangeshelper, helper2],axis=1)\n", " TransactionCost = np.cumsum(np.sum(np.abs(Prices)*np.abs(StrategyChanges),axis=2),axis=1)\n", " #TransactionCost = TransactionCost[:,1:]\n", " PortfolioValue = np.cumsum(np.sum(PriceChanges*outputs,axis=2),axis=1)\n", " one = np.ones(np.squeeze(PortfolioValue.shape), dtype = np.float32)\n", " loss = PortfolioValue + 0.0*p*one - epsilon*TransactionCost\n", " return loss \n", "\n", "######################\n", "# Define Model Class #\n", "######################\n", "class model(object):\n", " def __init__(self, FLAGS):\n", " #Placeholder for Data\n", " self.X = tf.placeholder(tf.float32, \n", " [FLAGS.BATCH_SIZE, FLAGS.TIME_STEPS, FLAGS.NUM_ASSETS],\n", " name='input_placeholder')\n", " self.y = tf.placeholder(tf.float32, [FLAGS.BATCH_SIZE],\n", " name='labels_placeholder')\n", " self.X_train = tf.placeholder(tf.float32, \n", " [FLAGS.NUM_SAMPLES, FLAGS.TIME_STEPS, FLAGS.NUM_ASSETS],\n", " name='input_train_placeholder')\n", " self.X_valid = tf.placeholder(tf.float32, \n", " [FLAGS.NUM_VALIDATION, FLAGS.TIME_STEPS, FLAGS.NUM_ASSETS],\n", " name='valid_input_placeholder')\n", " self.y_valid = tf.placeholder(tf.float32,[FLAGS.NUM_VALIDATION], name='valid_labels_placeholder')\n", " self.X_test = tf.placeholder(tf.float32, \n", " [FLAGS.NUM_TEST, FLAGS.TIME_STEPS, FLAGS.NUM_ASSETS],\n", " name='test_input_placeholder')\n", " self.y_test = tf.placeholder(tf.float32, [FLAGS.NUM_TEST],\n", " name='test_labels_placeholder')\n", " # Define RNN Cell\n", " self.initial_state = tf.zeros([FLAGS.BATCH_SIZE,FLAGS.NUM_ASSETS])\n", " for i in range(0, FLAGS.TIME_STEPS-1):\n", " with tf.variable_scope('rnn_cell'+ str(i)):\n", " W1 = tf.get_variable('W1',\n", " [FLAGS.NUM_ASSETS*2, FLAGS.hidden_dim1])\n", " b1 = tf.get_variable('b1', [FLAGS.hidden_dim1],\n", " initializer=tf.constant_initializer(0.0))\n", " W2 = tf.get_variable('W2',\n", " [FLAGS.hidden_dim1, FLAGS.hidden_dim2])\n", " b2 = tf.get_variable('b2', [FLAGS.hidden_dim2],\n", " initializer=tf.constant_initializer(0.0))\n", " W3 = tf.get_variable('W3',\n", " [FLAGS.hidden_dim2, FLAGS.NUM_ASSETS])\n", " b3 = tf.get_variable('b3', [FLAGS.NUM_ASSETS],\n", " initializer=tf.constant_initializer(0.0))\n", "\n", " # Build Network Graph\n", " state = self.initial_state\n", " weights3 = []\n", " bias3 = []\n", " weights2 = []\n", " bias2 = []\n", " weights1 = []\n", " bias1 = []\n", " rnn_outputs = []\n", " for i in range(0, FLAGS.TIME_STEPS-1):\n", " FLAGS.counter = i\n", " state, weight_matrix3, bias_vector3, weight_matrix2, bias_vector2, weight_matrix1, bias_vector1 = rnn_cell(FLAGS, self.X[:, i, :], state, name=i)\n", " rnn_outputs.append(state)\n", " weights3.append(weight_matrix3)\n", " bias3.append(bias_vector3)\n", " weights2.append(weight_matrix2)\n", " bias2.append(bias_vector2)\n", " weights1.append(weight_matrix1)\n", " bias1.append(bias_vector1)\n", " rnn_outputs = tf.stack(rnn_outputs, axis=1)\n", " weights3 = tf.stack(weights3, axis=1)\n", " bias3 = tf.stack(bias3, axis=1)\n", " weights2 = tf.stack(weights2, axis=1)\n", " bias2 = tf.stack(bias2, axis=1)\n", " weights1 = tf.stack(weights1, axis=1)\n", " bias1 = tf.stack(bias1, axis=1) \n", " self.hedging_weights = rnn_outputs\n", " self.test = rnn_outputs\n", "\n", " #Build Loss Graph and Optimization Step\n", " self.q = price(FLAGS) \n", " self.total_loss = QuadraticHedgingLoss(FLAGS,self.hedging_weights, self.y, self.X, self.q)\n", " #QuadraticHedgingLossRegularized(FLAGS, self.hedging_weights, weights3, bias3, weights2, bias2,weights1, bias1, self.y, self.X, self.q)\n", " optimizer = tf.train.AdamOptimizer(FLAGS.LEARNING_RATE)\n", " self.quad_loss = QuadraticHedgingLoss(FLAGS,self.hedging_weights, self.y, self.X, self.q)\n", " self.train_step = optimizer.minimize(self.total_loss,global_step = global_step)\n", " \n", " def step(self, sess, batch_X, batch_y):\n", " input_feed = {self.X: batch_X,\n", " self.y: np.squeeze(batch_y)}\n", " output_feed = [self.hedging_weights,\n", " self.total_loss,\n", " self.quad_loss,\n", " self.train_step,\n", " self.q\n", " ]\n", " outputs = sess.run(output_feed, input_feed)\n", " return (outputs[0], outputs[1], outputs[2],outputs[3], outputs[4])\n", "\n", " # Graphs for Sampling\n", " def sample_train(self, FLAGS):\n", " initial_state = tf.zeros(\n", " [FLAGS.NUM_SAMPLES, FLAGS.NUM_ASSETS])\n", " hedging_weights = []\n", " state = initial_state\n", " for i in range(0, FLAGS.TIME_STEPS-1):\n", " FLAGS.counter = i\n", " state,_,_,_,_,_,_ = rnn_cell(FLAGS,self.X_train[:, i, :], state, name = i)\n", " hedging_weights.append(state)\n", " hedging_weights = tf.stack(hedging_weights, axis = 1)\n", " return hedging_weights\n", "\n", " def sample(self, FLAGS):\n", " initial_state = tf.zeros([FLAGS.NUM_TEST, FLAGS.NUM_ASSETS])\n", " hedging_weights = []\n", " state = initial_state\n", " for i in range(0, FLAGS.TIME_STEPS-1):\n", " FLAGS.counter = i\n", " state,_,_,_,_,_,_ = rnn_cell(FLAGS,self.X_test[:, i, :], state, name = i)\n", " hedging_weights.append(state)\n", " hedging_weights = tf.stack(hedging_weights, axis = 1)\n", " return hedging_weights\n", "\n", " def sample_validate(self, FLAGS):\n", " initial_state = tf.zeros(\n", " [FLAGS.NUM_VALIDATION, FLAGS.NUM_ASSETS])\n", " hedging_weights = []\n", " state = initial_state\n", " for i in range(0, FLAGS.TIME_STEPS-1):\n", " FLAGS.counter = i\n", " state,_,_,_,_,_,_ = rnn_cell(FLAGS, \n", " self.X_valid[:, i, :], state, name = i)\n", " hedging_weights.append(state)\n", " hedging_weights = tf.stack(hedging_weights, axis = 1)\n", " return hedging_weights\n", "\n", "# Intializes Model\n", "def create_model(sess, FLAGS):\n", " char_model = model(FLAGS)\n", " sess.run(tf.global_variables_initializer())\n", " return char_model" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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ik9GfnPxroCbuS7mPZ37zDB/88AGjPhwFeO7CbpnE2ERaN2gdMMHvLxd2yxvW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\nN8aYIGPBb4wxQeb/A+f9U53w0/vXAAAAAElFTkSuQmCC\n", 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NOp2v9Q4wxqwFuuzuGGMeAR4JVqNU731aemDgZ4NcODGXn721h1W7HdxQPKLH\nr/vooL+qZHE/bqZ25vriETQ0efnB67tIjNtOZZ2bgozEoL+PUpFKV6hahCOEG2N355y8VPLTE3mv\nrHdDMyWHqhmfl0JmcmgWXd26cDT/uGw8r2w+xu5PXDrHXQ0qGu4W4XB5sIl/DHygiQgXTszl7/tP\n9rjeeovXx6bD1f2aAtkT91w4lhWLxwDh+a1GqXDRcLeIyjo3OanxxITphuHSCbmcbvay/kDP7qPv\nqKijocn7mc05QkFEuP/SCfz8uum9GjJSKtppuFvEQC9gam/emCyS7DG8t7tnUyJLDvr/JxDMmTKd\nERGunlXA0DTtuavBQ8PdIga69EB7CXExLBybzaoyR482s95wqJox2ck6VKJUiGi4W4TD5Qn5Dkzd\nuXBiLhW1bspOdF2C1+szbDhcHfIhGaUGMw13C2hq8VHd0BTyjbG7c8GEXABWdTM0U3aiDpe7JeQ3\nU5UazDTcLaC1KFY4pkG2lZuawPSCNN7rZrVqySH//HbtuSsVOhruFjCQOzB1Z+mEPLYcreFkfcel\nd8F/M3VEZhLD0nRRkVKhouFuAZG0EcWFE3MxBlZ30nv3tY63D8AsGaUGMw13CxjIjbG7M3n4EPKG\nxHdaSGyfo56axuYBmQKp1GCm4W4BDpebGJuQFaJl/L3h31s1jw/3OvG0nL1ateSQf377vDF6M1Wp\nUNJwt4DKOn/Fw0gpZ7tsYi4NTV42BG6ctlVysJrhaQlaxEupENNwt4DKOnfY57i3taAom/hY21mF\nxIwxlByqYu6YLALl/5VSIaLhbgGOOg95EXAztVWiPYbzxmbz3u7Kz6xWPeBs4GR9k95MVWoAaLhb\nQKXLHXEbP184MZej1afZ76g/81jrePtcHW9XKuQ03KOcp8VLTWNz2Fentrc0sFq17YKmDYeqyUmN\nZ1RWUriapdSgEXXhXudu5sO9Tlq8vnA3JSI4ImgaZFvD0hKZNGwI7wU2zjbGUHLQP79dx9uVCr2o\nC/fVux189bcb2Nfm1/3BzOEKbK8XYcMy4J81s+nIKU41NFFe3cgndW4dklFqgERduE/NTwNg+7Ha\nMLckMkTSAqb2lk7Mw2fgg71OSgL7pc7Tm6lKDYioC/dRWcmkJsSy7XhNuJsSET7dGDvyeu7T8tPI\nTonn3bJKPjpURVaynbG5KeFullKDQmy4G9BbNpswNT9Ne+4BDpeHuBghIyn8q1Pbs9mEpRNy+NuO\nT0iNj6U6I5S1AAAOgUlEQVRYx9uVGjBR13MHmFqQRtkJF00telPVvwNTQsSsTm1v6YQ8XO4WKmrd\nOr9dqQEUleE+LT+dJq+PPZ90vePPYOCo80TkzdRWi8ZlY4/x/zMr1s05lBow0RnuBf6bqlYbd++o\n0FZ3KuvcETfHva3k+FjmF2WRnhTHhKGp4W6OUoNGVIZ7QUYi6Ulxlhp3P1nvYeFPV/Pzd/b26nX+\nujKR23MH+OFVU/jd1+ZE7NCRUlYUleEu4r+pus1C4f6Ld/fidHl44sMDZ+aud8fd7KXO3RKR0yDb\nKsxMYuaIjHA3Q6lBJSrDHfxDM3srXbibez+UEWn2Vrp4oaScZRPzaPYaHv/gYI9e17o6NRKnQSql\nwqvbcBeRQhFZLSJlIrJTRO7t4BgRkV+KyH4R2SYis0LT3E9NzU+nxWcoO1EX6rcKuR+/UUZyfCwP\nXTONL8zM5/cfHTmzdV5XKl2Rs3eqUiqy9KTn3gLcZ4yZCMwD7haRSe2OuRQYF/haATwW1FZ2YHph\nYKXq8egemvlgr5P39zi5Z+k4MpPtfHPpWFp8hl+/f6Db10bSxthKqcjSbbgbY04YYzYHvncBZUB+\nu8OWA88Zv4+AdBEZFvTWtjF0SALZKfFRPe7e4vXxo//bxYjMJL66YCQAI7OS+eKsfF7YUM4ntV33\n3j8tPaDDMkqpz+rVmLuIjAJmAiXtnsoHjrb5+zHO/h8AIrJCREpFpNTpdPaupWefi2kF0b1S9eXS\nY+ytrOf+SycQHxtz5vFvLh2Hz2d47P39Xb7eUefGHmsjLTEu1E1VSkWZHoe7iKQArwDfMsa0H+ju\naI6bOesBY54wxsw2xszOycnpXUs7MDU/jX0OF41NLf0+10BzuZv5+Tt7mDMqg0umDP3Mc4WZSVw7\nu4AXNxylouZ0p+dwuPx7p+qSfqVUez0KdxGJwx/szxtj/tzBIceAwjZ/LwAq+t+8rk0rSMNnYGdF\n9N1Ufez9A5ysb+LfL5/UYTjffcFYDIZfd9F7r6xz63i7UqpDPZktI8DTQJkx5uedHPYq8NXArJl5\nQK0x5kQQ29mh1vK/0TbufuxUI0+tPcQXZuYzvTC9w2MKMpK4dnYhL208yvFOeu/+cNfxdqXU2XrS\ncz8PuAlYKiJbAl+XicgdInJH4Jg3gIPAfuBJ4K7QNPezcockMHRIAtuPRVcZgofe3IMA37n4nC6P\nu/uCsQA8urrj3rujzkNuBJceUEqFT7clf40xa+l4TL3tMQa4O1iN6o2pBWlsi6LpkJvLT/Hq1gq+\nuXQsw9MTuzw2Pz2R6+eM4MUN5dx5fhGFmZ/uPdrY1ILL0xLxpQeUUuERtStUW03LT+OgswGXuznc\nTemWMYYfvr6LnNR47ji/qEevueuCImwiZ/Xez+ydqj13pVQHoj7cpwYqRO44Hvk3Vf9v+wk2l9fw\n7YvGkxzfs31ShqUlckNxIX/adIyj1Y1nHtcFTEqprkR9uE8r8N+Q3B7h5X/dzV5++uZuJgxN5Zpz\nC7t/QRt3XTAWm0341ap9Zx6rdOkCJqVU56I+3DOT7RRkJEb8jJln1x3maPVp/v3yScT0svRt3pAE\nvlw8glc2H+fwyQaAM7VncrXnrpTqQNSHO/jnu0dyuFfVe3hk1X4unJDLwnHZfTrHXUuKiLUJv1rl\nH3uvrHMTH2tjSELUbYOrlBoAlgj3qfnplFc3UtPYFO6mdOgX7+6jsdnL/ZdN7PM5cockcOO8kfzl\n42McOtmAw+Uhb0iCrk5VSnXIEuHeuu1eJFaI3Ffp4oUN5dw4dwRjc1P6da47zi/CHmvjl+/t0wVM\nSqkuWSLcpwyP3JWqP3qjjCR7DPcuG9/vc+WkxnPTvJGs3HKcXRV1Ot6ulOqUJcI9LSmOUVlJEVch\nsrVW+zeXjiUz2R6Uc95+fhHxsTH+7fV0jrtSqhOWCHeAqQXpETUs0+L18cPXdzEyK4mbF4wK2nmz\nU+LP1H7XYRmlVGcsE+7T8tM4XnOak/WecDcFgBc3HmWfo577L534mVrtwXD74iJmjUhnzujMoJ5X\nKWUd1gn3CLqpWnu6mYff2cvc0ZlcPDkv6OfPTLbz57vOY9aIjKCfWyllDZYJ98n5aYjAtqPhD/dH\nVu3jVGMT/3FFx7XalVIq1CwT7inxsRTlpIS9DMHhkw08s+4w155bwJRAvXmllBpolgl38I+7h3s6\n5H/+rYy4GBvfvqjrWu1KKRVKlgr3qQVpOFyeMxUTB9r6A1W8tbOSu5YU6Rx0pVRYWSrcW2+q9qX3\nvunIKZ5eewif76x9vXvE6zP84PVd5Kcn8vVFY/p0DqWUChZLhfukYWnYhF5vu+dyN3Pn7zfxg9d3\n8Y8vb6Gpxdfr935l0zF2najjXy6dQEJccKc+KqVUb1kq3BPtMYzPS+31tnsPv7MPZ72HG4pHsHJL\nBbc9V0pjU0uPX1/vaeFnb+9h1oh0Pj9tWG+brZRSQWepcAeYmp/G9mO1+Ld17d7OilqeWXeILxeP\n4D+vnspPvziVNfuc3PhUSY+rTP7m/QM4XR6d+qiUihiWC/dpBWlUNTRRUdv9TVWfz/Aff91BRpKd\nf754AgBfmjOCX3/lXHZU1HHd4+v5pJvzHDvVyBNrDnLVjOHM1EVFSqkIYcFw92+7t+1o9+PuL5ce\nZXN5Df962UTSkuLOPH7JlKE8c8scKmrcfPGxdRx01nd6jp++uQebwD9fMqH/jVdKqSCxXLhPGJZK\nXIx0O+5e3dDET97cTfHoTK6elX/W8wuKsvnDinm4m71c+5v1HVac3HSkmte2VrBi0RiGpycG7RqU\nUqq/LBfu8bExnDM0tdvyvz/5Wxn17hZ+eNWUTsfJp+Sn8cc75pMQF8MNT37EugMnzzzn8xkefL2M\n3NR4bj+/KKjXoJRS/WW5cAf/tnvbjtV0elO19HA1L5ce49ZFoxmfl9rlucbkpPDKnQsYnp7A1367\nkTd3nADg1a0VbD1awz9fMoHkeN3HVCkVWSwZ7tMK0qhzt1Be3XjWc81eH//2lx0MT0vg3gvH9eh8\nQ9MSePn2+UzJH8Jdz2/m2XWH+embu5man8bVM88e0lFKqXCzZLhPze98peozfz/MnkoXD1w5mSR7\nz3vc6Ul2fv/1uSwal8MDr+7kRK2b/7hiEjabTn1USkWebsNdRH4rIg4R2dHJ80tEpFZEtgS+vhf8\nZvbO+LxU7LG2s2q7n6g9zcPv7uXCCblcNKn3ddaT7LE8+dXZfHX+SG5bNJpi3SxDKRWhetJ1fQZ4\nBHiui2PWGGOuCEqLgsAea2PisCFsa1eG4MHXduH1Gb5/5eQ+Lzayx9p4cPmUYDRTKaVCptueuzHm\nQ6B6ANoSVNPy09hxvO5MIbDVexz8bccnfHPpWAozk8LcOqWUCq1gjbnPF5GtIvI3EZkcpHP2y7SC\nNOo9LRw82YC72csDK3cyJieZ2xZrxUallPUFYw7fZmCkMaZeRC4D/gp0OA1FRFYAKwBGjBgRhLfu\nXOtK1e3Ha3h1awXl1Y288PW5Qd+sWimlIlG/e+7GmDpjTH3g+zeAOBHJ7uTYJ4wxs40xs3Nycvr7\n1l0qykkmMS6G17ae4DfvH2D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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1729061007499695\n", "Epoch 0, Loss: 12.482\n", "Unregularized Loss: 12.482\n", "Validate Loss: 4.020\n" ] }, { "data": { "image/png": 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Lw/s5YLGI3uVd1CrrvNh5tAI7iyux40jzz9MX41kEWHH3ZGSmxOlcpTkx2A2OFyl1XYPX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\nsJtIbK9wRIRZTDm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.203982323408127\n", "Epoch 1, Loss: 3.661\n", "Unregularized Loss: 3.661\n", "Validate Loss: 3.299\n" ] }, { "data": { "image/png": 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BYmYiAAfOHpCuGSEMEp8eT+uA1nRs1tHoUuqtznBXSoUqpbYrpY4ppY4opZ6p5hillHpH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\nQga3G0zfNn3rW3K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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.197788804769516\n", "Epoch 2, Loss: 3.055\n", "Unregularized Loss: 3.055\n", "Validate Loss: 2.770\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.202514559030533\n", "Epoch 3, Loss: 2.600\n", "Unregularized Loss: 2.600\n", "Validate Loss: 2.367\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.209967076778412\n", "Epoch 4, Loss: 2.266\n", "Unregularized Loss: 2.266\n", "Validate Loss: 2.107\n" ] }, { "data": { "image/png": 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Xvrn3m8tOcVSuFRVUeOauFzI5V4Ep4NHPC9ePeeamZ67ouRFBETzW/jHmbpnL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\nWu5KKeWB/h/6o3LxbcIACAAAAABJRU5ErkJggg==\n", 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Yrd0w3XwR/nlA1ZD7pz2PjbiNMcYFtALpPth3xBpc0UsbvA3YW9nEnPR4spJs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\nNT6ayxZk+mpYSqkgo+EfZga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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.207842767238617\n", "Epoch 5, Loss: 1.996\n", "Unregularized Loss: 1.996\n", "Validate Loss: 1.822\n" ] }, { "data": { "image/png": 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BYmYiAAfOHpCuGSEMEp8eT+uA1nRs1tHoUuqtznBXSoUqpbYrpY4ppY4opZ6p5hillHpH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\nQga3G0zfNn3rW3K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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.209264785051346\n", "Epoch 6, Loss: 1.764\n", "Unregularized Loss: 1.764\n", "Validate Loss: 1.665\n" ] }, { "data": { "image/png": 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XX0L8QwyLwZEkudvJkn1LCPQNdOuFidpzTdQ1zBw8kzd3vklVXZXR4Vjl00Of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\nm31mbd4buNHn1h5XS+6qnftcp67UuYl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.207951098680496\n", "Epoch 7, Loss: 1.567\n", "Unregularized Loss: 1.567\n", "Validate Loss: 1.446\n" ] }, { "data": { "image/png": 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HNz6K6SHT8frk15UuC10cuuDh8Iex7tg6nLp4qt2P/+rQV3hr11t4bORjJh3R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\nvmXwY/p49MHO+3YiOjgaS35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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2038696706295013\n", "Epoch 8, Loss: 1.340\n", "Unregularized Loss: 1.340\n", "Validate Loss: 1.315\n" ] }, { "data": { "image/png": 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HZ/wQuTCGvwcIDwxHt+Bu9Q7/wpJCpOSmXNHvr8QZP0SujeHvIRIiErA+a3297uu7KXsT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\n4Y1b3sDMoTNrPWs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w0vEW3vf9V6ltPR/pakU1DX8VFQKbu4Sj3X9XTRtnuwa4fs3MN/mM5/bNJXT3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\nr/yVUkqNI+rCX0SuFZFjIlI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2042720019817352\n", "Epoch 9, Loss: 1.129\n", "Unregularized Loss: 1.129\n", "Validate Loss: 1.077\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.203870266675949\n", "Epoch 10, Loss: 0.981\n", "Unregularized Loss: 0.981\n", "Validate Loss: 0.931\n" ] }, { "data": { "image/png": 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PX4yXu5fRkYSolKTQhVk+2PwBL615iQdbP8iPD/6Ip5un0ZGEqLSk0EWFaK2Z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\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.203322649002075\n", "Epoch 11, Loss: 0.863\n", "Unregularized Loss: 0.863\n", "Validate Loss: 0.795\n" ] }, { "data": { "image/png": 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EZabEDUUeF5EkEUnKyNCpx5Qqrm39tky9ZyoGw8xtM+267+dXPs8b379h130q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\nAytC/jkSp+e4AAAAAElFTkS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2026705741882324\n", "Epoch 12, Loss: 0.765\n", "Unregularized Loss: 0.765\n", "Validate Loss: 0.734\n" ] }, { "data": { "image/png": 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wMjzxwfFwtXM16eyS6qZq7Du7D2si10DBzN9dUzAF5gbNxYFzB0S/gs2uyIaD\njQNCPQbeZcmwsYK1r1vS1yqKxnpu5nOwt7HHTP+ZAlQmb0P6KWSMBQKYDOCUEMWQ22dnY4eEsASk\nFKSY7Lbrb/K+QYe+Q5Q2iUF8cDwqGitE3xzZmPnIQNe3BDd7N6vvcxfWFKJd3250f7u3sR5jUfZU\nGdZFrROgMnkzOrgZY84AvgXwB855fR9/vp4xls4YS6+qqjJljWSIEiMScbXlKr4//71JjpeUm4Rw\nr/ABB+SEZuhzizktkHOO7IqBZ5QYKBVKzBgzw+qDe6gzSm7m6egpyrc8qTPqvwhjzBZdof0l53x7\nX8/hnG/knEdzzqPVamGW+iTGmR8yHy4qF5PMLimrL8OxC8ewJnKNqHeu+Y/wR6hHqKh97vKGctQ0\n1wza3zaI9Y9FQXUBKq9XClyZdGl1WtgqbBHmFTb4k4nRjJlVwgD8B0A+5/wd4Usit8vexh5Lw5Yi\nuSD5ttslW3O3goObZW2SwcQHx+Nw6WHRVt4b6Fb3vhjWLTl+8bhgNUmdVqeFRq2hO51NzJgr7hkA\n1gKYwxjL6v7HPAtVkGFbFbEKNc01OHLhyG0dJyk3CdG+0Qj1HHgwzhzig+PR2NbY55rN5mC41d3Y\nr/3RvtGwt7G36gHK4cwoIYMzZlbJcc4545xP5JxHdf8jzrbixGgLQhbAWeWMbWeGP7ukqKYIGVcy\nJHG1DXStx8LAROtzZ+uyEegWaPT2WSqlCtP8plltn7umqQaXGy5jojcFt6lR199COdg64O5xdyO5\nIBkd+o5hHSMpJwkMDKvHrzZxdcPj7uCOKb5TROtzD3are1/iAuKQWZGJhtYGgaqSrpzKHAC0wa8Q\nKLgtWKImEVVNVcNaG5pzjqTcJMQFxMHPVTrT9uOD4nGy7CQa2xrNel7D1ltDDe5Y/1jouV6Su/gI\n7XZnlJD+UXBbsEWhi+Bo6zis2SVZFVkorCmUTJvEID44Hh36DrNvVJBbmQs91xs9o8TgF2N+ASVT\nWuXGClqdFl6OXvBx9hG7FItDwW3BHG0dsSR0Cbbnb0envnNIr03KTYKNwgaJEYkCVTc8M/xnwN7G\n3ux9bsOMkqFePTqrnDF51GSr7HMbBiZpAwTTo+C2cKsiVkF3XTekKWl6rkdSbhIWhCwY0sJA5mC4\nBdrswV2RDWeVM4Ldg4f82lj/WJwqOyXJ3eqF0qnvRG5lLg1MCoSC28ItCl0EBxuHIa1d8sPFH1BW\nXya5NonvMMDOAAAQ5ElEQVRBfFA8cipzUNFYYbZzaiu1mOA9YVh38cUFxKG1sxXp5ekCVCZNZ6+e\nRXNHM/W3BULBbeGcVc5YFLoI3+Z/a/RWWkm5SXCwcUBCeILA1Q2P4fZ3U93SP5ih3OreF8MiSdbU\nLqGBSWGZd0V8IopVEauwPX873v7xbfi6+KKtsw1tnW1o72z/76/17T2PbT2zFUvDlsJZ5Sx26X2K\n8omCh4MHDpw7gPsmCL+N2sW6i6hrrRvywKSBl6MXNF4aHL1wFM/NfM7E1UmTVqeFgikQoaYVoIVA\nwW0FloQugYvKBc8eeHbA5ymYAiqlCo62jnhsymNmqm7olAol5gTN6VnmVejBr6He6t6XWP9YbDmz\nBZ36zkFXFrQEWp0W4zzHmW1TaWtDwW0FXOxcUPS7ItQ210KlVEGlVMFWYdv1b6Vtz+/lFCjxQfH4\nJu8bFNcWY5znOEHPlV2RDQaGCSOHvjSpQWxALDb+vLFrx3Ir2D9Rq9Mixi9G7DIsFgW3lfBx9rGo\n+bS9l3kVPLh12QjxCLmt1lHvjRUsPbgbWhtw/tp5PDL5EbFLsVg0OElkKdg9GIFugWaZFjicW91v\nFuAWAP8R/lYxQJlbmQuABiaFRMFNZIkxhvigeHx//vsh31w0FI1tjThbe9Ykm0jE+lvHBsI0o0R4\nFNxEtuKD41HXWoeMKxmCnSNHlwMOPuwZJb3F+sdCd12HktoSE1QmXVqdFq52rvAf4S92KRaLgpvI\n1pygOQCE3c7MFDNKDGb4zwAAnLps2Vu2Gm5WolvdhUPBTWRL7aTGpJGTsD1/O5rbmwU5h1anxQi7\nESa5egzzDIONwgb5VfkmqEyaOOe0eYIZUHATWfv9tN8j40oG4jbHoay+zOTHz9Zlm2yhJFulLULc\nQ5BfbbnBfbHuIupb6ym4BUbBTWTtV5N/hZTVKSioLkD0xmj8cPEHkx1bz/XQ6rQm3d1eo9agoLrA\nZMeTGhqYNA8KbiJ7CeEJOPXrU3C1c8Vdn96Fj9I/Mslxz189j8a2RpMMTBqEe4ajuLZYtA2PhWYI\n7kjvSJErsWwU3MQiRKgj8NP/9xPmBs/FY989hsd2Poa2zrbbOqYpByYNNGoNOvQdOHf1nMmOKSXa\nSi2C3ILgaucqdikWjYKbWAw3ezfsXLMTz854Fh9lfIS5n82FrlE37ONlV2RDwRQmvXrUeGkAwGL7\n3DQwaR4U3MSiKBVKvBH/Bras3IKM8gxM2Thl2OtgZ+uyTb5QUphXGABY5MwSw76cFNzCo+AmFml1\n5Gr8+MiPsFHYYOammfg8+/MhH8MUt7rfzNXOFX4ufiiosbwByryqPOi5noLbDCi4icWK8olC+vp0\nTB8zHQ+mPIin9z6NDn2HUa+ta6lD6bVSkwc3AIR7hVvkFTfNKDEfCm5i0bwcvbD3gb14ctqTePfk\nu4j8IBIvfP8CMsozBlwzxBBCppxRYqDx6poSaGlrlmh1WjjYOCDEPUTsUiweBTexeLZKW7y38D1s\nTdyKUS6j8Prx1xH9cTQC/xmIJ3c/icOlh2+5EhdiRomBRq1BQ1sDyhvKTX5sMWkrtYj0jpTVuu5y\nRcFNrMY94+/BoXWHoPsfHT5J+ARRPlHY+PNG3PXpXfB52we/Sv0VdhTuQHN7M7Q6LTwdPOHr4mvy\nOsK9wgFY1swSw76c1CYxD9pIgVgdL0cvPBT1EB6KegiNbY3YW7IXyQXJ2J6/HZ9kfQInWycoFUpE\n+0YLslCSYUpgQXVBz4YQclfRWIGa5hoKbjOh4CZWzVnljJURK7EyYiXaOttwuPQwUgpSsLtkN5aN\nWybIOX2cfeBq52pRA5Q0MGleFNyEdFMpVZgfMh/zQ+YLeh7GWNcApQVNCTQE9wTv4e/LSYxHPW5C\nRKBRayzrirtSCz8XP3g6eopdilWg4CZEBOGe4bjSeAV1LXVil3LbOOf46fJP1CYxIwpuQkSgUf93\ngFLucipzUFRThKXjlopditWg4CZEBJa02FRSThKUTInEiESxS7EaFNyEiCDIPQgqpUr2V9ycc2w5\nswXxwfFQO6nFLsdqUHATIgIbhQ1CPUJlf8V9suwkSq+VYk3kGrFLsSoU3ISIxBIWm9qSuwV2Sjus\n0KwQuxSrMmhwM8Y2McYqGWO55iiIEGuh8dLg3NVzaO1oFbuUYenUd+LrvK+xZNwS2vHGzIy54t4M\nYKHAdRBidTRqDTp5J0pqS8QuZVgOlx5GRWMF7h1/r9ilWJ1Bg5tzfhRArRlqIcSqGBabkusAZVJu\nEpxVzrh73N1il2J1TNbjZoytZ4ylM8bSq6qqTHVYQixWmGf3NmYyHKBs62zDt/nfYnn4cpNu7UaM\nY7Lg5pxv5JxHc86j1WqaFkTIYJxUTvAf4S/L4N5bshfXWq7RbBKR0KwSQkRk2A1HbpJyk+Dh4IF5\nwfPELsUqUXATIiJDcOu5XuxSjHa97TpSC1ORqEmErdJW7HKskjHTAZMAnAAQxhgrY4w9InxZhFiH\ncK9wNLU3oay+TOxSjLazaCea2puwZgK1ScQy6HrcnHP6dAgRiGGxqfyqfPiP8Be5GuMk5SbB18UX\nsf6xYpditahVQoiI5Lb/5LWWa9hdshurx6+mTYFFRMFNiIjUjmp4OHjIZoBye/52tHW20WwSkVFw\nEyIiwzZmcrni3pK7BSHuIYj2jRa7FKtGwU2IyOSy2JSuUYeD5w/i3sh7wRgTuxyrRsFNiMg0XhpU\nNVWhpqlG7FIGtC1vG/RcT20SCaDgJkRkctnGLCk3CRO8J2C893ixS7F6FNyEiEwOi01duHYBP176\nka62JYKCmxCRBYwIgL2NvaQHKLee2QoAWB25WuRKCEDBTYjolAolxnmOk3RwJ+UmYZrfNAS7B4td\nCgEFNyGSIOXFpgqqC5BVkUVtEgmh4CZEAjReGpy/eh7N7c1il3KLLblboGAK3DP+HrFLId0ouAmR\ngHCvcHBwFNcWC3aO1o5WvH7sdaz5dg0OnDsAzvmgr+GcIyk3CbMDZ2OUyyjBaiNDQ8FNiAT0XmxK\nCMcuHMPkjybjL9//BbuLd2Pe5/Nwx8Y78FXOV2jvbO/3dZkVmSiqKaJ9JSWGgpsQCQj1CAUDM/kA\nZW1zLX6d9mvEbY5Dc0czdt23C7r/0eH/lv4fWjpacP/2+zH2/x+Ld0+8i4bWhlten5STBFuFLVZG\nrDRpXeT2UHATIgEOtg4Icg8y2QAl5xxfaL9A+L/DsTlrM56Z/gzO/PYMFoUugp2NHR654xGc+e0Z\npN2bhkC3QDy972n4v+ePPx/4M640XAEA6LkeW89sxYKxC+Dh4GGSuohpDLoeNyHEPEy12FRxTTF+\n891vcPD8QUzzm4YDDx7AxJETb3megimwNGwploYtxamyU3j7xNt468e38M7Jd/DAhAcww38GLtVf\nwhvxb9x2TcS0KLgJkYhwr3AcPH8QnfrOYa113dbZhn/88A+8dvQ12NnY4YPFH+DR6EehYIN/sZ42\nehq2rdqGs7Vn8c6Jd/BJ1ifYlLUJDjYOWBa2bDhvhwiIgpsQidB4adDS0YILdReGfKPLsQvH8OjO\nR5FfnY97xt+D9xa8N6xZICE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2046495974063873\n", "Epoch 13, Loss: 0.732\n", "Unregularized Loss: 0.732\n", "Validate Loss: 0.709\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2029629349708557\n", "Epoch 14, Loss: 0.679\n", "Unregularized Loss: 0.679\n", "Validate Loss: 0.548\n" ] }, { "data": { "image/png": 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cO1VKVD2GO1EFen89jl86jhkbZ2BIpyFYMGxBrfrp1bYXXh70Mr5K/gobj260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\nIiIXxHAnInJB/w+hLhuzUHI6lQAAAABJRU5ErkJggg==\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2014255821704865\n", "Epoch 15, Loss: 0.501\n", "Unregularized Loss: 0.501\n", "Validate Loss: 0.476\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.199166864156723\n", "Epoch 16, Loss: 0.465\n", "Unregularized Loss: 0.465\n", "Validate Loss: 0.457\n" ] }, { "data": { "image/png": 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9vBattc/tlSnOZdVW0i3pXN/jerNDMY3MUPVySikSoxNJzkx2+r3MmMBkl9A6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\nRK5CYII=\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1994291245937347\n", "Epoch 17, Loss: 0.453\n", "Unregularized Loss: 0.453\n", "Validate Loss: 0.448\n" ] }, { "data": { "image/png": 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5NGPJ5H62tYPtBdW8f+k0bBNckgEIC7Zz5TwH/zpcSbdzwrosKDVpbDvWsyp1zbyxrTpP\n07nu1kzurxw5Q2e34YYlE1+S6XXdohRqmtvZW6KlGaU8bUdBDWkJEcxyjcBHKzU+Aptocreclw5W\nMCshgkXTY3wWw+q5SYQF29h4SEszSnlSR5eTXcW1XJ419oWJIUE2ZkyJmNQNxCyX3Gua23mzsIYb\nlkwbdJPciRIZGsTqOQ42Hj6DU0szSnnMvtJ6Wju6uTzrvC0hRmWyb5ZtueT+Wn4VToNPZskMdO3i\nqVQ1tbP/pG7Iq5Sn7CioJsgmrJg9vvUr6YmRnKhuYQK7j/sV7+1s4SUfzZ7BgmkxzJ0a7etQWDPP\nQUiQjQ2HzpCdFu/rcJQKCDsKargwdQrRY5gC2V96YiQtHd1UN7fjiA7zUHTWYbmRu4iwaHqsr8MA\nIDosmCuykth4uEJLM0p5QG1zO4fLG8ZdkoF+DcSqJ2dpxnLJ3d9cv2QqFQ1tHCg76+tQlLK8Nwpr\nMAYunzP+Lq99rX8nad1dk/s4vW9+MsF2YePhM74ORSnL21FQQ1xEMIs98Nv5tLhwQuy2STtjRpP7\nOMWEBXN5VhIvH6yYtBdulPIEYww7Cqq5NDPRI/2i7DYhNSFi0s511+TuAdcumsrps+c4dLrB16Eo\nZVkFVc1UNrZzhQfq7b3SEiZvAzFN7h5w1YJkgmzChkNamlFqrLa7NrW+bByLlwbKSIqkpLZ1Uk54\n0OTuAXERIazMTGTjYS3NKDVW2wtqmJ0UyfS4cI+9ZlpCJB1dTsobznnsNa1ixOQuIjNFZKuI5IvI\nERH5yiDHiIj8RkQKReSgiFzonXD913WLplJa20peRaOvQ1HKcto6u9lTXMsVHpgl0196XwOxVo++\nrhW4M3LvAr5hjJkPLAfuEpEFA465Fshyfd0J/N6jUVrAuoU9m4Zs1NKMUqOWW1JPe5eTKzxYkoF3\nk/uJmsm3c9qIyd0YU2GM2e+63QTkA9MHHPYB4C+mx24gTkRSPB6tH4uPDGF5RjwbDmlpRqnR2l5Q\nTbBduCTDsyu9k2NCCQ+2c0JH7sMTkTTgAmDPgIemA6f6fV/G+f8BBLxrF6VQXNPCcd1fValR2X68\nmuxZ8USEeLYjioi4ttybfD+Tbid3EYkCngW+aowZWFgebFLqecNXEblTRHJFJLe6unp0kVrA1Qun\nYhPYoG2AlXJbVWMbR880cfkcz02B7C8jsWfGzGTjVnIXkWB6EvsTxpjnBjmkDJjZ7/sZQPnAg4wx\nDxtjso0x2UlJnq2t+YOk6FBy0uM1uSs1Cm8U1gB4vN7eKy0xgpN1rXROsg3t3ZktI8AjQL4x5v4h\nDnsRuM01a2Y50GCMmZQZ7rrFKRRUNVNQ2eTrUJSyhB0FNSREhrAgxTub76QlRNLtNJTVj2465NO5\np3hiT6lXYpoI7ozcLwU+BawRkXdcX9eJyOdF5POuYzYAxUAh8Efgi94J1/9dvXAqImivGaXc4HT2\ntBy4LCvRa/shZySNfj/VkpoWvvv8YR5544RXYpoII169MMa8weA19f7HGOAuTwVlZckxYWTPmsKG\nQxV8+X1Zvg5HKb+Wf6aRmuaOcW2pN5I01z6sxTUtXOnmc/775Tw6up1UN7Z7LS5v0xWqXnDtohSO\nnmmiuHryXaFXajR2FPTW271zMRV6pinHhAW5PXLfeqyKzflVzJgSTlN7Fy3tXV6LzZs0uXvBNYum\nAlqaUWokOwqqmTc1GkeM93ZKEpGeLffcSO4dXU5+tD6PjMRI7r4yE4CqJmuO3jW5e8G0uHAuSI1j\n4+FJeU1ZKbe0dnSx90S9R3ZdGom7yf1Pb57gRE0L37thATOmRABQ2djm7fC8QpO7l1y3KIXDpxs5\nOQnn1yrljj0n6ujodnq13t4rLTGS8oZztHV2D3lMZWMbD2wpYO38ZFbPdZAcE9p3vxVpcveSd0sz\nOnpXajA7jtcQGmQjJ937m8unJ0ZiDJysG3qwdd/Go3Q6Df/5/vkAfZtqV2tZRvU3Mz6CJTNidUGT\nUkPYUVBNTno8YcF2r79XbwOx4iE2y84tqeP5t09z5+UZzHLNrokJDyI0yKYjd3W+6xancKCsgbJ6\nLc0o1V/52XMUVDV7bVXqQGnDbJbd7TT8YP0RUmLD+OKVs/vuFxGSY8KotOh0SE3uXnRtb2lG2wAr\n9R5vuKZAequfzEAxYcEkRoVwYpCR+1N7T3H4dCP3Xjf/vMZlyTGhOnJX55uVEMnSmXH8dU/ppOtr\nodRwthdU44gOZW5y9IS9Z3piJCcGjNwbWjv5+StHyUmP5/1Lzu9S7ogJ06mQanBfXpNJaW0rz+wr\n83UoSvmFbqfhjcIaLs9Koqd11cQYbLPs+zcdo+FcJz+4YeGgsTiiQ6nSkbsazJp5DpbNjOM3WwqG\nnYal1GRxpLyBs62dXDFBJZle6UmRVDe10+xacXr0TCOP7y7lk8tnsWDa4E3LkmPCaOno7nuOlWhy\n9zIR4Zvr5lLR0Mbf3zrp63CU8rntx3v2crg0c4KTe8K7DcSMMXz/n0eIDQ/m61fNGfI5Vp7rrsl9\nAlyamcDyjHge3FrEuQ4dvavJbXtBDQunxZAYFTqh75ue1LufagsvH6pgz4k6vnn1XOIiQoZ8TrJr\nrrsmdzUoEeEb6+ZS09zOY7tKfB2OUj7T3N7F/tJ6rpgz8Zv1zIrvSe55FY38+OV8Fk6L4eaLU4d9\nTm/PmyoLTofU5D5BLk6LZ9WcJB56vYimtk5fh6P82Km6Vv6Re4r2rsD7LW93US1dTjMh/WQGCg+x\nkxIbxiNvnKCioY0f3rgQ+wg95B2uskxVk47c1TC+sW4OZ1s7+dMbJb4ORfmxH67P41vPHGTt/a/z\n8sEKerZLCAzbC6oJD7Zz0awpPnn/9MRIOrqcfHDZNLLTRm57EB0aRHiw3ZILmTS5T6AlM+K4emEy\n/7ejmLOtHb4OR/mhqqY2th6rYu38ZCJDgrjrb/u56aFdvH2y3tehecSOghqWZ8QTGuT9lgODmTc1\nhsgQO/9+3Xy3ju9ZpWrNhUya3CfY166aQ3NHF3/YXuzrUJQfen7/abqdhnuuncfLX76c+z68mNLa\nVj70u5186cm3OTVM4yt/d6qulRM1LRPSBXIoX183h1e+dgXJo+gf74gJ05q7Gtm8qTHcsGQaj75Z\nYtluc8o7jDE8nXuKi2ZNIdMRhd0m3JyTyrZvreZLazLZlHeG993/OvdtPEqjBa/bbM6vBODKeQ6f\nxRAVGtTXp91dyTFhWnNX7vnq2iw6up38fluRr0NRfuTtU2cpqm7hY9kz3nN/VGgQ31g3l9e+sZr3\nL07hodeLWP3zbTy+q4QuC7W1ePVIJVmOqL4OjVbhiA6lsrHdctc+NLn7QEZSFB+5cDp/3VNKRcM5\nX4ej/MQ/ck8RHmzn+iXTBn18Wlw49398GevvvowsRxT/+c8jXPPrHewqqp3gSEfvbGsHb5XUcdWC\nZF+HMmrJMaGc6+ymyWKrVEdM7iLyJxGpEpHDQzy+WkQaROQd19f3PB9m4PnSmiyMMTzwWqGvQ1F+\noLWji/UHKrhucQpRoUHDHrt4Rix/v3M5f/jURXR2O/nsY3v9vv/J1mNVdDuNRZN771x3//47Hsid\nkfujwDUjHLPDGLPM9fWj8YcV+GbGR3Dzxak8vfeUbsWn+NfhMzS3d51XkhmKiHD1wqk8dkcOnd2G\n+/511MsRjs+mvEoc0aEsnRHn61BGzdG3StVa18hGTO7GmO1A3QTEMuncvSYTu0349ZYCX4eifOzp\n3FOkJUSMesu5tMRIPnt5Os/tP82+Uv+cLtnW2c22Y9WsXZCMbYRFQ/4o2aILmTxVc18hIgdEZKOI\nLPTQawa85Jgwblsxi+ffLqOwqnlUz+12WuvijhpaaW0Lu4vruOmiGWNqgXvXlZkkx4TygxeP4PTD\nfxe7impp7ei2ZEkG3m1BEHAjdzfsB2YZY5YCDwAvDHWgiNwpIrkikltdXe2Bt7a+z6+aTViwnV9t\nPj7isTXN7fx1dym3/nE3c767kZcOlk9AhMrbntlXhgh85CL3SjIDRYYGce918zl0uoF/7Dvl4ejG\n79W8SiJD7KycneDrUMYkKjSIyBC75RYyjTu5G2MajTHNrtsbgGARGbRxhDHmYWNMtjEmOynJdwsZ\n/ElCVCj/dmk6Lx2sIK+88bzHq5raeHxXCbc8vJucH2/muy8c5kxDG0lRoTz0epHlpmdZwUSOfrud\nhmf3lXFFVhIpseFjfp0bl04je9YUfvavns0n/IXTadicX8nquQ6frUr1hGQLLmQad3IXkani+l1S\nRHJcr+n/c7P8yP+7PIPosCDu39Qzeq9qbOMvu0r4+B92ccn/bOE//3mEqqY27r4yk41fuZwt31jF\n3WsyOXy6kf0nz/o2+ACz7VgVy370KluPVk3I+71ZWEN5Qxsfy545rtcREX5w40LqWjv4jR9dw3mn\n7CzVTe2WLcn0cliwBcHwc64AEXkSWA0kikgZ8H0gGMAY8xBwE/AFEekCzgE3Gx1OjkpsRDCfuyKD\nX7x6nA/97k3eOXUWYyDLEcWX12Rx3eIU5iRHvace+6ELpvPTjUf5y64SnzVhCjT7Suv4/F/30dbp\n5I87iidkJeXTuaeIiwhm7YLxv9ei6bHcfHEqj+0s4eaLZ5I1gfuTDmVTXiV2m3DlXN+tSvWE5Jgw\n3rbYQGrE5G6MuWWExx8EHvRYRJPUpy9N56ncU7S0d/GV92Vx/eKUYX84I0ODuCl7Bn/dXcp/XD+/\nb7qWGpv8ikbu+PNeUmLDWTUniUd3lnCipsWrqynPtnbw6pFKbr0k1WMli2+um8PLB8v54fo8Hv9M\nzoTuUTqYTXmVXJI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1985286474227905\n", "Epoch 18, Loss: 0.447\n", "Unregularized Loss: 0.447\n", "Validate Loss: 0.441\n" ] }, { "data": { "image/png": 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yzOUIon+FNYCRXUey68gu1h9Yb3UojZrtkvtHaz+iw987NMjKL41hJsi68Pby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\nlNWhKA+R1DmJPm36MPnHyRS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.198183238506317\n", "Epoch 19, Loss: 0.442\n", "Unregularized Loss: 0.442\n", "Validate Loss: 0.435\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.198328971862793\n", "Epoch 20, Loss: 0.440\n", "Unregularized Loss: 0.440\n", "Validate Loss: 0.436\n" ] }, { "data": { "image/png": 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2d5CI3CMidhGxt7S0BKlp/pUU59zY5eG3dKxfBZ8tK4maMzrdU00tKOFvjOky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\nwuJMfv5OLcMjnk/77Bsc4S8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.19819113612175\n", "Epoch 21, Loss: 0.438\n", "Unregularized Loss: 0.438\n", "Validate Loss: 0.433\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1980053186416626\n", "Epoch 22, Loss: 0.437\n", "Unregularized Loss: 0.437\n", "Validate Loss: 0.431\n" ] }, { "data": { "image/png": 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E0pRS8R214xWqZBh3jbwL06OmY8HGBcg6neXQNj7c8yGyTmdhyeQlLg12oKH3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\nkCUAAAAASUVORK5CYII=\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.197982221841812\n", "Epoch 23, Loss: 0.436\n", "Unregularized Loss: 0.436\n", "Validate Loss: 0.429\n" ] }, { "data": { "image/png": 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BxSMuZvrw6QwfMNzSY7uLJnc32HxkM+B79XbwvuS+IWcDqTmpXPv3azlbd9bu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\nM8SEx+ifCeVXel9y37+eyUM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Hnj1JiTOLuy9fOqvnWbc4n6tXL+DHr9TNeLH+5WoXtlTFJcus/2k9kpn7EHC1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\nHqXUQaXUQZfLNfPRRsELJ9t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1980978548526764\n", "Epoch 24, Loss: 0.436\n", "Unregularized Loss: 0.436\n", "Validate Loss: 0.428\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.198011726140976\n", "Epoch 25, Loss: 0.435\n", "Unregularized Loss: 0.435\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.1979403495788574\n", "Epoch 26, Loss: 0.435\n", "Unregularized Loss: 0.435\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.198023945093155\n", "Epoch 27, Loss: 0.434\n", "Unregularized Loss: 0.434\n", "Validate Loss: 0.431\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.19827339053154\n", "Epoch 28, Loss: 0.433\n", "Unregularized Loss: 0.433\n", "Validate Loss: 0.428\n" ] }, { "data": { "image/png": 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Lb13MkYIjDJg2gO8zvz/l9aPHj/L88ucZGDWQK2OudKhK76dhGYdtPbSVm2fd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\nIQAAAABJRU5ErkJggg==\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.198563665151596\n", "Epoch 29, Loss: 0.430\n", "Unregularized Loss: 0.430\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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zHvi0Nt3bPH/DiQbqjteFRX7f0ldo4EHa0ZMafovW8geeBv4h5KXkYTB91R2e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\nuZalU5YGumkqzDgiHNy68FYA2/L7loJ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obzHhzl8exB2/OIA/H+v2WwHSMjCBx/a24NZLirCtpiDo57x6uQHbawvw2N5z3jWjzmFL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\nd3YQly/JRZZa6fP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.200251668691635\n", "Epoch 30, Loss: 0.423\n", "Unregularized Loss: 0.423\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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SuxyDMMWd4P/6818BAP8ZqdtDvhHBI9DTpyeWn17e7ASYgnsF2Kvcixk9Z8DW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\n4O/ij3cef0e0Wii4CSFER8u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DwU3iVL/Tg711FqyfmyPoaTdjoR43Bfeozlr60e1woyTEiUkAUCoYiug0HBLHPj1jhsvj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\nLa6cYwh7kvIfx9q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2004279494285583\n", "Epoch 31, Loss: 0.420\n", "Unregularized Loss: 0.420\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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KNLjPYFsOnCY1LoKLF2jGS7BIiA5n9qyogNhULa5upiAjjoRo3xcLG0th1uCm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\nFvl7OF4RHxVOUXaiV9bdqxq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.200448662042618\n", "Epoch 32, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.422\n" ] }, { "data": { "image/png": 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bTUZWhoujU0VhT8v9GyCqgDIrjTGtba/Xix+WUu6tnH85nmj7BHN2zvGKm46r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\niEmOYc/JPdfKNqnShA61Olx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5Z9uZihl3rVer+o8zC2R/AVT0QyxKWY6I8PjiKYyKDOHB13b0qu2wNyipPs3O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\nOYpvXzTGpfNwNrnrF6pKqUE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2003985941410065\n", "Epoch 33, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.421\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.200426757335663\n", "Epoch 34, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.427\n" ] }, { "data": { "image/png": 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Dg4KCXNicZxnz+xhGrh3J6/e+TqfbOzkdR0TygWwXurX2TWvtbdbaCkA3YKG1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\nVQAAAABJRU5ErkJggg==\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.200474292039871\n", "Epoch 35, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.422\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2006018459796906\n", "Epoch 36, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.425\n" ] }, { "data": { "image/png": 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epdRCpZSnlXKJfITuDcW/rD8da3U0OooQwk5YUtBdgObAXK11M+A6MO2vGyml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\nApAzxOh9wBn4XGv9psGRLKa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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2005370259284973\n", "Epoch 37, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.428\n" ] }, { "data": { "image/png": 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OGi10KYIK8w6Dm6ObJPYssYvgvlB5ATvP78SScUvg7eItdDnEiuw9uHVch9T8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\nFHderDTUzeabcHN0s8rFZps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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2006164491176605\n", "Epoch 38, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.424\n" ] }, { "data": { "image/png": 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+L1l9JPnGoDdYkb6Cvyz+Czc1v4lm9ZpVulxSRhKzts1iUt9JLvlMxhb1W/Bo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\nfdnLI4A55d/P4fx/HpdzlX1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "BS price: [2.2871506]\n", "Deep Hedge price: 2.2006314992904663\n", "Epoch 39, Loss: 0.419\n", "Unregularized Loss: 0.419\n", "Validate Loss: 0.427\n", "Loss on Test Data (unstopped): 0.422\n", "INFO:tensorflow:Restoring parameters from ./model/my-test-model\n", "Loss on Test Data (stopped): 0.417\n", "Runtime (in sec): 1969.434\n" ] } ], "source": [ "#if __name__ == '__main__':\n", "FLAGS = parameters()\n", "#Generate Correlation Matrix\n", "if FLAGS.correlated:\n", " FLAGS.corr = corr(FLAGS.NUM_ASSETS)\n", "#Generate Data\n", "train_data = generate_data(FLAGS)\n", "FLAGS.data = train_data\n", "X_valid, y_valid = generate_validation_data(FLAGS)\n", "X_test, y_test = generate_test_data(FLAGS)\n", "EarlyTrainLoss =np.zeros(FLAGS.NUM_EPOCHS)\n", "EarlyValidateLoss =np.zeros(FLAGS.NUM_EPOCHS)\n", "\n", "with tf.Session() as sess:\n", " model = create_model(sess, FLAGS)\n", " saver = tf.train.Saver()\n", " \n", "#########################\n", "# Train Hedging Network #\n", "#########################\n", " for idx, epoch in enumerate(generate_epochs(FLAGS)):\n", " training_losses = []\n", " quad_losses = []\n", " for step, (input_X, input_y) in enumerate(epoch):\n", " predictions, total_loss, quad_loss, after_loss, q = model.step(sess, input_X, input_y)\n", " training_losses.append(total_loss)\n", " quad_losses.append(quad_loss)\n", " model_weights = delta_BS(input_X,T = float(FLAGS.TIME_STEPS)/365.)\n", " model_weights = np.concatenate([model_weights[:,:,0:FLAGS.NUM_RELAVENT],np.zeros([FLAGS.BATCH_SIZE,FLAGS.TIME_STEPS-1,FLAGS.NUM_ASSETS-FLAGS.NUM_RELAVENT])], axis = 2)\n", " model_hedge_loss = q+HedgingLossNP(model_weights, input_y, input_X, q)\n", " deep_hedge_loss = HedgingLossNP(predictions, input_y, input_X, q)\n", " plt.hist(model_hedge_loss,range=(np.min(deep_hedge_loss),np.max(deep_hedge_loss)),color='green')\n", " plt.show()\n", " plt.hist(deep_hedge_loss)\n", " plt.show()\n", " i = np.random.randint(0,257,1)[0]\n", " model_hedge_loss_tra = q[i:i+1]+HedgingLossNPcum(model_weights[i:i+1,:,:], input_y[i:i+1,:], input_X[i:i+1,:,:], q[i:i+1])\n", " deep_hedge_loss_tra = HedgingLossNPcum(predictions[i:i+1,:,:], input_y[i:i+1,:], input_X[i:i+1,:,:], q[i:i+1])\n", " plt.plot(model_hedge_loss_tra[0,:],color='green')\n", " plt.show()\n", " plt.plot(deep_hedge_loss_tra[0,:])\n", " plt.show()\n", " print(\"BS price: \", q[i:i+1])\n", " print(\"Deep Hedge price:\", deep_hedge_loss_tra[0,0])\n", " print(\"Epoch %i, Loss: %.3f\" % (idx,np.mean(training_losses)))\n", " print(\"Unregularized Loss: %.3f\" % (np.mean(quad_losses)))\n", " FLAGS.training = 2\n", " train_batch = model.sample_train(FLAGS)\n", " X_train, y_train = train_data\n", " test_weights = sess.run([train_batch],{model.X_train: X_train})\n", " FLAGS.training = 3\n", " p = price_valid(FLAGS)\n", " validate_graph = model.sample_validate(FLAGS)\n", " loss = QuadraticHedgingLoss(FLAGS, validate_graph,model.y_valid, model.X_valid, p)\n", " validate_loss,test_weights,certain_equivalent=sess.run([loss, validate_graph, model.q],{model.X_valid: X_valid,model.y_valid:np.squeeze(y_valid)})\n", " print(\"Validate Loss: %.3f\" % (validate_loss))\n", " FLAGS.training = 1\n", "\n", " #Save Model for Early Stopping\n", " if validate_loss < FLAGS.minimal_loss:\n", " FLAGS.minimal_loss = validate_loss\n", " save_path = saver.save(sess, './model/my-test-model')\n", " \n", " EarlyTrainLoss[idx] = np.mean(training_losses)\n", " EarlyValidateLoss[idx] = validate_loss\n", "\n", " # Generate Batch Normalization Parameters for Testing\n", " FLAGS.training = 2\n", " train_batch = model.sample_train(FLAGS)\n", " X_train, y_train = train_data\n", " test_weights = sess.run([train_batch], {model.X_train: X_train})\n", "\n", " # Generate Predictions\n", " FLAGS.training = 3\n", " p = price_test(FLAGS)\n", " test_graph = model.sample(FLAGS)\n", " loss = QuadraticHedgingLoss(FLAGS, test_graph,model.y_test, model.X_test, p)\n", " test_loss, test_weights, certain_equivalent = sess.run([loss, test_graph, model.q],{model.X_test: X_test,model.y_test: np.squeeze(y_test)})\n", " print(\"Loss on Test Data (unstopped): %.3f\" % (test_loss))\n", " p_np = (BlackScholes(100, T = float(FLAGS.TIME_STEPS)/365.) * FLAGS.NUM_RELAVENT)\n", "\n", "#######################################\n", "# Evaluate Network for Early Stopping #\n", "#######################################\n", "new_saver = tf.train.import_meta_graph('./model/my-test-model.meta', clear_devices=True)\n", "with tf.Session() as sess1:\n", " # Generate Batch Normalization Parameters for Testing\n", " new_saver.restore(sess1,tf.train.latest_checkpoint('./model/'))\n", " FLAGS.training = 2\n", " train_batch = model.sample_train(FLAGS)\n", " X_train, y_train = train_data\n", " test_weights = sess1.run([train_batch],{model.X_train: X_train})\n", " \n", " # Generate Predictions\n", " FLAGS.training = 3\n", " p = price_test(FLAGS)\n", " test_graph = model.sample(FLAGS)\n", " loss = QuadraticHedgingLoss(FLAGS, test_graph,model.y_test, model.X_test, p)\n", " test_loss, test_weights, certain_equivalent = sess1.run([loss, test_graph, model.q],{model.X_test: X_test, model.y_test: np.squeeze(y_test)})\n", " print(\"Loss on Test Data (stopped): %.3f\" % (test_loss))\n", "\n", "# Print Runtime \n", "t1 = time.time()\n", "total_time=t1-t0\n", "print(\"Runtime (in sec): %.3f\" % (total_time))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "################\n", "# Save Results #\n", "################\n", "\n", "np.save('deep_weights', test_weights)\n", "deep_hedge_loss = HedgingLossNP(test_weights, y_test, X_test, p_np)\n", "model_weights = delta_BS(X_test,T = float(FLAGS.TIME_STEPS)/365.)\n", "#model_weights = np.concatenate([model_weights[:,:,0:FLAGS.NUM_RELAVENT],np.zeros([FLAGS.NUM_TEST,FLAGS.TIME_STEPS-1,FLAGS.NUM_ASSETS-FLAGS.NUM_RELAVENT])], axis = 2)\n", "if FLAGS.NUM_ASSETS-FLAGS.NUM_RELAVENT != 0:\n", " model_weights = np.concatenate(\n", " [model_weights[:,:,0:FLAGS.NUM_RELAVENT],\n", " np.zeros([FLAGS.NUM_TEST,FLAGS.TIME_STEPS-1,\n", " FLAGS.NUM_ASSETS-FLAGS.NUM_RELAVENT])], axis = 2)\n", "np.save('model_weights', model_weights)\n", "model_hedge_loss = HedgingLossNP(model_weights, y_test, X_test, p_np)+p_np\n", "np.save('stock_prices', X_test)\n", "df = pd.DataFrame(deep_hedge_loss)\n", "df.to_csv('deep_hedge_loss.csv')\n", "df = pd.DataFrame(model_hedge_loss)\n", "df.to_csv('model_hedge_loss.csv')" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "stock_prices=np.load('stock_prices.npy')\n", "model_hedge_loss = pd.read_csv('model_hedge_loss.csv')\n", "deep_hedge_loss = pd.read_csv('deep_hedge_loss.csv')" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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DrvfsETadJjV8wA5jIXIM7HoXOk0Efevre9ogSrNQbJuBp4sVQ4ellB4speqT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\nkiRJ3dz/AxZ/jkkDPqriAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(10):\n", " plt.plot(stock_prices[i,1:,:])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[]],\n", " dtype=object)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model_hedge_loss.hist(column='0',color='green')\n", "deep_hedge_loss.hist(column='0')" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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qsH77AyNZ77aNI1mttCq4BSBJjVpSACQ5mGRfkieSPNbV3pRkb5Jnu8ezunqSfCbJVJIn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\nGIJHAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.show()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from IPython.display import clear_output, Image, display, HTML\n", "\n", "def strip_consts(graph_def, max_const_size=32):\n", " \"\"\"Strip large constant values from graph_def.\"\"\"\n", " strip_def = tf.GraphDef()\n", " for n0 in graph_def.node:\n", " n = strip_def.node.add() \n", " n.MergeFrom(n0)\n", " if n.op == 'Const':\n", " tensor = n.attr['value'].tensor\n", " size = len(tensor.tensor_content)\n", " if size > max_const_size:\n", " tensor.tensor_content = bytes(\"\"%size, 'utf-8')#\"\"%size\n", " return strip_def\n", "\n", "def show_graph(graph_def, max_const_size=32):\n", " \"\"\"Visualize TensorFlow graph.\"\"\"\n", " if hasattr(graph_def, 'as_graph_def'):\n", " graph_def = graph_def.as_graph_def()\n", " strip_def = strip_consts(graph_def, max_const_size=max_const_size)\n", " code = \"\"\"\n", " \n", " \n", "
\n", " \n", "
\n", " \"\"\".format(data=repr(str(strip_def)), id='graph'+str(np.random.rand()))\n", "\n", " iframe = \"\"\"\n", " \n", " \"\"\".format(code.replace('\"', '"'))\n", " display(HTML(iframe))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "#show_graph(tf.get_default_graph().as_graph_def())" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "weights=np.load('deep_weights.npy')" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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6kxfX7ndf1g5uzNwdu6B6spHgLrzD/m+MTGz8NcbCoL09E9yzCir4Ylch15+dZMy51ho+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\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "S = stock_prices[7,1:,:]\n", "S = S.T\n", "delta = delta_BS(S, sigma = 0.2, K = 100., r = 0., T =30./365.)\n", "plt.plot(delta[0])\n", "plt.plot(weights[7,1:])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }