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Last active December 10, 2021 11:29
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CAS_interest_rates_202112.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/jteichma/1b33360fb793d00fbfd9ad332c6cf4de/cas_interest_rates_202112.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CnNlDCMUH6gy"
},
"source": [
"# Basic principles of pricing and hedging and Risk management"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "m2La_36jH6g4"
},
"source": [
"We shall first go through basic principles of modeling in mathematical Finance before we introduce concepts of interest rate theory."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gPQlpWmRH6g5"
},
"source": [
"We shall denote by $ S^i_t $ the price of asset $i$ and by $ H^i_t $ the holdings in asset $i$ at time $t$ (can be any real number here, no market frictions assumed). $ H^i_t $ is 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.\n",
"\n",
"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."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cSDQ3mWJH6g7"
},
"source": [
"Notice that this argument holds for any numeraire $S^0$: it only has to be default-free, i.e. never attaining the price $0$. We can calculate self-financing portfolios with respect to convenient numeraires and then switch back to the original undiscounted terms."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3GkrRDhqH6g8"
},
"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",
"It turns out that absence of arbitrage is precisely what we need to evaluate derivative contracts rationally."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "lI7EDqeSH6g8"
},
"source": [
"### We assume from now on that any positive outcome of a self-financing portfolio cannot come for free, i.e. the initial capital $x$ has to be positive, too."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7wkdiCiMH6g9"
},
"source": [
"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 hear \"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\\} $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ozuvgWYZH6g9"
},
"source": [
"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."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D4qev8QqH6g_"
},
"source": [
"This generalizes of course to the multi-period case."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "nya98xqLH6hA"
},
"source": [
"### 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",
"\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",
"source": [
"!apt install libgraphviz-dev\n",
"%pip install graphviz\n",
"%pip install pygraphviz\n",
"import numpy as np\n",
"from itertools import product"
],
"metadata": {
"id": "ZfUp5oKZraHO",
"outputId": "ffb3c06e-be32-49f5-84df-ea34a5032e54",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 24,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Reading package lists... Done\n",
"Building dependency tree \n",
"Reading state information... Done\n",
"libgraphviz-dev is already the newest version (2.40.1-2).\n",
"0 upgraded, 0 newly installed, 0 to remove and 37 not upgraded.\n",
"Requirement already satisfied: graphviz in /usr/local/lib/python3.7/dist-packages (0.10.1)\n",
"Requirement already satisfied: pygraphviz in /usr/local/lib/python3.7/dist-packages (1.7)\n"
]
}
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 268
},
"id": "AXOe0p6cH6hA",
"outputId": "e2b1dbed-9de9-47b2-80b3-12b50d1dab80"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 25
}
],
"source": [
"# EUROPEAN\n",
"S0 = 100.\n",
"u = 1.1\n",
"d = 0.9\n",
"payoffE = lambda S: 2*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": 26,
"metadata": {
"id": "zcehYnf4H6hE",
"outputId": "b5458e08-f21b-431c-d7e0-2e0e3f6868d6",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 268
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 26
}
],
"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": 27,
"metadata": {
"id": "Ks6RVf_UH6hE"
},
"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": {
"id": "Rx67Ga1SH6hE"
},
"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": 28,
"metadata": {
"id": "fzpy-gLpH6hF",
"outputId": "01e2e124-0e35-421e-b860-ed0afb900f54",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 268
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 28
}
],
"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": {
"id": "tFubtCV2H6hF"
},
"source": [
"# No arbitrage, hedging and a bit of machine learning"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QnX212qcH6hG"
},
"source": [
"In the sequel we look at the above ideas in a continuous time setting, which can be seen as a limit for many trading times and a particular scenario generation structure. Additionally we shall not 'calculate' the solution withing a given model, but learn it in a model-independent way. The method is called 'deep hedging' and applies machine learning technology.\n",
"\n",
"Deep Hedging goes back to the following [paper](https://arxiv.org/abs/1802.03042) by Hans Bühler, Lukas Gonon, Josef Teichmann and Ben Wood. \n",
"\n",
"The main idea is to parametrize the hedging strategies (at each time) via neural networks which can depend on input variables chosen by the user, for instance the current price, the past strategy, etc.\n",
"This then allows to solve a potentially high dimensional hedging problem for many assets whose dynamics are described by an arbitrary given arbitrage free model even in the presence of transaction costs.\n",
"\n",
"Let us exemplify first the idea by the Black Scholes model in one dimension."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j4ZJqpgbH6hH"
},
"source": [
"Let $T$ be a finite time horizon and consider on a filtered probability space $(\\Omega, (\\mathcal{F}_{0\\leq t\\leq T}), \\mathcal{F}_T, P)$ a standard Black Scholes model with interest rate $r=0$ and the price of the risky asset $S$ being described by\n",
"\n",
"$$\n",
"dS_t=S_t\\mu dt + S_t\\sigma dW^{\\mathbb{P}}_t, \\quad S_0=S_0\n",
"$$\n",
"\n",
"under the physical measure $\\mathbb{P}$. Here $\\mu \\geq 0$, $\\sigma \\neq 0$, $S_0 >0$ and $W^{\\mathbb{P}}$ is a Brownian motion (under $\\mathbb{P}$).\n",
"\n",
"Under the unique risk neutral probability measure, denoted by $\\mathbb{Q}$, the dynamics are then given by\n",
"\n",
"$$\n",
"dS_t= S_t\\sigma dW_t, \\quad S_0=S_0\n",
"$$\n",
"\n",
"where $W$ is a $\\mathbb{Q}$ Brownian motion \n",
"\n",
"We consider here the problem of hedging a $\\mathcal{F}_T$-measurable claim $f(S_T)$. In the case of the Black Scholes model the hedging strategy can be found by the Delta hedge, i.e. \n",
"\n",
"$$\n",
"\\Delta(t,s)=\\partial_s \\mathbb{E}_{Q}[f(S_T)| S_t=s].\n",
"$$\n",
"\n",
"In more involved models this is no longer possible. In particular in incomplete models not every claim can be hedged and we thus need to optimize a hedging criterion. We here consider a __quadratic hedging criterion__ but other risk measures are of course also possible.\n",
"\n",
"Let $\\pi$ denote the price of the option, i.e. $\\mathbb{E}_Q[f(S_T)]$. Then the goal is solve the following optimization problem \n",
"\n",
"$$\n",
"\\inf_{H \\text{ predictable }}\\mathbb{E}[( f(S_T)- \\pi- (H\\bullet S)_T)^2],\n",
"$$\n",
"\n",
"where $(H_t)$ ranges over all predictable process and $(H \\bullet S)_T= \\int_0^T H_t dS_t$ denotes the stochastic Ito integral. Optimizing over all predictabel processes is infeasable. \n",
"\n",
"Therefore we choose to specify $H_t$ in a smaller set: for each $t$ as a neural network whose input can be specified. In complete Markovian models, as it is the case of the Black Scholes model, we know from the delta hedging strategy that it makes sense to parameterize $H_t$ as a function of the current price $S_t$. In the current setting we therefore choose that the input of each neural network in the implementation below depends only on the current price, i.e. \n",
"\n",
"$$\n",
"H_t=g_t(S_t)\n",
"$$\n",
"\n",
"and $g_t$ denotes a neural network.\n",
"\n",
"We can view the above as supervised learning problem: the input data $x_i$ correspond to trajectories of $(S_t(\\omega_i))_{0 \\leq T}$, the output $y_i$ should be $0$ and the\n",
"the loss function is given by \n",
"\n",
"$$\n",
"\\mathcal{L}= \\left(f(S_T(\\omega_i))- \\pi- \\int_0^T g_t(S_t (\\omega_i)) dS_t(\\omega_i)\\right)^2.\n",
"$$\n",
"\n",
"To implement this we need to generate input data which will be our training data set. Consider the log price of $S_t$ under $\\mathbb{Q}$, i.e.\n",
"\n",
"$$\n",
"d\\log(S_t)= -\\frac{\\sigma^2}{2} dt + \\sigma dW_t.\n",
"$$\n",
"\n",
"The practical implementation requires a time discretization.\n",
"If we discretize our time interval $[0,T]$ in $N$ time steps of length $T/N$ we can write \n",
"\n",
"$$\n",
"\\log(S_i)= \\log(S_{i-1}) -\\frac{\\sigma^2}{2} \\frac{T}{N} + \\sigma \\sqrt{\\frac{T}{N}} Z_i, i=1, \\ldots, N\n",
"$$\n",
"\n",
"where $Z_i$ are independent $N(0,1)$ distributed random variables. The discretized price $(S_0, S_1, \\ldots S_N)$ is obtained by exponentiation.\n",
"\n",
"In this disretized form the whole trajetory of the price $(S_0, S_1, \\ldots S_N)$ is therefore determined by $(S_0, Z_1, \\ldots, Z_N)$ or in other words $(S_0, X_1, \\ldots, X_N)$ where $X_i$ are independent $N(-\\frac{\\sigma^2}{2} \\frac{T}{N} ,\\sigma^2 \\frac{T}{N})$ distributed random variables. Considering $K$ many samples thereof constitutes the input training data set. The outputs are simply $K$ zeros.\n",
"\n",
"In the above loss function we also need to disretize the \n",
"stochastic integral\n",
"\n",
"$$\n",
"\\int_0^T g_t(S_t (\\omega)) dS_t(\\omega).\n",
"$$\n",
"\n",
"We do this by choosing $N$ neural networks $g_0, \\ldots, g_{N-1}$ and disretizing the integral as follows:\n",
"\n",
"$$\n",
"\\sum_{i=0}^{N-1} g_i(S_i(\\omega)) (S_{i+1}(\\omega)-S_i(\\omega))\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "AaYuvPjnH6hH",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "9dfa404f-4720-4dab-d79a-5b9119304be1"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"TensorFlow 1.x selected.\n"
]
},
{
"output_type": "stream",
"name": "stderr",
"text": [
"Using TensorFlow backend.\n"
]
}
],
"source": [
"%tensorflow_version 1.x\n",
"import numpy as np\n",
"import tensorflow as tf\n",
"\n",
"from keras.models import Sequential\n",
"from keras.layers import Input, Dense, Conv2D, Concatenate, Dropout, Subtract, \\\n",
" Flatten, MaxPooling2D, Multiply, Lambda, Add, Dot\n",
"from keras.backend import constant\n",
"from keras import optimizers\n",
"\n",
"from keras.engine.topology import Layer\n",
"from keras.models import Model\n",
"from keras.layers import Input\n",
"from keras import initializers\n",
"from keras.constraints import max_norm\n",
"import keras.backend as K\n",
"\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "hqlyn6IvH6hI",
"outputId": "b584ae25-986e-4208-e7ce-95371d18953d",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
}
},
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# Trajectories of the Black scholes model\n",
"# Let it run to initialize the following parameters, the trajectories \n",
"# are not needed afterwards\n",
"\n",
"N=20 # time disrectization\n",
"S0=1 # initial value of the asset\n",
"strike=1 # strike for the call option \n",
"T=1.0 # maturity\n",
"sigma=0.2 # volatility in Black Scholes\n",
"R=10 # number of Trajectories\n",
"\n",
"logS= np.zeros((N,R))\n",
"logS[0,]=np.log(S0)*np.ones((1,R))\n",
"\n",
"for i in range(R):\n",
" for j in range(N-1):\n",
" increment = np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N))\n",
" logS[j+1,i] =logS[j,i]+increment\n",
"\n",
"S=np.exp(logS)\n",
"\n",
"for i in range(R):\n",
" plt.plot(S[:,i])\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "G-ka3ebXH6hJ",
"outputId": "eb9f2be5-59e0-49e6-fec1-25d18f010fb6",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Price of a Call option in the Black scholes model with initial price 1 strike 1 maturity 1.0 and volatility 0.2 is equal to 0.07965567455405798\n"
]
}
],
"source": [
"import scipy.stats as scipy\n",
"from scipy.stats import norm\n",
"\n",
"#Blackscholes price\n",
"\n",
"def BS(S0, strike, T, sigma):\n",
" return S0*scipy.norm.cdf((np.log(S0/strike)+0.5*T*sigma**2)/(np.sqrt(T)*sigma))-strike*scipy.norm.cdf((np.log(S0/strike)-0.5*T*sigma**2)/(np.sqrt(T)*sigma))\n",
"\n",
"priceBS=BS(S0,strike,T,sigma)\n",
"print('Price of a Call option in the Black scholes model with initial price', S0, 'strike', strike, 'maturity', T , 'and volatility' , sigma, 'is equal to', BS(S0,strike,T,sigma))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "AydbckklH6hJ"
},
"outputs": [],
"source": [
"#Definition of neural networks for heding strategies\n",
"\n",
"m = 1 # dimension of price\n",
"d = 2 # number of layers in strategy\n",
"n = 32 # nodes in the first but last layers\n",
"\n",
"# architecture is the same for all networks\n",
"layers = []\n",
"for j in range(N):\n",
" for i in range(d):\n",
" if i < d-1:\n",
" nodes = n\n",
" layer = Dense(nodes, activation='relu',trainable=True,\n",
" kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',\n",
" bias_initializer='random_normal',\n",
" name=str(i)+str(j))\n",
" else:\n",
" nodes = m\n",
" layer = Dense(nodes, activation='linear', trainable=True,\n",
" kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',\n",
" bias_initializer='random_normal',\n",
" name=str(i)+str(j))\n",
" layers = layers + [layer]\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "nNunHVAXH6hJ",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "129a925b-5d94-4d31-fd87-4b6dfae24913"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"WARNING:tensorflow:From /tensorflow-1.15.2/python3.7/tensorflow_core/python/ops/resource_variable_ops.py:1630: calling BaseResourceVariable.__init__ (from tensorflow.python.ops.resource_variable_ops) with constraint is deprecated and will be removed in a future version.\n",
"Instructions for updating:\n",
"If using Keras pass *_constraint arguments to layers.\n"
]
}
],
"source": [
"#Implementing the loss function\n",
"# Inputs is the training set below, containing the price S0, \n",
"#the initial hedging being 0, and the increments of the log price process \n",
"price = Input(shape=(m,))\n",
"hedge = Input(shape=(m,))\n",
"\n",
"inputs = [price]+[hedge]\n",
"outputs = []\n",
"\n",
"for j in range(N):\n",
" outputs = outputs + [hedge]\n",
" payoff= Lambda(lambda x : 0.5*(K.abs(x-strike)+x-strike) - priceBS )(price) \n",
" outputs = outputs + [payoff]\n",
" strategy = price\n",
" for k in range(d):\n",
" strategy= layers[k+(j)*d](strategy) # strategy at j is the hedging strategy at j , i.e. the neural network g_j\n",
" incr = Input(shape=(m,))\n",
" logprice= Lambda(lambda x : K.log(x))(price)\n",
" logprice = Add()([logprice, incr])\n",
" pricenew=Lambda(lambda x : K.exp(x))(logprice)# creating the price at time j+1\n",
" priceincr=Subtract()([pricenew, price])\n",
" hedgenew = Multiply()([strategy, priceincr])\n",
" #mult = Lambda(lambda x : K.sum(x,axis=1))(mult) # this is only used for m > 1\n",
" hedge = Add()([hedge,hedgenew]) # building up the discretized stochastic integral\n",
" inputs = inputs + [incr]\n",
" price=pricenew\n",
" \n",
"outputs = outputs + [hedge]\n",
"payoff= Lambda(lambda x : 0.5*(K.abs(x-strike)+x-strike) - priceBS )(price)\n",
"outputs = outputs + [payoff]\n",
"inputs = inputs\n",
"outputs= Concatenate()(outputs)\n",
"\n",
"model_hedge = Model(inputs=inputs, outputs=outputs)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "K-jnrk08H6hK"
},
"outputs": [],
"source": [
"Ktrain = 2*10**4\n",
"initialprice = S0\n",
"\n",
"# xtrain consists of the price S0, \n",
"#the initial hedging being 0, and the increments of the log price process \n",
"xtrain = ([initialprice*np.ones((Ktrain,m))] +\n",
" [np.zeros((Ktrain,m))]+\n",
" [np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N),(Ktrain,m)) for i in range(N)])\n",
"\n",
"ytrain=np.zeros((Ktrain,2*N+2))\n",
"\n",
"Ktest = 1\n",
"initialprice = S0\n",
"\n",
"# xtrain consists of the price S0, \n",
"#the initial hedging being 0, and the increments of the log price process \n",
"xtest = ([initialprice*np.ones((Ktest,m))] +\n",
" [np.zeros((Ktest,m))]+\n",
" [np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N),(Ktest,m)) for i in range(N)])\n",
"\n",
"ytest=np.zeros((Ktest,2*N+2))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "zfj5ggMjH6hL"
},
"outputs": [],
"source": [
"from keras import losses\n",
"def custom_loss(y_true,y_pred):\n",
" z1 = y_pred[:,2*N+1]\n",
" z2 = y_pred[:,2*N]\n",
" z = z1-z2\n",
" z=K.mean(K.square(z))\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "GFGLnEw5H6hM"
},
"outputs": [],
"source": [
"#sgd=optimizers.SGD(lr=0.0001)\n",
"#model_hedge.compile(optimizer=sgd,loss='mean_squared_error')\n",
"model_hedge.compile(optimizer='adam',loss=custom_loss)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "zYA71OGUH6hM",
"outputId": "4db8cf1f-02de-4e57-b973-2096eb8c935a",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"WARNING:tensorflow:From /tensorflow-1.15.2/python3.7/keras/backend/tensorflow_backend.py:422: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.\n",
"\n",
"Epoch 1/1\n",
"20000/20000 [==============================] - 4s 222us/step - loss: 0.0370\n"
]
},
{
"output_type": "display_data",
"data": {
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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": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 136us/step - loss: 0.0018\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 139us/step - loss: 0.0015\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 155us/step - loss: 0.0012\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 139us/step - loss: 0.0011\n"
]
},
{
"output_type": "display_data",
"data": {
"image/png": 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sF7T86mu5VDd28PgHOtzSVUprfe9mI4OZnBJNenz4oP30q4uqmTI6mvFJw3tt8qwjb3TKYv/gESdjRWSpiBSKSOHhw4eHtY+JyVE8ds0sljs45G1Oz0zgK9PG8Pi6vVQ16B16XGFPjW9PZtYfEWFeTgoflR6hvbP/i/VqmjooPFA/7NY8wOiYMEZFhugQSz/hiKCvBDL6fJ1uXTbQ8pMYY5YbYwqMMQVJSUnDLmRB3minhLzNXYunYAz8frUOt3SFkpoWvxlx09f83BSOdffyUemRfte/WXQIYxh2/zxY/qBYTshqi94fOCLoVwLXWUffnAk0GmOqgTXAAhGJt56EXWBd5rXS4yNYeu54Vm6tYtOBoV2qrobOdlcpfxhx09fsrASiw4IG7L75z/ZqspOjmDjCawvyUmPYU9PMsW6d5sPX2TO88kVgPTBZRCpE5EYRuVlEbrZusgooA0qBJ4AfABhj6oDfAhutH/dal3m1m8+bQEpMKL/51w56e9073LKyoZ2H3yulqcM3L2UvqWnxq/55m+DAAM6blMS7u2pOeo/VNnewcX/diLptbPJTY+nuNcengVa+K2iwDYwxVw+y3gC3DLBuBbBieKV5psjQIH62aAo/emUrr39eyRWz0l1eQ1dPL3/7eB9/fruE9q4eOrp6+PGCyS6vw5ka27s41NThk7cPtMf83BT+va2aLRUNzBz7xajkNcU11m4bBwT98ROyjcfnqVe+ySNOxnqbS6encVpGHH98cxetx1w73HLzwXq+9teP+H+rdnHWhFGcPWEUz316wOeGfZYen/rA/1r0AOdPSiYwQE7qvlm1rZoJSZEOmfsnIz6C6NAgvULWD2jQD0NAgHDP13KpbT7Go+/vdckxG9u6uPuN7Xz90U9oaOvisWtm8tT1Bfxo/iQa2rp4tbDCJXW4SkmNbTIz/2zRx0YEMzsz4UuzWR5pOcaGfUdZMnUMIiM/bxEQIDplsZ/QoB+mmWPjuXR6Kss/LKO8rs1pxzHG8M8tlVz03+/z4mcH+e45Wbzz4/NYlG/5ZS/ITGDm2Die/KiMHjefM3CkktoWwoIDSI/3rxE3fc3LTWFPTQsHj1reX2uKD9HroG4bm7zUWHZWN/nUe0edTIN+BH62eAoB4rzhlvuOtHLtU5/xw5e2kBYXzspb5/DLr+YSFfrlUytLzx1PeV07bxYdckod7mCb+sDfRtz0Nc82yZm1Vb96+yGyEiOZMtpx/+Xkp8XQ0dVL2WE9IevLNOhHYExsODefN4H/bK9mQ9lRh+33WHcP//POHhb+zzq2ljfw20vyeP0H5wx4wmx+7mgyR0WwfN1en5l4rbS2hUl+MDXxqYwbFUl2chTv7KyhrrWT9WVHWTJ1tEO6bWxs7yntvvFtg466Uaf2/XMn8MrGcr73TCHTMmLJHRNDzpgYclNjmJAURXDg0P6WflJ6hF/8o4iyI6187bRUfvmVHJJjwk75nMAA4ca54/nlP4rYuL+e2VkJI/mW3K6po4vqxg4m+vjNRuwxLzeF5evKeLWwnJ5ew+IhTkk8mPGJkYQGBVBc2cRlMxy6a+VBNOhHKDwkkOXXFfC/nx5gR3UTz64/wDHrDZ5DAgPITomyBL/tD8CYGGIjgk/az5GWY/zuPzt54/NKxo2K4Jnvzua8SfZfJXzFzHT+/PYelq/b6/VBbxtx4+8terDcjOTR9/fyl3dLGDcqgrzUGIfuPygwgJwxekLW12nQO0B+Wiy///o0ALp7etl3pJUd1U3sqG5iZ3Uz7++u5bVNX4yKSYsLP97qzx0TzZGWTu5fs5u2zm5uu3Ait1wwcchTOYSHBHLtmeP4y7sllNa2ePXUvrYRN75+n1h7TM+IIzEqhCMtnSzOd8xomxPlpcawcmsVxhin7F+5nwa9gwUFBpCdEk12SjSXTP9iss7a5g52Vjezo6qJndY/Amt31WAb7HDm+AT+76VTRxTQ1501jsc+2MuTH5Yd/8PjjUpqbCNu7L8Pqq8KDBAunJLMK4UVI5rb5lTy02J5fsNByuvah3TvWeU9NOhdJDk6jOTosC91x7R39rCnppnWzm7OGj9qxK2pUVGhXDErnVcLK/jRgkkkR5+6b99T7altYUJSFIF+POKmr++fN4FxoyKZ6qSrV/P73ENWg9436agbNwoPCeS0jDjOnpDosH+Zvzd3PF29vTy3/oBD9ucOpTXNfnuhVH8mJEVxywUTndatMml0FEEBolMW+zANeh+TlRjJgtwUr50Wobmji6rGDq8+x+BtQoMCyU6J1imLfZgGvQ9aeu54r50W4fiIG23Ru1R+agzFVY0+cx2G+jINeh80a1wCs8bF8+RHZXT39Lq7nCGxTZnrr5OZuUteagxHWjqpbT7m7lKUE2jQ+6ib5lqmRVhTfOp7j3qaPTXNhAYFkJGgJwVd6fgVspXaT++LNOh91PzcFK+cFqFER9y4Rc6YGETQKYt9lAa9jwoMEL43dzxbKxr5bJ/33NirpKbZIXOtq6GJDA0iKzFSW/Q+SoPeh10xK52EyBCe+LDM3aXYxTbixl/vKuVu+amx2qL3URr0PiwsOJDrzhrHOztrKa1tdnc5g/L3u0q5W15qDJUN7dS3drq7FOVgGvQ+7tozxxEaFMCTH+5zdymDKtGhlW5lOyGrrXrfo0Hv42zTIry+uZLa5g53l3NKJTrixq1sM2PqFbK+R4PeD9imRXj2E8+eFkFH3LhXXEQIaXHhFGmL3udo0PuBvtMitB7z3GkRSmpadGpiN8tPi6FYR974HA16P7H03Ak0tnfxamG5u0vpV8uxbiob2rV/3s3yUmPZd7SVFg9uEKih06D3E7PGxTNrXDxPfbzPI6dFsI240cnM3Cs/LQZjYGe1dt/4Eg16P7L0XMu0CG8WH3J3KSex3VVKW/TudXxueu2+8Sl2Bb2ILBKR3SJSKiJ39rN+nIi8KyLbROR9EUnvs65HRLZYP1Y6sng1NPNyUshKjOSJdWUeNy1CSW0LIUEBjNURN26VHBNGYlSoDrH0MYMGvYgEAg8Di4Fc4GoRyT1hsz8BzxpjpgH3Avf1WddujJlu/bjYQXWrYQgMEG6ck8XWikY2DGNaBGMMJTXNPLS2hEse/pjf/WeHw2orqWnWETceIj8tRlv0PsaeFv1soNQYU2aM6QReAi45YZtcYK318Xv9rFce4vi0COvsmxaht9ew+WA9963eyYUPfMD8P6/jT2/toaaxgyc/2seuQ45p+e2padErYj1EfmospbUtdHT1uLsU5SD2BH0a0HeoRoV1WV9bgcutjy8DokVklPXrMBEpFJFPReTS/g4gIkut2xQePnx4COWrobJNi/DuroGnRejs7mXdnsPc/cZ2zrzvXS5/5BOe+nAf6fHh/PbSfD696yLW3H4uUaFB/GnN7hHX1Hp8xI0GvSfIS42hu9ewp8bzp81Q9nHUzcHvAB4Ske8A64BKwNYcGGeMqRSR8cBaEdlujNnb98nGmOXAcoCCggLP6jz2Qdedlcmj7+/liXX7+MMV0wBL2H6w5zBrig+xdlctzR3dhAcHcv7kJBbkpXDh5BRiI4K/tJ+bz5vA/Wt2s+lAHbPGJQy7ni9G3OiJWE/wxdz0TUxLj3NzNcoR7An6SiCjz9fp1mXHGWOqsLboRSQK+LoxpsG6rtL6uUxE3gdmAF8KeuVaCZEhfKMgnVc2VpCXFsMHuw/zYekROrt7iY8IZlHeaBbkjWZudiJhwYED7ueGczL528f7+eObu3lp6ZnDvnn1F3PcaIveE6THhxMTFqRTIfgQe4J+I5AtIllYAv4q4Ft9NxCRRKDOGNML3AWssC6PB9qMMces25wD/NGB9ath+t6c8Ty/4SC/+mcxaXHhfGv2WBbmjeb0zHiCAu0bdRsREsRtF07knpXFfFhyhHMnJQ2rlpKaZkICdcSNpxAR8lJjdSoEHzJo0BtjukXkVmANEAisMMYUi8i9QKExZiVwPnCfiBgsXTe3WJ+eAzwuIr1Yzgf83hjjuKEaatgyEyN56aYziQwNIi81Ztit8atmZ7B8XRn3r9nN3OzEYe1nT00z45Mi7f4Do5wvPy2GZ9cfoLunV38uPsCuPnpjzCpg1QnLftXn8WvAa/087xNg6ghrVE5yxvhRg280iNCgQJbNn8Qdr25lddEhlkwdM+R9lNS2MHNs/IhrUY6TlxrLse5e9h5uZfJoPXfi7fRPtRqxy2akkZ0cxQNv7R7y9Aqtx7qpqG/XoZUeJj/NMmWxjqf3DRr0asQCA4QfL5jM3sOtvP555eBP6GPvYetdpXTqA4+SlRhFeHCgXiHrIzTolUMszEvhtPRY/vJOCce67b/QZk+NLei1Re9JAgOEnDHRFOnIG5+gQa8cQkT4ycIpVDa08/ynB+1+XkmtZcTNOB1x43Hy02LZWdVEb6/9l7YYY6ht7mDzwXpWbq1i35FWJ1ao7OWoC6aUYk52ImdPGMXD75Vy5ekZRIYO/vYqqWnRETceKi/VMvLmYF0bmYmRgCXIj7Z2UlHfTnldGxX17VTUWz6X17dRWd/Ose4vztOMT4rk7WXn6RxGbqZBrxzqJwsnc9kjn7Dio33cdlH2oNuX1DYzPUNH3HiiPOuUxfesLEaE46He0fXlE+7xEcGkx0cwOSWaeTkppMeHkx4fTkV9O7/6ZzErt1Zy2Yz0/g6hXESDXjnUjLHxzM9NYfm6Mq45cxzxkSEDbtvW2U15XTvfmJUx4DbKfSalRJMWF87WigbS48OZmBTF+ZOSrEEeQUZCBGnx4UQN8J9bb6/hxc/KefDdUr42LVX/a3MjDXrlcHcsmMyiv6zjsQ/2cteSnAG321tr6b/VqQ88U0hQAB/97IJhX0wXECAsm5fN0uc28Y8tVVwxS1v17qJ/YpXDTR4dzWXT03j6k/0cauwYcDvb7Ig6mZnnGm7I28zPTSE/LYa/ri2hywNvYekvNOiVUyybP4leY/jr2pIBtympbSE4UMgcpSNufJWIsGzeJA4cbeONzUO7xkI5jga9coqMhAiunj2WlzeWc+Bo/0PsSmqaGZ8YpX23Pu7CKcmclh7Lg2tL6OzWVr076G+YcppbL5hIUKDw32/v6Xd9SW2LXijlB0SE2+dPoqK+nb9vrnB3OX5Jg145TXJMGDeck8XKrVXsrP7ypfTtnT2U17eRrf3zfuH8SUlMz4jjobWl2qp3Aw165VQ3nzuB6NAgHnjry7cc3Hu4BWN0xI2/EBF+NH8SlQ3tvFJYPvgTlENp0Cunio0I5vvnTeCdnbVsOlB3fLltxI1OZuY/5mYnUjAunoffK9Ubj7uYBr1yuhvOySQxKpQ/vrkbYyzzpthG3IzTETd+Q0RYNn8S1Y0dvLxRW/WupEGvnM52y8EN++pYV3IE+GLETbCOuPErZ08YxeysBB55X1v1rqS/Zcolrp49lvT4cO5fswtjDHtqWpio/fN+xzauvqbpGC9ssH+WUzUyGvTKJUKCAlg2bxJFlU288Xkl5fVtTNIRN37prAmjOGv8KB79YC/tndqqdwUNeuUyl1pvOXjPymKM0ZuN+LNl8ydxuPkYz2844O5S/IIGvXIZ2y0Hmzu6AR1a6c9mZyUwZ2Iij76/l7bObneX4/M06JVLLcxL4bSMOOuIm0h3l6PcaNn8bI62dvLcem3VO5sGvXIpEeEvV07noW/N1BE3fm7WuATOnZTE4+vKaD2mrXpn0t805XKZiZEszBvt7jKUB1g2L5u61k6eWb/f3aX4NA16pZTbzBgbz4VTklm+rozmji53l+OzNOiVUm51+7xsGtq6eOaT/e4uxWfZFfQiskhEdotIqYjc2c/6cSLyrohsE5H3RSS9z7rrRaTE+nG9I4tXSnm/aelxzMux3Ge4SVv1TjFo0ItIIPAwsBjIBa4WkdwTNvsT8KwxZhpwL3Cf9bkJwD3AGcBs4B4RiXdc+UopX3D7vGyaOrpZ8dE+d5fik+xp0c8GSo0xZcaYTuAl4JITtskF1lofv9dn/ULgbWNMnTGmHngbWDTyspVSviQ/LZaFeSk89dE+Gtu0Ve9o9gR9GtB3qrkK67K+tgKXWx9fBkSLyCg7n4uILBWRQhEpPHz4sL21K6V8yO3zJtHc0c1TH5W5u5wOKJMAABAfSURBVBSf46iTsXcA54nI58B5QCVg9yQWxpjlxpgCY0xBUlKSg0pSSnmTnDExLJk6mhUf76ehrdPd5fgUe4K+Esjo83W6ddlxxpgqY8zlxpgZwN3WZQ32PFcppWx+eNEkWju7eeJDbdU7kj1BvxHIFpEsEQkBrgJW9t1ARBJFxLavu4AV1sdrgAUiEm89CbvAukwppU4yeXQ0X5k6hqc/3k9dq7bqHWXQoDfGdAO3YgnoncArxphiEblXRC62bnY+sFtE9gApwO+sz60Dfovlj8VG4F7rMqWU6tft87Jp6+ph+Tpt1TuK2G7t5ikKCgpMYWGhu8tQSrnRD1/6nLd31LD+rouIDQ92dzleQUQ2GWMK+lunV8YqpTzO0nPH09bZw0uf6V2oHEGDXinlcfJSYzlr/Cie+WQ/XT297i7H62nQK6U80o1zsqhq7GB10SF3l+L1NOiVUh7pwinJZCVG8tRH+/C0c4neRoNeKeWRAgKE756TydbyBjYfrHd3OV5Ng14p5bG+Piud2PBgnvxQJzsbCQ16pZTHiggJ4ltnjGVN8SHK69rcXY7X0qBXSnm068/KJECEp/XGJMOmQa+U8mijY8P46rQxvLyxXG83OEwa9Eopj3fjnPG0HOvm5Y3lg2+sTqJBr5TyeFPTY5mdmcDfPt5Pt15ANWQa9Eopr3Dj3CwqG9p5a0eNu0vxOhr0SimvMC8nhbEJETyl95UdMg16pZRXCAwQbjgnk00H6vlcL6AaEg16pZTX+EZBBtFhQdqqHyINeqWU14gKDeLq2WNZXXSIyoZ2d5fjNTTolVJe5fqzMwF4Ri+gspsGvVLKq6TFhbM4fzQvfnaQlmPd7i7HK2jQK6W8zo1zsmju6ObVQr2Ayh4a9EoprzNjbDyzxsXzt4/309Orc9UPRoNeKeWVbpyTxcG6Nt7ZqRdQDUaDXinllRbkppAWF85TOlf9oDTolVJeKSgwgBvOyeSz/XVsq2hwdzkeTYNeKeW1rjw9g6hQvYBqMBr0SimvFR0WzDcLMvjPtmoONXa4uxyPpUGvlPJqN5yTSa8xPLN+v7tL8Vh2Bb2ILBKR3SJSKiJ39rN+rIi8JyKfi8g2EVliXZ4pIu0issX68ZijvwGllH/LSIhgYd5oXthwkLZOvYCqP4MGvYgEAg8Di4Fc4GoRyT1hs18ArxhjZgBXAY/0WbfXGDPd+nGzg+pWSqnjvjc3i8b2Lv6+qcLdpXgke1r0s4FSY0yZMaYTeAm45IRtDBBjfRwLVDmuRKWUOrWZY+M5LSOOFR/vp1cvoDqJPUGfBvS9zrjCuqyvXwPXiEgFsAq4rc+6LGuXzgciMre/A4jIUhEpFJHCw4cP21+9UkoBIsKNc7LYd6SVtbtq3V2Ox3HUydirgaeNMenAEuA5EQkAqoGx1i6dHwEviEjMiU82xiw3xhQYYwqSkpIcVJJSyp8szh9NamyYDrXshz1BXwlk9Pk63bqsrxuBVwCMMeuBMCDRGHPMGHPUunwTsBeYNNKilVLqRMGBAVx/dibry45SXNU45Od3dPVQ3djOwaNtTqjOvYLs2GYjkC0iWVgC/irgWydscxC4CHhaRHKwBP1hEUkC6owxPSIyHsgGyhxWvVJK9XHV7LH85d0SnvpwH/dcnEddayd1rceoa+360uejrZ3Ut3ZS19p5/HFrZ8/x/fxk4WRuuWCiG78Txxo06I0x3SJyK7AGCARWGGOKReReoNAYsxL4MfCEiCzDcmL2O8YYIyLnAveKSBfQC9xsjKlz2nejlPJrseGWC6ie/mQ/r39+YseDRWhQAKMiQ0iICiEhMpSsxEgSIkNJiAwmITKU93bX8t9v7+GMrAQKMhNc/B04hxjjWWeoCwoKTGFhobvLUEp5qaMtx3ju0wNEhQaREBlCfGSIJditHxEhp27fNnd0seTBD+nthVX/NZfYiGAXVT4yIrLJGFPQ7zoNeqWU+rIt5Q1c8egnzM9N4ZFvz0RE3F3SoE4V9DoFglJKnWB6Rhx3LJzM6qJDvPDZQXeXM2Ia9Eop1Y+lc8czNzuRe/+1gz01ze4uZ0Q06JVSqh8BAcID3zyN6LAgbn1hMx1dPYM/yUNp0Cul1ACSo8N44JvT2VPTwm//vcPd5QybBr1SSp3CeZOSWHrueJ7fcJA3i6rdXc6waNArpdQg7lgwmWnpsfz0tW1UNrS7u5wh06BXSqlBhAQF8OBVM+jpNfzwxc/p7ul1d0lDokGvlFJ2yEyM5HeXTaXwQD0Pri11dzlDokGvlFJ2unRGGpfPTOOhtSV8WnbU3eXYTYNeKaWG4LeX5DNuVCS3v7SF+tZOd5djFw16pZQagsjQIP569QyOth7jJ69tw9OmkemPBr1SSg1RflosP1s0hXd21vDs+gPuLmdQGvRKKTUMN87J4oLJSfxu1U52VDW5u5xT0qBXSqlhEBH+9I3TiA0P5rYXN9PW2e3ukgakQa+UUsM0KiqU/7lyOmVHWvnNSs+dIkGDXimlRuCciYn8n/Mm8HJhOf/aWuXucvqlQa+UUiO0bP4kZoyN4+evb6e8zvNuLq5Br5RSIxQcaJkiAYGbni2kqaPL3SV9iQa9Uko5QEZCBI98eyaltS3c8vxmujxoPhwNeqWUcpC52Un8v8un8mHJEe5+Y7vHXEx16tuhK6WUGpJvFmRQUdfGg2tLyYiP4LaLst1dkga9Uko52rL5kyivb+eBt/eQnhDOZTPS3VqPBr1SSjmYiPCHr0+jurGdn762jdEx4Zw1YZTb6tE+eqWUcoKQoAAev6aAcaMi+f5zhZTWNrutFruCXkQWichuESkVkTv7WT9WRN4Tkc9FZJuILOmz7i7r83aLyEJHFq+UUp4sNiKYv33ndEKCArl+xUZqmzvcUsegQS8igcDDwGIgF7haRHJP2OwXwCvGmBnAVcAj1ufmWr/OAxYBj1j3p5RSfiEjIYIV3ymgrrWTG58udMucOPa06GcDpcaYMmNMJ/AScMkJ2xggxvo4FrBdB3wJ8JIx5pgxZh9Qat2fUkr5jWnpcfz16hkUVzXyXy9+Tk+va4dd2hP0aUB5n68rrMv6+jVwjYhUAKuA24bwXERkqYgUikjh4cOH7SxdKaW8x7zcFH59cR7v7Kzl3n8Vu3SMvaNOxl4NPG2MSQeWAM+JiN37NsYsN8YUGGMKkpKSHFSSUkp5luvOyuSmuVk8s/4AT320z2XHtWd4ZSWQ0efrdOuyvm7E0gePMWa9iIQBiXY+Vyml/MZdi3OoqG/nd6t2khYXzuKpY5x+THta3RuBbBHJEpEQLCdXV56wzUHgIgARyQHCgMPW7a4SkVARyQKygc8cVbxSSnmbgADhz1dOZ0ZGHLe/vIVNB+qdf8zBNjDGdAO3AmuAnVhG1xSLyL0icrF1sx8DN4nIVuBF4DvGohh4BdgBvAncYozpccY3opRS3iIsOJAnritgdGwYNz1byP4jrU49nnjKpDs2BQUFprCw0N1lKKWU0+070srlj3xMXEQIf/8/Z5MQGTLsfYnIJmNMQX/r9MpYpZRyk6zESJ64roDKhnaWPltIR5dzOjw06JVSyo0KMhP48zenU3ignh+/upVeJ4yx10nNlFLKzb4ybQwV9VNo6+xBxPH716BXSikP8P3zJjht39p1o5RSPk6DXimlfJwGvVJK+TgNeqWU8nEa9Eop5eM06JVSysdp0CullI/ToFdKKR/ncZOaichh4MAIdpEIHHFQOY6kdQ2N1jU0WtfQ+GJd44wx/d65yeOCfqREpHCgGdzcSesaGq1raLSuofG3urTrRimlfJwGvVJK+ThfDPrl7i5gAFrX0GhdQ6N1DY1f1eVzffRKKaW+zBdb9EoppfrQoFdKKR/nlUEvIotEZLeIlIrInf2sDxWRl63rN4hIpgtqyhCR90Rkh4gUi8gP+9nmfBFpFJEt1o9fObuuPsfeLyLbrcc96e7rYvGg9TXbJiIzXVDT5D6vxRYRaRKR20/YxiWvmYisEJFaESnqsyxBRN4WkRLr5/gBnnu9dZsSEbneBXXdLyK7rD+nN0QkboDnnvJn7oS6fi0ilX1+VksGeO4pf3+dUNfLfWraLyJbBniuM1+vfvPBZe8xY4xXfQCBwF5gPBACbAVyT9jmB8Bj1sdXAS+7oK4xwEzr42hgTz91nQ/8202v234g8RTrlwCrAQHOBDa44ed6CMtFHy5/zYBzgZlAUZ9lfwTutD6+E/hDP89LAMqsn+Otj+OdXNcCIMj6+A/91WXPz9wJdf0auMOOn/Mpf38dXdcJ6x8AfuWG16vffHDVe8wbW/SzgVJjTJkxphN4CbjkhG0uAZ6xPn4NuEjEGXdi/IIxptoYs9n6uBnYCaQ585gOdgnwrLH4FIgTkTEuPP5FwF5jzEiuih42Y8w6oO6ExX3fR88Al/bz1IXA28aYOmNMPfA2sMiZdRlj3jLGdFu//BRId9TxRlKXnez5/XVKXdYM+CbwoqOOZ69T5INL3mPeGPRpQHmfrys4OVCPb2P9hWgERrmkOsDaVTQD2NDP6rNEZKuIrBaRPFfVBBjgLRHZJCJL+1lvz+vqTFcx8C+gu16zFGNMtfXxISCln23c/bp9F8t/Yv0Z7GfuDLdau5RWDNAN4c7Xay5QY4wpGWC9S16vE/LBJe8xbwx6jyYiUcDfgduNMU0nrN6MpWviNOCvwD9cWNocY8xMYDFwi4ic68Jjn5KIhAAXA6/2s9qdr9lxxvI/tEeNRRaRu4Fu4PkBNnH1z/xRYAIwHajG0k3iSa7m1K15p79ep8oHZ77HvDHoK4GMPl+nW5f1u42IBAGxwFFnFyYiwVh+iM8bY14/cb0xpskY02J9vAoIFpFEZ9dlPV6l9XMt8AaWf6H7sud1dZbFwGZjTM2JK9z5mgE1tu4r6+fafrZxy+smIt8Bvgp82xoQJ7HjZ+5QxpgaY0yPMaYXeGKA47nr9QoCLgdeHmgbZ79eA+SDS95j3hj0G4FsEcmytgSvAlaesM1KwHZm+gpg7UC/DI5i7f97CthpjPnvAbYZbTtXICKzsbz+rvgDFCki0bbHWE7mFZ2w2UrgOrE4E2js8y+lsw3Y0nLXa2bV9310PfDPfrZZAywQkXhrV8UC6zKnEZFFwE+Bi40xbQNsY8/P3NF19T2nc9kAx7Pn99cZ5gG7jDEV/a109ut1inxwzXvMGWeYnf2BZYTIHixn7++2LrsXyxsfIAxLN0Ap8Bkw3gU1zcHyb9c2YIv1YwlwM3CzdZtbgWIsIw0+Bc520es13nrMrdbj216zvrUJ8LD1Nd0OFLiotkgswR3bZ5nLXzMsf2iqgS4sfaA3Yjmv8y5QArwDJFi3LQCe7PPc71rfa6XADS6oqxRLn63tfWYbYZYKrDrVz9zJdT1nfe9swxJgY06sy/r1Sb+/zqzLuvxp23uqz7aufL0GygeXvMd0CgSllPJx3th1o5RSagg06JVSysdp0CullI/ToFdKKR+nQa+UUj5Og14ppXycBr1SSvm4/w/zIi+V7lKIKgAAAABJRU5ErkJggg==\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": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 147us/step - loss: 9.6629e-04\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 146us/step - loss: 9.3481e-04\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 152us/step - loss: 9.2772e-04\n"
]
},
{
"output_type": "display_data",
"data": {
"image/png": 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sF7T86mu5VDd28PgHOtzSVUprfe9mI4OZnBJNenz4oP30q4uqmTI6mvFJw3tt8qwjb3TKYv/gESdjRWSpiBSKSOHhw4eHtY+JyVE8ds0sljs45G1Oz0zgK9PG8Pi6vVQ16B16XGFPjW9PZtYfEWFeTgoflR6hvbP/i/VqmjooPFA/7NY8wOiYMEZFhugQSz/hiKCvBDL6fJ1uXTbQ8pMYY5YbYwqMMQVJSUnDLmRB3minhLzNXYunYAz8frUOt3SFkpoWvxlx09f83BSOdffyUemRfte/WXQIYxh2/zxY/qBYTshqi94fOCLoVwLXWUffnAk0GmOqgTXAAhGJt56EXWBd5rXS4yNYeu54Vm6tYtOBoV2qrobOdlcpfxhx09fsrASiw4IG7L75z/ZqspOjmDjCawvyUmPYU9PMsW6d5sPX2TO88kVgPTBZRCpE5EYRuVlEbrZusgooA0qBJ4AfABhj6oDfAhutH/dal3m1m8+bQEpMKL/51w56e9073LKyoZ2H3yulqcM3L2UvqWnxq/55m+DAAM6blMS7u2pOeo/VNnewcX/diLptbPJTY+nuNcengVa+K2iwDYwxVw+y3gC3DLBuBbBieKV5psjQIH62aAo/emUrr39eyRWz0l1eQ1dPL3/7eB9/fruE9q4eOrp6+PGCyS6vw5ka27s41NThk7cPtMf83BT+va2aLRUNzBz7xajkNcU11m4bBwT98ROyjcfnqVe+ySNOxnqbS6encVpGHH98cxetx1w73HLzwXq+9teP+H+rdnHWhFGcPWEUz316wOeGfZYen/rA/1r0AOdPSiYwQE7qvlm1rZoJSZEOmfsnIz6C6NAgvULWD2jQD0NAgHDP13KpbT7Go+/vdckxG9u6uPuN7Xz90U9oaOvisWtm8tT1Bfxo/iQa2rp4tbDCJXW4SkmNbTIz/2zRx0YEMzsz4UuzWR5pOcaGfUdZMnUMIiM/bxEQIDplsZ/QoB+mmWPjuXR6Kss/LKO8rs1pxzHG8M8tlVz03+/z4mcH+e45Wbzz4/NYlG/5ZS/ITGDm2Die/KiMHjefM3CkktoWwoIDSI/3rxE3fc3LTWFPTQsHj1reX2uKD9HroG4bm7zUWHZWN/nUe0edTIN+BH62eAoB4rzhlvuOtHLtU5/xw5e2kBYXzspb5/DLr+YSFfrlUytLzx1PeV07bxYdckod7mCb+sDfRtz0Nc82yZm1Vb96+yGyEiOZMtpx/+Xkp8XQ0dVL2WE9IevLNOhHYExsODefN4H/bK9mQ9lRh+33WHcP//POHhb+zzq2ljfw20vyeP0H5wx4wmx+7mgyR0WwfN1en5l4rbS2hUl+MDXxqYwbFUl2chTv7KyhrrWT9WVHWTJ1tEO6bWxs7yntvvFtg466Uaf2/XMn8MrGcr73TCHTMmLJHRNDzpgYclNjmJAURXDg0P6WflJ6hF/8o4iyI6187bRUfvmVHJJjwk75nMAA4ca54/nlP4rYuL+e2VkJI/mW3K6po4vqxg4m+vjNRuwxLzeF5evKeLWwnJ5ew+IhTkk8mPGJkYQGBVBc2cRlMxy6a+VBNOhHKDwkkOXXFfC/nx5gR3UTz64/wDHrDZ5DAgPITomyBL/tD8CYGGIjgk/az5GWY/zuPzt54/NKxo2K4Jnvzua8SfZfJXzFzHT+/PYelq/b6/VBbxtx4+8terDcjOTR9/fyl3dLGDcqgrzUGIfuPygwgJwxekLW12nQO0B+Wiy///o0ALp7etl3pJUd1U3sqG5iZ3Uz7++u5bVNX4yKSYsLP97qzx0TzZGWTu5fs5u2zm5uu3Ait1wwcchTOYSHBHLtmeP4y7sllNa2ePXUvrYRN75+n1h7TM+IIzEqhCMtnSzOd8xomxPlpcawcmsVxhin7F+5nwa9gwUFBpCdEk12SjSXTP9iss7a5g52Vjezo6qJndY/Amt31WAb7HDm+AT+76VTRxTQ1501jsc+2MuTH5Yd/8PjjUpqbCNu7L8Pqq8KDBAunJLMK4UVI5rb5lTy02J5fsNByuvah3TvWeU9NOhdJDk6jOTosC91x7R39rCnppnWzm7OGj9qxK2pUVGhXDErnVcLK/jRgkkkR5+6b99T7altYUJSFIF+POKmr++fN4FxoyKZ6qSrV/P73ENWg9436agbNwoPCeS0jDjOnpDosH+Zvzd3PF29vTy3/oBD9ucOpTXNfnuhVH8mJEVxywUTndatMml0FEEBolMW+zANeh+TlRjJgtwUr50Wobmji6rGDq8+x+BtQoMCyU6J1imLfZgGvQ9aeu54r50W4fiIG23Ru1R+agzFVY0+cx2G+jINeh80a1wCs8bF8+RHZXT39Lq7nCGxTZnrr5OZuUteagxHWjqpbT7m7lKUE2jQ+6ib5lqmRVhTfOp7j3qaPTXNhAYFkJGgJwVd6fgVspXaT++LNOh91PzcFK+cFqFER9y4Rc6YGETQKYt9lAa9jwoMEL43dzxbKxr5bJ/33NirpKbZIXOtq6GJDA0iKzFSW/Q+SoPeh10xK52EyBCe+LDM3aXYxTbixl/vKuVu+amx2qL3URr0PiwsOJDrzhrHOztrKa1tdnc5g/L3u0q5W15qDJUN7dS3drq7FOVgGvQ+7tozxxEaFMCTH+5zdymDKtGhlW5lOyGrrXrfo0Hv42zTIry+uZLa5g53l3NKJTrixq1sM2PqFbK+R4PeD9imRXj2E8+eFkFH3LhXXEQIaXHhFGmL3udo0PuBvtMitB7z3GkRSmpadGpiN8tPi6FYR974HA16P7H03Ak0tnfxamG5u0vpV8uxbiob2rV/3s3yUmPZd7SVFg9uEKih06D3E7PGxTNrXDxPfbzPI6dFsI240cnM3Cs/LQZjYGe1dt/4Eg16P7L0XMu0CG8WH3J3KSex3VVKW/TudXxueu2+8Sl2Bb2ILBKR3SJSKiJ39rN+nIi8KyLbROR9EUnvs65HRLZYP1Y6sng1NPNyUshKjOSJdWUeNy1CSW0LIUEBjNURN26VHBNGYlSoDrH0MYMGvYgEAg8Di4Fc4GoRyT1hsz8BzxpjpgH3Avf1WddujJlu/bjYQXWrYQgMEG6ck8XWikY2DGNaBGMMJTXNPLS2hEse/pjf/WeHw2orqWnWETceIj8tRlv0PsaeFv1soNQYU2aM6QReAi45YZtcYK318Xv9rFce4vi0COvsmxaht9ew+WA9963eyYUPfMD8P6/jT2/toaaxgyc/2seuQ45p+e2padErYj1EfmospbUtdHT1uLsU5SD2BH0a0HeoRoV1WV9bgcutjy8DokVklPXrMBEpFJFPReTS/g4gIkut2xQePnx4COWrobJNi/DuroGnRejs7mXdnsPc/cZ2zrzvXS5/5BOe+nAf6fHh/PbSfD696yLW3H4uUaFB/GnN7hHX1Hp8xI0GvSfIS42hu9ewp8bzp81Q9nHUzcHvAB4Ske8A64BKwNYcGGeMqRSR8cBaEdlujNnb98nGmOXAcoCCggLP6jz2Qdedlcmj7+/liXX7+MMV0wBL2H6w5zBrig+xdlctzR3dhAcHcv7kJBbkpXDh5BRiI4K/tJ+bz5vA/Wt2s+lAHbPGJQy7ni9G3OiJWE/wxdz0TUxLj3NzNcoR7An6SiCjz9fp1mXHGWOqsLboRSQK+LoxpsG6rtL6uUxE3gdmAF8KeuVaCZEhfKMgnVc2VpCXFsMHuw/zYekROrt7iY8IZlHeaBbkjWZudiJhwYED7ueGczL528f7+eObu3lp6ZnDvnn1F3PcaIveE6THhxMTFqRTIfgQe4J+I5AtIllYAv4q4Ft9NxCRRKDOGNML3AWssC6PB9qMMces25wD/NGB9ath+t6c8Ty/4SC/+mcxaXHhfGv2WBbmjeb0zHiCAu0bdRsREsRtF07knpXFfFhyhHMnJQ2rlpKaZkICdcSNpxAR8lJjdSoEHzJo0BtjukXkVmANEAisMMYUi8i9QKExZiVwPnCfiBgsXTe3WJ+eAzwuIr1Yzgf83hjjuKEaatgyEyN56aYziQwNIi81Ztit8atmZ7B8XRn3r9nN3OzEYe1nT00z45Mi7f4Do5wvPy2GZ9cfoLunV38uPsCuPnpjzCpg1QnLftXn8WvAa/087xNg6ghrVE5yxvhRg280iNCgQJbNn8Qdr25lddEhlkwdM+R9lNS2MHNs/IhrUY6TlxrLse5e9h5uZfJoPXfi7fRPtRqxy2akkZ0cxQNv7R7y9Aqtx7qpqG/XoZUeJj/NMmWxjqf3DRr0asQCA4QfL5jM3sOtvP555eBP6GPvYetdpXTqA4+SlRhFeHCgXiHrIzTolUMszEvhtPRY/vJOCce67b/QZk+NLei1Re9JAgOEnDHRFOnIG5+gQa8cQkT4ycIpVDa08/ynB+1+XkmtZcTNOB1x43Hy02LZWdVEb6/9l7YYY6ht7mDzwXpWbq1i35FWJ1ao7OWoC6aUYk52ImdPGMXD75Vy5ekZRIYO/vYqqWnRETceKi/VMvLmYF0bmYmRgCXIj7Z2UlHfTnldGxX17VTUWz6X17dRWd/Ose4vztOMT4rk7WXn6RxGbqZBrxzqJwsnc9kjn7Dio33cdlH2oNuX1DYzPUNH3HiiPOuUxfesLEaE46He0fXlE+7xEcGkx0cwOSWaeTkppMeHkx4fTkV9O7/6ZzErt1Zy2Yz0/g6hXESDXjnUjLHxzM9NYfm6Mq45cxzxkSEDbtvW2U15XTvfmJUx4DbKfSalRJMWF87WigbS48OZmBTF+ZOSrEEeQUZCBGnx4UQN8J9bb6/hxc/KefDdUr42LVX/a3MjDXrlcHcsmMyiv6zjsQ/2cteSnAG321tr6b/VqQ88U0hQAB/97IJhX0wXECAsm5fN0uc28Y8tVVwxS1v17qJ/YpXDTR4dzWXT03j6k/0cauwYcDvb7Ig6mZnnGm7I28zPTSE/LYa/ri2hywNvYekvNOiVUyybP4leY/jr2pIBtympbSE4UMgcpSNufJWIsGzeJA4cbeONzUO7xkI5jga9coqMhAiunj2WlzeWc+Bo/0PsSmqaGZ8YpX23Pu7CKcmclh7Lg2tL6OzWVr076G+YcppbL5hIUKDw32/v6Xd9SW2LXijlB0SE2+dPoqK+nb9vrnB3OX5Jg145TXJMGDeck8XKrVXsrP7ypfTtnT2U17eRrf3zfuH8SUlMz4jjobWl2qp3Aw165VQ3nzuB6NAgHnjry7cc3Hu4BWN0xI2/EBF+NH8SlQ3tvFJYPvgTlENp0Cunio0I5vvnTeCdnbVsOlB3fLltxI1OZuY/5mYnUjAunoffK9Ubj7uYBr1yuhvOySQxKpQ/vrkbYyzzpthG3IzTETd+Q0RYNn8S1Y0dvLxRW/WupEGvnM52y8EN++pYV3IE+GLETbCOuPErZ08YxeysBB55X1v1rqS/Zcolrp49lvT4cO5fswtjDHtqWpio/fN+xzauvqbpGC9ssH+WUzUyGvTKJUKCAlg2bxJFlU288Xkl5fVtTNIRN37prAmjOGv8KB79YC/tndqqdwUNeuUyl1pvOXjPymKM0ZuN+LNl8ydxuPkYz2844O5S/IIGvXIZ2y0Hmzu6AR1a6c9mZyUwZ2Iij76/l7bObneX4/M06JVLLcxL4bSMOOuIm0h3l6PcaNn8bI62dvLcem3VO5sGvXIpEeEvV07noW/N1BE3fm7WuATOnZTE4+vKaD2mrXpn0t805XKZiZEszBvt7jKUB1g2L5u61k6eWb/f3aX4NA16pZTbzBgbz4VTklm+rozmji53l+OzNOiVUm51+7xsGtq6eOaT/e4uxWfZFfQiskhEdotIqYjc2c/6cSLyrohsE5H3RSS9z7rrRaTE+nG9I4tXSnm/aelxzMux3Ge4SVv1TjFo0ItIIPAwsBjIBa4WkdwTNvsT8KwxZhpwL3Cf9bkJwD3AGcBs4B4RiXdc+UopX3D7vGyaOrpZ8dE+d5fik+xp0c8GSo0xZcaYTuAl4JITtskF1lofv9dn/ULgbWNMnTGmHngbWDTyspVSviQ/LZaFeSk89dE+Gtu0Ve9o9gR9GtB3qrkK67K+tgKXWx9fBkSLyCg7n4uILBWRQhEpPHz4sL21K6V8yO3zJtHc0c1TH5W5u5wOKJMAABAfSURBVBSf46iTsXcA54nI58B5QCVg9yQWxpjlxpgCY0xBUlKSg0pSSnmTnDExLJk6mhUf76ehrdPd5fgUe4K+Esjo83W6ddlxxpgqY8zlxpgZwN3WZQ32PFcppWx+eNEkWju7eeJDbdU7kj1BvxHIFpEsEQkBrgJW9t1ARBJFxLavu4AV1sdrgAUiEm89CbvAukwppU4yeXQ0X5k6hqc/3k9dq7bqHWXQoDfGdAO3YgnoncArxphiEblXRC62bnY+sFtE9gApwO+sz60Dfovlj8VG4F7rMqWU6tft87Jp6+ph+Tpt1TuK2G7t5ikKCgpMYWGhu8tQSrnRD1/6nLd31LD+rouIDQ92dzleQUQ2GWMK+lunV8YqpTzO0nPH09bZw0uf6V2oHEGDXinlcfJSYzlr/Cie+WQ/XT297i7H62nQK6U80o1zsqhq7GB10SF3l+L1NOiVUh7pwinJZCVG8tRH+/C0c4neRoNeKeWRAgKE756TydbyBjYfrHd3OV5Ng14p5bG+Piud2PBgnvxQJzsbCQ16pZTHiggJ4ltnjGVN8SHK69rcXY7X0qBXSnm068/KJECEp/XGJMOmQa+U8mijY8P46rQxvLyxXG83OEwa9Eopj3fjnPG0HOvm5Y3lg2+sTqJBr5TyeFPTY5mdmcDfPt5Pt15ANWQa9Eopr3Dj3CwqG9p5a0eNu0vxOhr0SimvMC8nhbEJETyl95UdMg16pZRXCAwQbjgnk00H6vlcL6AaEg16pZTX+EZBBtFhQdqqHyINeqWU14gKDeLq2WNZXXSIyoZ2d5fjNTTolVJe5fqzMwF4Ri+gspsGvVLKq6TFhbM4fzQvfnaQlmPd7i7HK2jQK6W8zo1zsmju6ObVQr2Ayh4a9EoprzNjbDyzxsXzt4/309Orc9UPRoNeKeWVbpyTxcG6Nt7ZqRdQDUaDXinllRbkppAWF85TOlf9oDTolVJeKSgwgBvOyeSz/XVsq2hwdzkeTYNeKeW1rjw9g6hQvYBqMBr0SimvFR0WzDcLMvjPtmoONXa4uxyPpUGvlPJqN5yTSa8xPLN+v7tL8Vh2Bb2ILBKR3SJSKiJ39rN+rIi8JyKfi8g2EVliXZ4pIu0issX68ZijvwGllH/LSIhgYd5oXthwkLZOvYCqP4MGvYgEAg8Di4Fc4GoRyT1hs18ArxhjZgBXAY/0WbfXGDPd+nGzg+pWSqnjvjc3i8b2Lv6+qcLdpXgke1r0s4FSY0yZMaYTeAm45IRtDBBjfRwLVDmuRKWUOrWZY+M5LSOOFR/vp1cvoDqJPUGfBvS9zrjCuqyvXwPXiEgFsAq4rc+6LGuXzgciMre/A4jIUhEpFJHCw4cP21+9UkoBIsKNc7LYd6SVtbtq3V2Ox3HUydirgaeNMenAEuA5EQkAqoGx1i6dHwEviEjMiU82xiw3xhQYYwqSkpIcVJJSyp8szh9NamyYDrXshz1BXwlk9Pk63bqsrxuBVwCMMeuBMCDRGHPMGHPUunwTsBeYNNKilVLqRMGBAVx/dibry45SXNU45Od3dPVQ3djOwaNtTqjOvYLs2GYjkC0iWVgC/irgWydscxC4CHhaRHKwBP1hEUkC6owxPSIyHsgGyhxWvVJK9XHV7LH85d0SnvpwH/dcnEddayd1rceoa+360uejrZ3Ut3ZS19p5/HFrZ8/x/fxk4WRuuWCiG78Txxo06I0x3SJyK7AGCARWGGOKReReoNAYsxL4MfCEiCzDcmL2O8YYIyLnAveKSBfQC9xsjKlz2nejlPJrseGWC6ie/mQ/r39+YseDRWhQAKMiQ0iICiEhMpSsxEgSIkNJiAwmITKU93bX8t9v7+GMrAQKMhNc/B04hxjjWWeoCwoKTGFhobvLUEp5qaMtx3ju0wNEhQaREBlCfGSIJditHxEhp27fNnd0seTBD+nthVX/NZfYiGAXVT4yIrLJGFPQ7zoNeqWU+rIt5Q1c8egnzM9N4ZFvz0RE3F3SoE4V9DoFglJKnWB6Rhx3LJzM6qJDvPDZQXeXM2Ia9Eop1Y+lc8czNzuRe/+1gz01ze4uZ0Q06JVSqh8BAcID3zyN6LAgbn1hMx1dPYM/yUNp0Cul1ACSo8N44JvT2VPTwm//vcPd5QybBr1SSp3CeZOSWHrueJ7fcJA3i6rdXc6waNArpdQg7lgwmWnpsfz0tW1UNrS7u5wh06BXSqlBhAQF8OBVM+jpNfzwxc/p7ul1d0lDokGvlFJ2yEyM5HeXTaXwQD0Pri11dzlDokGvlFJ2unRGGpfPTOOhtSV8WnbU3eXYTYNeKaWG4LeX5DNuVCS3v7SF+tZOd5djFw16pZQagsjQIP569QyOth7jJ69tw9OmkemPBr1SSg1RflosP1s0hXd21vDs+gPuLmdQGvRKKTUMN87J4oLJSfxu1U52VDW5u5xT0qBXSqlhEBH+9I3TiA0P5rYXN9PW2e3ukgakQa+UUsM0KiqU/7lyOmVHWvnNSs+dIkGDXimlRuCciYn8n/Mm8HJhOf/aWuXucvqlQa+UUiO0bP4kZoyN4+evb6e8zvNuLq5Br5RSIxQcaJkiAYGbni2kqaPL3SV9iQa9Uko5QEZCBI98eyaltS3c8vxmujxoPhwNeqWUcpC52Un8v8un8mHJEe5+Y7vHXEx16tuhK6WUGpJvFmRQUdfGg2tLyYiP4LaLst1dkga9Uko52rL5kyivb+eBt/eQnhDOZTPS3VqPBr1SSjmYiPCHr0+jurGdn762jdEx4Zw1YZTb6tE+eqWUcoKQoAAev6aAcaMi+f5zhZTWNrutFruCXkQWichuESkVkTv7WT9WRN4Tkc9FZJuILOmz7i7r83aLyEJHFq+UUp4sNiKYv33ndEKCArl+xUZqmzvcUsegQS8igcDDwGIgF7haRHJP2OwXwCvGmBnAVcAj1ufmWr/OAxYBj1j3p5RSfiEjIYIV3ymgrrWTG58udMucOPa06GcDpcaYMmNMJ/AScMkJ2xggxvo4FrBdB3wJ8JIx5pgxZh9Qat2fUkr5jWnpcfz16hkUVzXyXy9+Tk+va4dd2hP0aUB5n68rrMv6+jVwjYhUAKuA24bwXERkqYgUikjh4cOH7SxdKaW8x7zcFH59cR7v7Kzl3n8Vu3SMvaNOxl4NPG2MSQeWAM+JiN37NsYsN8YUGGMKkpKSHFSSUkp5luvOyuSmuVk8s/4AT320z2XHtWd4ZSWQ0efrdOuyvm7E0gePMWa9iIQBiXY+Vyml/MZdi3OoqG/nd6t2khYXzuKpY5x+THta3RuBbBHJEpEQLCdXV56wzUHgIgARyQHCgMPW7a4SkVARyQKygc8cVbxSSnmbgADhz1dOZ0ZGHLe/vIVNB+qdf8zBNjDGdAO3AmuAnVhG1xSLyL0icrF1sx8DN4nIVuBF4DvGohh4BdgBvAncYozpccY3opRS3iIsOJAnritgdGwYNz1byP4jrU49nnjKpDs2BQUFprCw0N1lKKWU0+070srlj3xMXEQIf/8/Z5MQGTLsfYnIJmNMQX/r9MpYpZRyk6zESJ64roDKhnaWPltIR5dzOjw06JVSyo0KMhP48zenU3ignh+/upVeJ4yx10nNlFLKzb4ybQwV9VNo6+xBxPH716BXSikP8P3zJjht39p1o5RSPk6DXimlfJwGvVJK+TgNeqWU8nEa9Eop5eM06JVSysdp0CullI/ToFdKKR/ncZOaichh4MAIdpEIHHFQOY6kdQ2N1jU0WtfQ+GJd44wx/d65yeOCfqREpHCgGdzcSesaGq1raLSuofG3urTrRimlfJwGvVJK+ThfDPrl7i5gAFrX0GhdQ6N1DY1f1eVzffRKKaW+zBdb9EoppfrQoFdKKR/nlUEvIotEZLeIlIrInf2sDxWRl63rN4hIpgtqyhCR90Rkh4gUi8gP+9nmfBFpFJEt1o9fObuuPsfeLyLbrcc96e7rYvGg9TXbJiIzXVDT5D6vxRYRaRKR20/YxiWvmYisEJFaESnqsyxBRN4WkRLr5/gBnnu9dZsSEbneBXXdLyK7rD+nN0QkboDnnvJn7oS6fi0ilX1+VksGeO4pf3+dUNfLfWraLyJbBniuM1+vfvPBZe8xY4xXfQCBwF5gPBACbAVyT9jmB8Bj1sdXAS+7oK4xwEzr42hgTz91nQ/8202v234g8RTrlwCrAQHOBDa44ed6CMtFHy5/zYBzgZlAUZ9lfwTutD6+E/hDP89LAMqsn+Otj+OdXNcCIMj6+A/91WXPz9wJdf0auMOOn/Mpf38dXdcJ6x8AfuWG16vffHDVe8wbW/SzgVJjTJkxphN4CbjkhG0uAZ6xPn4NuEjEGXdi/IIxptoYs9n6uBnYCaQ585gOdgnwrLH4FIgTkTEuPP5FwF5jzEiuih42Y8w6oO6ExX3fR88Al/bz1IXA28aYOmNMPfA2sMiZdRlj3jLGdFu//BRId9TxRlKXnez5/XVKXdYM+CbwoqOOZ69T5INL3mPeGPRpQHmfrys4OVCPb2P9hWgERrmkOsDaVTQD2NDP6rNEZKuIrBaRPFfVBBjgLRHZJCJL+1lvz+vqTFcx8C+gu16zFGNMtfXxISCln23c/bp9F8t/Yv0Z7GfuDLdau5RWDNAN4c7Xay5QY4wpGWC9S16vE/LBJe8xbwx6jyYiUcDfgduNMU0nrN6MpWviNOCvwD9cWNocY8xMYDFwi4ic68Jjn5KIhAAXA6/2s9qdr9lxxvI/tEeNRRaRu4Fu4PkBNnH1z/xRYAIwHajG0k3iSa7m1K15p79ep8oHZ77HvDHoK4GMPl+nW5f1u42IBAGxwFFnFyYiwVh+iM8bY14/cb0xpskY02J9vAoIFpFEZ9dlPV6l9XMt8AaWf6H7sud1dZbFwGZjTM2JK9z5mgE1tu4r6+fafrZxy+smIt8Bvgp82xoQJ7HjZ+5QxpgaY0yPMaYXeGKA47nr9QoCLgdeHmgbZ79eA+SDS95j3hj0G4FsEcmytgSvAlaesM1KwHZm+gpg7UC/DI5i7f97CthpjPnvAbYZbTtXICKzsbz+rvgDFCki0bbHWE7mFZ2w2UrgOrE4E2js8y+lsw3Y0nLXa2bV9310PfDPfrZZAywQkXhrV8UC6zKnEZFFwE+Bi40xbQNsY8/P3NF19T2nc9kAx7Pn99cZ5gG7jDEV/a109ut1inxwzXvMGWeYnf2BZYTIHixn7++2LrsXyxsfIAxLN0Ap8Bkw3gU1zcHyb9c2YIv1YwlwM3CzdZtbgWIsIw0+Bc520es13nrMrdbj216zvrUJ8LD1Nd0OFLiotkgswR3bZ5nLXzMsf2iqgS4sfaA3Yjmv8y5QArwDJFi3LQCe7PPc71rfa6XADS6oqxRLn63tfWYbYZYKrDrVz9zJdT1nfe9swxJgY06sy/r1Sb+/zqzLuvxp23uqz7aufL0GygeXvMd0CgSllPJx3th1o5RSagg06JVSysdp0CullI/ToFdKKR+nQa+UUj5Og14ppXycBr1SSvm4/w/zIi+V7lKIKgAAAABJRU5ErkJggg==\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": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 162us/step - loss: 9.1540e-04\n"
]
},
{
"output_type": "display_data",
"data": {
"image/png": 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sF7T86mu5VDd28PgHOtzSVUprfe9mI4OZnBJNenz4oP30q4uqmTI6mvFJw3tt8qwjb3TKYv/gESdjRWSpiBSKSOHhw4eHtY+JyVE8ds0sljs45G1Oz0zgK9PG8Pi6vVQ16B16XGFPjW9PZtYfEWFeTgoflR6hvbP/i/VqmjooPFA/7NY8wOiYMEZFhugQSz/hiKCvBDL6fJ1uXTbQ8pMYY5YbYwqMMQVJSUnDLmRB3minhLzNXYunYAz8frUOt3SFkpoWvxlx09f83BSOdffyUemRfte/WXQIYxh2/zxY/qBYTshqi94fOCLoVwLXWUffnAk0GmOqgTXAAhGJt56EXWBd5rXS4yNYeu54Vm6tYtOBoV2qrobOdlcpfxhx09fsrASiw4IG7L75z/ZqspOjmDjCawvyUmPYU9PMsW6d5sPX2TO88kVgPTBZRCpE5EYRuVlEbrZusgooA0qBJ4AfABhj6oDfAhutH/dal3m1m8+bQEpMKL/51w56e9073LKyoZ2H3yulqcM3L2UvqWnxq/55m+DAAM6blMS7u2pOeo/VNnewcX/diLptbPJTY+nuNcengVa+K2iwDYwxVw+y3gC3DLBuBbBieKV5psjQIH62aAo/emUrr39eyRWz0l1eQ1dPL3/7eB9/fruE9q4eOrp6+PGCyS6vw5ka27s41NThk7cPtMf83BT+va2aLRUNzBz7xajkNcU11m4bBwT98ROyjcfnqVe+ySNOxnqbS6encVpGHH98cxetx1w73HLzwXq+9teP+H+rdnHWhFGcPWEUz316wOeGfZYen/rA/1r0AOdPSiYwQE7qvlm1rZoJSZEOmfsnIz6C6NAgvULWD2jQD0NAgHDP13KpbT7Go+/vdckxG9u6uPuN7Xz90U9oaOvisWtm8tT1Bfxo/iQa2rp4tbDCJXW4SkmNbTIz/2zRx0YEMzsz4UuzWR5pOcaGfUdZMnUMIiM/bxEQIDplsZ/QoB+mmWPjuXR6Kss/LKO8rs1pxzHG8M8tlVz03+/z4mcH+e45Wbzz4/NYlG/5ZS/ITGDm2Die/KiMHjefM3CkktoWwoIDSI/3rxE3fc3LTWFPTQsHj1reX2uKD9HroG4bm7zUWHZWN/nUe0edTIN+BH62eAoB4rzhlvuOtHLtU5/xw5e2kBYXzspb5/DLr+YSFfrlUytLzx1PeV07bxYdckod7mCb+sDfRtz0Nc82yZm1Vb96+yGyEiOZMtpx/+Xkp8XQ0dVL2WE9IevLNOhHYExsODefN4H/bK9mQ9lRh+33WHcP//POHhb+zzq2ljfw20vyeP0H5wx4wmx+7mgyR0WwfN1en5l4rbS2hUl+MDXxqYwbFUl2chTv7KyhrrWT9WVHWTJ1tEO6bWxs7yntvvFtg466Uaf2/XMn8MrGcr73TCHTMmLJHRNDzpgYclNjmJAURXDg0P6WflJ6hF/8o4iyI6187bRUfvmVHJJjwk75nMAA4ca54/nlP4rYuL+e2VkJI/mW3K6po4vqxg4m+vjNRuwxLzeF5evKeLWwnJ5ew+IhTkk8mPGJkYQGBVBc2cRlMxy6a+VBNOhHKDwkkOXXFfC/nx5gR3UTz64/wDHrDZ5DAgPITomyBL/tD8CYGGIjgk/az5GWY/zuPzt54/NKxo2K4Jnvzua8SfZfJXzFzHT+/PYelq/b6/VBbxtx4+8terDcjOTR9/fyl3dLGDcqgrzUGIfuPygwgJwxekLW12nQO0B+Wiy///o0ALp7etl3pJUd1U3sqG5iZ3Uz7++u5bVNX4yKSYsLP97qzx0TzZGWTu5fs5u2zm5uu3Ait1wwcchTOYSHBHLtmeP4y7sllNa2ePXUvrYRN75+n1h7TM+IIzEqhCMtnSzOd8xomxPlpcawcmsVxhin7F+5nwa9gwUFBpCdEk12SjSXTP9iss7a5g52Vjezo6qJndY/Amt31WAb7HDm+AT+76VTRxTQ1501jsc+2MuTH5Yd/8PjjUpqbCNu7L8Pqq8KDBAunJLMK4UVI5rb5lTy02J5fsNByuvah3TvWeU9NOhdJDk6jOTosC91x7R39rCnppnWzm7OGj9qxK2pUVGhXDErnVcLK/jRgkkkR5+6b99T7altYUJSFIF+POKmr++fN4FxoyKZ6qSrV/P73ENWg9436agbNwoPCeS0jDjOnpDosH+Zvzd3PF29vTy3/oBD9ucOpTXNfnuhVH8mJEVxywUTndatMml0FEEBolMW+zANeh+TlRjJgtwUr50Wobmji6rGDq8+x+BtQoMCyU6J1imLfZgGvQ9aeu54r50W4fiIG23Ru1R+agzFVY0+cx2G+jINeh80a1wCs8bF8+RHZXT39Lq7nCGxTZnrr5OZuUteagxHWjqpbT7m7lKUE2jQ+6ib5lqmRVhTfOp7j3qaPTXNhAYFkJGgJwVd6fgVspXaT++LNOh91PzcFK+cFqFER9y4Rc6YGETQKYt9lAa9jwoMEL43dzxbKxr5bJ/33NirpKbZIXOtq6GJDA0iKzFSW/Q+SoPeh10xK52EyBCe+LDM3aXYxTbixl/vKuVu+amx2qL3URr0PiwsOJDrzhrHOztrKa1tdnc5g/L3u0q5W15qDJUN7dS3drq7FOVgGvQ+7tozxxEaFMCTH+5zdymDKtGhlW5lOyGrrXrfo0Hv42zTIry+uZLa5g53l3NKJTrixq1sM2PqFbK+R4PeD9imRXj2E8+eFkFH3LhXXEQIaXHhFGmL3udo0PuBvtMitB7z3GkRSmpadGpiN8tPi6FYR974HA16P7H03Ak0tnfxamG5u0vpV8uxbiob2rV/3s3yUmPZd7SVFg9uEKih06D3E7PGxTNrXDxPfbzPI6dFsI240cnM3Cs/LQZjYGe1dt/4Eg16P7L0XMu0CG8WH3J3KSex3VVKW/TudXxueu2+8Sl2Bb2ILBKR3SJSKiJ39rN+nIi8KyLbROR9EUnvs65HRLZYP1Y6sng1NPNyUshKjOSJdWUeNy1CSW0LIUEBjNURN26VHBNGYlSoDrH0MYMGvYgEAg8Di4Fc4GoRyT1hsz8BzxpjpgH3Avf1WddujJlu/bjYQXWrYQgMEG6ck8XWikY2DGNaBGMMJTXNPLS2hEse/pjf/WeHw2orqWnWETceIj8tRlv0PsaeFv1soNQYU2aM6QReAi45YZtcYK318Xv9rFce4vi0COvsmxaht9ew+WA9963eyYUPfMD8P6/jT2/toaaxgyc/2seuQ45p+e2padErYj1EfmospbUtdHT1uLsU5SD2BH0a0HeoRoV1WV9bgcutjy8DokVklPXrMBEpFJFPReTS/g4gIkut2xQePnx4COWrobJNi/DuroGnRejs7mXdnsPc/cZ2zrzvXS5/5BOe+nAf6fHh/PbSfD696yLW3H4uUaFB/GnN7hHX1Hp8xI0GvSfIS42hu9ewp8bzp81Q9nHUzcHvAB4Ske8A64BKwNYcGGeMqRSR8cBaEdlujNnb98nGmOXAcoCCggLP6jz2Qdedlcmj7+/liXX7+MMV0wBL2H6w5zBrig+xdlctzR3dhAcHcv7kJBbkpXDh5BRiI4K/tJ+bz5vA/Wt2s+lAHbPGJQy7ni9G3OiJWE/wxdz0TUxLj3NzNcoR7An6SiCjz9fp1mXHGWOqsLboRSQK+LoxpsG6rtL6uUxE3gdmAF8KeuVaCZEhfKMgnVc2VpCXFsMHuw/zYekROrt7iY8IZlHeaBbkjWZudiJhwYED7ueGczL528f7+eObu3lp6ZnDvnn1F3PcaIveE6THhxMTFqRTIfgQe4J+I5AtIllYAv4q4Ft9NxCRRKDOGNML3AWssC6PB9qMMces25wD/NGB9ath+t6c8Ty/4SC/+mcxaXHhfGv2WBbmjeb0zHiCAu0bdRsREsRtF07knpXFfFhyhHMnJQ2rlpKaZkICdcSNpxAR8lJjdSoEHzJo0BtjukXkVmANEAisMMYUi8i9QKExZiVwPnCfiBgsXTe3WJ+eAzwuIr1Yzgf83hjjuKEaatgyEyN56aYziQwNIi81Ztit8atmZ7B8XRn3r9nN3OzEYe1nT00z45Mi7f4Do5wvPy2GZ9cfoLunV38uPsCuPnpjzCpg1QnLftXn8WvAa/087xNg6ghrVE5yxvhRg280iNCgQJbNn8Qdr25lddEhlkwdM+R9lNS2MHNs/IhrUY6TlxrLse5e9h5uZfJoPXfi7fRPtRqxy2akkZ0cxQNv7R7y9Aqtx7qpqG/XoZUeJj/NMmWxjqf3DRr0asQCA4QfL5jM3sOtvP555eBP6GPvYetdpXTqA4+SlRhFeHCgXiHrIzTolUMszEvhtPRY/vJOCce67b/QZk+NLei1Re9JAgOEnDHRFOnIG5+gQa8cQkT4ycIpVDa08/ynB+1+XkmtZcTNOB1x43Hy02LZWdVEb6/9l7YYY6ht7mDzwXpWbq1i35FWJ1ao7OWoC6aUYk52ImdPGMXD75Vy5ekZRIYO/vYqqWnRETceKi/VMvLmYF0bmYmRgCXIj7Z2UlHfTnldGxX17VTUWz6X17dRWd/Ose4vztOMT4rk7WXn6RxGbqZBrxzqJwsnc9kjn7Dio33cdlH2oNuX1DYzPUNH3HiiPOuUxfesLEaE46He0fXlE+7xEcGkx0cwOSWaeTkppMeHkx4fTkV9O7/6ZzErt1Zy2Yz0/g6hXESDXjnUjLHxzM9NYfm6Mq45cxzxkSEDbtvW2U15XTvfmJUx4DbKfSalRJMWF87WigbS48OZmBTF+ZOSrEEeQUZCBGnx4UQN8J9bb6/hxc/KefDdUr42LVX/a3MjDXrlcHcsmMyiv6zjsQ/2cteSnAG321tr6b/VqQ88U0hQAB/97IJhX0wXECAsm5fN0uc28Y8tVVwxS1v17qJ/YpXDTR4dzWXT03j6k/0cauwYcDvb7Ig6mZnnGm7I28zPTSE/LYa/ri2hywNvYekvNOiVUyybP4leY/jr2pIBtympbSE4UMgcpSNufJWIsGzeJA4cbeONzUO7xkI5jga9coqMhAiunj2WlzeWc+Bo/0PsSmqaGZ8YpX23Pu7CKcmclh7Lg2tL6OzWVr076G+YcppbL5hIUKDw32/v6Xd9SW2LXijlB0SE2+dPoqK+nb9vrnB3OX5Jg145TXJMGDeck8XKrVXsrP7ypfTtnT2U17eRrf3zfuH8SUlMz4jjobWl2qp3Aw165VQ3nzuB6NAgHnjry7cc3Hu4BWN0xI2/EBF+NH8SlQ3tvFJYPvgTlENp0Cunio0I5vvnTeCdnbVsOlB3fLltxI1OZuY/5mYnUjAunoffK9Ubj7uYBr1yuhvOySQxKpQ/vrkbYyzzpthG3IzTETd+Q0RYNn8S1Y0dvLxRW/WupEGvnM52y8EN++pYV3IE+GLETbCOuPErZ08YxeysBB55X1v1rqS/Zcolrp49lvT4cO5fswtjDHtqWpio/fN+xzauvqbpGC9ssH+WUzUyGvTKJUKCAlg2bxJFlU288Xkl5fVtTNIRN37prAmjOGv8KB79YC/tndqqdwUNeuUyl1pvOXjPymKM0ZuN+LNl8ydxuPkYz2844O5S/IIGvXIZ2y0Hmzu6AR1a6c9mZyUwZ2Iij76/l7bObneX4/M06JVLLcxL4bSMOOuIm0h3l6PcaNn8bI62dvLcem3VO5sGvXIpEeEvV07noW/N1BE3fm7WuATOnZTE4+vKaD2mrXpn0t805XKZiZEszBvt7jKUB1g2L5u61k6eWb/f3aX4NA16pZTbzBgbz4VTklm+rozmji53l+OzNOiVUm51+7xsGtq6eOaT/e4uxWfZFfQiskhEdotIqYjc2c/6cSLyrohsE5H3RSS9z7rrRaTE+nG9I4tXSnm/aelxzMux3Ge4SVv1TjFo0ItIIPAwsBjIBa4WkdwTNvsT8KwxZhpwL3Cf9bkJwD3AGcBs4B4RiXdc+UopX3D7vGyaOrpZ8dE+d5fik+xp0c8GSo0xZcaYTuAl4JITtskF1lofv9dn/ULgbWNMnTGmHngbWDTyspVSviQ/LZaFeSk89dE+Gtu0Ve9o9gR9GtB3qrkK67K+tgKXWx9fBkSLyCg7n4uILBWRQhEpPHz4sL21K6V8yO3zJtHc0c1TH5W5u5wOKJMAABAfSURBVBSf46iTsXcA54nI58B5QCVg9yQWxpjlxpgCY0xBUlKSg0pSSnmTnDExLJk6mhUf76ehrdPd5fgUe4K+Esjo83W6ddlxxpgqY8zlxpgZwN3WZQ32PFcppWx+eNEkWju7eeJDbdU7kj1BvxHIFpEsEQkBrgJW9t1ARBJFxLavu4AV1sdrgAUiEm89CbvAukwppU4yeXQ0X5k6hqc/3k9dq7bqHWXQoDfGdAO3YgnoncArxphiEblXRC62bnY+sFtE9gApwO+sz60Dfovlj8VG4F7rMqWU6tft87Jp6+ph+Tpt1TuK2G7t5ikKCgpMYWGhu8tQSrnRD1/6nLd31LD+rouIDQ92dzleQUQ2GWMK+lunV8YqpTzO0nPH09bZw0uf6V2oHEGDXinlcfJSYzlr/Cie+WQ/XT297i7H62nQK6U80o1zsqhq7GB10SF3l+L1NOiVUh7pwinJZCVG8tRH+/C0c4neRoNeKeWRAgKE756TydbyBjYfrHd3OV5Ng14p5bG+Piud2PBgnvxQJzsbCQ16pZTHiggJ4ltnjGVN8SHK69rcXY7X0qBXSnm068/KJECEp/XGJMOmQa+U8mijY8P46rQxvLyxXG83OEwa9Eopj3fjnPG0HOvm5Y3lg2+sTqJBr5TyeFPTY5mdmcDfPt5Pt15ANWQa9Eopr3Dj3CwqG9p5a0eNu0vxOhr0SimvMC8nhbEJETyl95UdMg16pZRXCAwQbjgnk00H6vlcL6AaEg16pZTX+EZBBtFhQdqqHyINeqWU14gKDeLq2WNZXXSIyoZ2d5fjNTTolVJe5fqzMwF4Ri+gspsGvVLKq6TFhbM4fzQvfnaQlmPd7i7HK2jQK6W8zo1zsmju6ObVQr2Ayh4a9EoprzNjbDyzxsXzt4/309Orc9UPRoNeKeWVbpyTxcG6Nt7ZqRdQDUaDXinllRbkppAWF85TOlf9oDTolVJeKSgwgBvOyeSz/XVsq2hwdzkeTYNeKeW1rjw9g6hQvYBqMBr0SimvFR0WzDcLMvjPtmoONXa4uxyPpUGvlPJqN5yTSa8xPLN+v7tL8Vh2Bb2ILBKR3SJSKiJ39rN+rIi8JyKfi8g2EVliXZ4pIu0issX68ZijvwGllH/LSIhgYd5oXthwkLZOvYCqP4MGvYgEAg8Di4Fc4GoRyT1hs18ArxhjZgBXAY/0WbfXGDPd+nGzg+pWSqnjvjc3i8b2Lv6+qcLdpXgke1r0s4FSY0yZMaYTeAm45IRtDBBjfRwLVDmuRKWUOrWZY+M5LSOOFR/vp1cvoDqJPUGfBvS9zrjCuqyvXwPXiEgFsAq4rc+6LGuXzgciMre/A4jIUhEpFJHCw4cP21+9UkoBIsKNc7LYd6SVtbtq3V2Ox3HUydirgaeNMenAEuA5EQkAqoGx1i6dHwEviEjMiU82xiw3xhQYYwqSkpIcVJJSyp8szh9NamyYDrXshz1BXwlk9Pk63bqsrxuBVwCMMeuBMCDRGHPMGHPUunwTsBeYNNKilVLqRMGBAVx/dibry45SXNU45Od3dPVQ3djOwaNtTqjOvYLs2GYjkC0iWVgC/irgWydscxC4CHhaRHKwBP1hEUkC6owxPSIyHsgGyhxWvVJK9XHV7LH85d0SnvpwH/dcnEddayd1rceoa+360uejrZ3Ut3ZS19p5/HFrZ8/x/fxk4WRuuWCiG78Txxo06I0x3SJyK7AGCARWGGOKReReoNAYsxL4MfCEiCzDcmL2O8YYIyLnAveKSBfQC9xsjKlz2nejlPJrseGWC6ie/mQ/r39+YseDRWhQAKMiQ0iICiEhMpSsxEgSIkNJiAwmITKU93bX8t9v7+GMrAQKMhNc/B04hxjjWWeoCwoKTGFhobvLUEp5qaMtx3ju0wNEhQaREBlCfGSIJditHxEhp27fNnd0seTBD+nthVX/NZfYiGAXVT4yIrLJGFPQ7zoNeqWU+rIt5Q1c8egnzM9N4ZFvz0RE3F3SoE4V9DoFglJKnWB6Rhx3LJzM6qJDvPDZQXeXM2Ia9Eop1Y+lc8czNzuRe/+1gz01ze4uZ0Q06JVSqh8BAcID3zyN6LAgbn1hMx1dPYM/yUNp0Cul1ACSo8N44JvT2VPTwm//vcPd5QybBr1SSp3CeZOSWHrueJ7fcJA3i6rdXc6waNArpdQg7lgwmWnpsfz0tW1UNrS7u5wh06BXSqlBhAQF8OBVM+jpNfzwxc/p7ul1d0lDokGvlFJ2yEyM5HeXTaXwQD0Pri11dzlDokGvlFJ2unRGGpfPTOOhtSV8WnbU3eXYTYNeKaWG4LeX5DNuVCS3v7SF+tZOd5djFw16pZQagsjQIP569QyOth7jJ69tw9OmkemPBr1SSg1RflosP1s0hXd21vDs+gPuLmdQGvRKKTUMN87J4oLJSfxu1U52VDW5u5xT0qBXSqlhEBH+9I3TiA0P5rYXN9PW2e3ukgakQa+UUsM0KiqU/7lyOmVHWvnNSs+dIkGDXimlRuCciYn8n/Mm8HJhOf/aWuXucvqlQa+UUiO0bP4kZoyN4+evb6e8zvNuLq5Br5RSIxQcaJkiAYGbni2kqaPL3SV9iQa9Uko5QEZCBI98eyaltS3c8vxmujxoPhwNeqWUcpC52Un8v8un8mHJEe5+Y7vHXEx16tuhK6WUGpJvFmRQUdfGg2tLyYiP4LaLst1dkga9Uko52rL5kyivb+eBt/eQnhDOZTPS3VqPBr1SSjmYiPCHr0+jurGdn762jdEx4Zw1YZTb6tE+eqWUcoKQoAAev6aAcaMi+f5zhZTWNrutFruCXkQWichuESkVkTv7WT9WRN4Tkc9FZJuILOmz7i7r83aLyEJHFq+UUp4sNiKYv33ndEKCArl+xUZqmzvcUsegQS8igcDDwGIgF7haRHJP2OwXwCvGmBnAVcAj1ufmWr/OAxYBj1j3p5RSfiEjIYIV3ymgrrWTG58udMucOPa06GcDpcaYMmNMJ/AScMkJ2xggxvo4FrBdB3wJ8JIx5pgxZh9Qat2fUkr5jWnpcfz16hkUVzXyXy9+Tk+va4dd2hP0aUB5n68rrMv6+jVwjYhUAKuA24bwXERkqYgUikjh4cOH7SxdKaW8x7zcFH59cR7v7Kzl3n8Vu3SMvaNOxl4NPG2MSQeWAM+JiN37NsYsN8YUGGMKkpKSHFSSUkp5luvOyuSmuVk8s/4AT320z2XHtWd4ZSWQ0efrdOuyvm7E0gePMWa9iIQBiXY+Vyml/MZdi3OoqG/nd6t2khYXzuKpY5x+THta3RuBbBHJEpEQLCdXV56wzUHgIgARyQHCgMPW7a4SkVARyQKygc8cVbxSSnmbgADhz1dOZ0ZGHLe/vIVNB+qdf8zBNjDGdAO3AmuAnVhG1xSLyL0icrF1sx8DN4nIVuBF4DvGohh4BdgBvAncYozpccY3opRS3iIsOJAnritgdGwYNz1byP4jrU49nnjKpDs2BQUFprCw0N1lKKWU0+070srlj3xMXEQIf/8/Z5MQGTLsfYnIJmNMQX/r9MpYpZRyk6zESJ64roDKhnaWPltIR5dzOjw06JVSyo0KMhP48zenU3ignh+/upVeJ4yx10nNlFLKzb4ybQwV9VNo6+xBxPH716BXSikP8P3zJjht39p1o5RSPk6DXimlfJwGvVJK+TgNeqWU8nEa9Eop5eM06JVSysdp0CullI/ToFdKKR/ncZOaichh4MAIdpEIHHFQOY6kdQ2N1jU0WtfQ+GJd44wx/d65yeOCfqREpHCgGdzcSesaGq1raLSuofG3urTrRimlfJwGvVJK+ThfDPrl7i5gAFrX0GhdQ6N1DY1f1eVzffRKKaW+zBdb9EoppfrQoFdKKR/nlUEvIotEZLeIlIrInf2sDxWRl63rN4hIpgtqyhCR90Rkh4gUi8gP+9nmfBFpFJEt1o9fObuuPsfeLyLbrcc96e7rYvGg9TXbJiIzXVDT5D6vxRYRaRKR20/YxiWvmYisEJFaESnqsyxBRN4WkRLr5/gBnnu9dZsSEbneBXXdLyK7rD+nN0QkboDnnvJn7oS6fi0ilX1+VksGeO4pf3+dUNfLfWraLyJbBniuM1+vfvPBZe8xY4xXfQCBwF5gPBACbAVyT9jmB8Bj1sdXAS+7oK4xwEzr42hgTz91nQ/8202v234g8RTrlwCrAQHOBDa44ed6CMtFHy5/zYBzgZlAUZ9lfwTutD6+E/hDP89LAMqsn+Otj+OdXNcCIMj6+A/91WXPz9wJdf0auMOOn/Mpf38dXdcJ6x8AfuWG16vffHDVe8wbW/SzgVJjTJkxphN4CbjkhG0uAZ6xPn4NuEjEGXdi/IIxptoYs9n6uBnYCaQ585gOdgnwrLH4FIgTkTEuPP5FwF5jzEiuih42Y8w6oO6ExX3fR88Al/bz1IXA28aYOmNMPfA2sMiZdRlj3jLGdFu//BRId9TxRlKXnez5/XVKXdYM+CbwoqOOZ69T5INL3mPeGPRpQHmfrys4OVCPb2P9hWgERrmkOsDaVTQD2NDP6rNEZKuIrBaRPFfVBBjgLRHZJCJL+1lvz+vqTFcx8C+gu16zFGNMtfXxISCln23c/bp9F8t/Yv0Z7GfuDLdau5RWDNAN4c7Xay5QY4wpGWC9S16vE/LBJe8xbwx6jyYiUcDfgduNMU0nrN6MpWviNOCvwD9cWNocY8xMYDFwi4ic68Jjn5KIhAAXA6/2s9qdr9lxxvI/tEeNRRaRu4Fu4PkBNnH1z/xRYAIwHajG0k3iSa7m1K15p79ep8oHZ77HvDHoK4GMPl+nW5f1u42IBAGxwFFnFyYiwVh+iM8bY14/cb0xpskY02J9vAoIFpFEZ9dlPV6l9XMt8AaWf6H7sud1dZbFwGZjTM2JK9z5mgE1tu4r6+fafrZxy+smIt8Bvgp82xoQJ7HjZ+5QxpgaY0yPMaYXeGKA47nr9QoCLgdeHmgbZ79eA+SDS95j3hj0G4FsEcmytgSvAlaesM1KwHZm+gpg7UC/DI5i7f97CthpjPnvAbYZbTtXICKzsbz+rvgDFCki0bbHWE7mFZ2w2UrgOrE4E2js8y+lsw3Y0nLXa2bV9310PfDPfrZZAywQkXhrV8UC6zKnEZFFwE+Bi40xbQNsY8/P3NF19T2nc9kAx7Pn99cZ5gG7jDEV/a109ut1inxwzXvMGWeYnf2BZYTIHixn7++2LrsXyxsfIAxLN0Ap8Bkw3gU1zcHyb9c2YIv1YwlwM3CzdZtbgWIsIw0+Bc520es13nrMrdbj216zvrUJ8LD1Nd0OFLiotkgswR3bZ5nLXzMsf2iqgS4sfaA3Yjmv8y5QArwDJFi3LQCe7PPc71rfa6XADS6oqxRLn63tfWYbYZYKrDrVz9zJdT1nfe9swxJgY06sy/r1Sb+/zqzLuvxp23uqz7aufL0GygeXvMd0CgSllPJx3th1o5RSagg06JVSysdp0CullI/ToFdKKR+nQa+UUj5Og14ppXycBr1SSvm4/w/zIi+V7lKIKgAAAABJRU5ErkJggg==\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": "stream",
"name": "stdout",
"text": [
"Epoch 1/1\n",
"20000/20000 [==============================] - 3s 167us/step - loss: 9.2402e-04\n"
]
},
{
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"for i in range(10):\n",
" model_hedge.fit(x=xtrain,y=ytrain, epochs=1,verbose=True)\n",
" helper = model_hedge.predict(xtest)\n",
" for j in range(2*N):\n",
" pricetrajectory = np.exp(np.cumsum(np.array([0]+[xtest[2+k][0][0] for k in range(N)])))\n",
" hedgetrajectory = [helper[0,2*k] for k in range(N)]\n",
" payofftrajectory = [helper[0,2*k+1] for k in range(N)]\n",
" plt.plot(pricetrajectory)\n",
" plt.show()\n",
" plt.plot(hedgetrajectory)\n",
" plt.plot(payofftrajectory)\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pT0uyCPBH6hM"
},
"source": [
"This provides us with a precise view on hedging and the machine learning way to construct hedging strategies."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9y5a4oJnH6hN"
},
"source": [
"# Fixed income markets -- basic notions"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "sC_7FtwjH6hN"
},
"source": [
"Prices of zero-coupon bonds (ZCB) with maturity $ T $ are denoted by $P(t,T)$. Interest rates are governed by a market of (default free) zero-coupon bonds modeled by stochastic processes \n",
"$ {(P(t,T))}_{0 \\leq t \\leq T} $ for $ T \\geq 0 $. We assume the normalization $ P(T,T)=1 $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "k1_IXgjmH6hN"
},
"source": [
"$T$ denotes the maturity of the bond, $P(t,T)$ its price at a time $t$ before maturity $T$."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "W3LSgcFaH6hO"
},
"source": [
"The yield\n",
"$$\n",
"Y(t,T) = - \\frac{1}{T-t} \\log P(t,T)\n",
"$$\n",
"describes the compound interest rate p.a. for maturity $T$."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "A4TX1bpnH6hO"
},
"source": [
"The curve $f$ is called the forward rate curve of the bond market\n",
"\\begin{align*}\n",
"P(t,T) & =\\exp(-\\int_{t}^{T}f(t,s)ds)\n",
"\\end{align*}\n",
"for $0\\leq t\\leq T$."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wfqDNuXZH6hO"
},
"source": [
"Let us understand a bit the dynamics of yield curves and forward rate curves at this point:"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZNb7_fHOH6hO"
},
"source": [
"### We are now applying our principles from the first general part to this large market. We use extensively that we can choose the asset $S^0$ for our convenience. In different market situations we can have different ways of discounting. We shall see two: discounting by the bank account process and discounting by a (forward) bond $ P(t,T^*) $. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Hl-2CfbXH6hP"
},
"source": [
"The short rate process is given through $R_{t}=f(t,t)$ for $t\\geq0$ defining the \"bank account process\"\n",
"$$\n",
"(B(t))_{t \\geq 0}:=(\\exp(\\int_{0}^{t}R_{s}ds))_{t \\geq 0}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pqga3tI3H6hP"
},
"source": [
"Consider now $ P(t,T) $ as price of a contract which promises $ 1 $ at time $ T $ and do the discounting with $ S^0 $ equal the bank account process."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fbS7u8-QH6hP"
},
"source": [
"No arbitrage is then guaranteed if on the filtered probability space $ (\\Omega,\\mathcal{F},Q) $ with filtration\n",
"$ {(\\mathcal{F}_t)}_{t \\geq 0} $,\n",
"$$\n",
"E(\\exp(-\\int_t^T R_s ds)|\\mathcal{F}_t) = P(t,T)\n",
"$$\n",
"holds true for $ 0 \\leq t \\leq T $ for some equivalent (martingale) measure $ Q $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "SoP8ZqajH6hP"
},
"source": [
"This is a useful and important approach but not feasible for many market situations. There it is better to take another discounting unit."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D8I32Y3cH6hQ"
},
"source": [
"Consider a bond market $(P(t,T))_{t \\leq T}$ with $P(T,T) = 1$ and $P(t,T) > 0$. Let $t \\leq T \\leq T^{\\ast}$. We define the simple forward rate through\n",
"\\begin{align*}\n",
"F(t;T,T^{\\ast}) := \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{P(t,T)}{P(t,T^{\\ast})} - 1 \\bigg).\n",
"\\end{align*}\n",
"and the simple spot rate through\n",
"\\begin{align*}\n",
"F(t,T) := F(t;t,T).\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wqbALC7CH6hQ"
},
"source": [
"Apparently $P(t,T^{\\ast}) F(t;T,T^{\\ast})$ is first a traded portfolio (long in the $T$ bond and short in the $T^*$ bond) and the fair value at time $t$ of a contract paying $F(T,T^{\\ast})$ at time $T^{\\ast}$, since $ P(T^*,T^*) = 1 $.\n",
"\n",
"Indeed, note that\n",
"\\begin{align*}\n",
"P(t,T^{\\ast}) F(t;T,T^{\\ast}) &= \\frac{P(t,T) - P(t,T^{\\ast})}{T^{\\ast} - T},\n",
"\\\\ F(T,T^{\\ast}) &= \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{1}{P(T,T^{\\ast})} - 1 \\bigg).\n",
"\\end{align*}\n",
"Fair value means that we can build a portfolio at time $ t $ and at price $ \\frac{P(t,T) - P(t,T^{\\ast})}{T^{\\ast} - T} $ yielding $ F(T,T^{\\ast}) $ at time $ T^{\\ast} $:\n",
"\n",
"-> Holding a ZCB with maturity $ T $ at time $ t $ has value $ P(t,T) $, being additionally short in a ZCB with maturity $ T^{\\ast} $ amounts all together to $P(t,T) - P(t,T^{\\ast})$.\n",
"\n",
"-> at time $T$ we have to rebalance the portfolio by buying with the maturing ZCB another bond with maturity $ T^{\\ast} $, precisely an amount $ 1/P(T,T^{\\ast}) $. \n",
"\n",
"-> at time $ T^{\\ast} $ we receive $ 1/P(T,T^{\\ast}) - 1 $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AOkXdjnYH6hR"
},
"source": [
"In this setup it is of course much better to take $ S^0 $ the $ T^*$ bond and to have $ X_t = F(t,T,T^*) $ as discounted price with respect to $ S^0 $. We can use all models for discounted prices like the binomial model or the Black-Scholes model for this situation.\n",
"\n",
"In the sequel we apply the binomial tree model with one timestep with a simple forward rate process and the foward bond starting at $0.9$ and terminating at $1$. Here discounting matters what you can see in the difference between the first (format time / numeraire / foward rate time $T^*$ bond) and second tree (format time / simple forward rate)."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"id": "3MUu6doJH6hR",
"outputId": "71aac6de-dcc6-4a8e-de91-2a2140e955a9",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 172
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
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+wKBB1h0IbYiM1LvlRLpgokSkqa2VPeojR2TjkZVl3cOur5fX9OkjPU4pKXKianKydTwhQd/2EwGS7J89K4VbtSE3Vx6PHJGdBEDO4xs0SHYA0tJkfPBgYOBAFnskaoaJElF7mppkb1vb+z5+3LrhOXkSuHBBXhcc3Dp56tNHhr59JZHiBoi6q65ODh0XFACnTrVOivLyrL9Js9n6m0xOliRf6x1NSuL5REQdwESJqDua771ryVPz8aIiSbQ0cXGSMPXtKwlUYiLQr59MS0yUopq9e/McKV9UXy+9PcXFUvIiP19+W82TooICue2Hxt9ffjstE3RtPCGByRBRNzFRInKlpiY5mfzMGdnwaY8tN4A1Nbbvi4oCYmMlaerdWxIsbbx3b7laLypKzhuJjAQiIvT5fuRYWZlcMVZWJucFFRVJElRSIuPnzln/LiwEKips3x8eLgl1YqJtQq099u0rvws/3tucyJWYKBEZQXm5JE0lJbLx1Daq2lBYaH2upMS2lwqQjaWWNGkJVPNESht69pQhIkIOFYaE2I5HRvp2D0RTkyQsVVVyzlplpe14ZaXcwLmszHbQEqLmf7cUEGDtMYyNtSbCMTGS+GpJcEyM9Dbyth5EhsBEicjTKCXJkrZxtreRtje9rEw28tXVyEci/ogV+D1ew3X4xvbzg4KsSVNwsAx+ftZeq5AQeY3JZL0Syt40jdksn+FIVJT96RaLJJCO1NRYT7LXlktZmYzX1sq5PIA1abE3rbpapldUyLh2bs+vChGP3+JTPIeFmIzNQFiYJDAtE9CWSWnzv6OiZOCl9EQeifd4IPI0JpO196GTLBbgn/8E/t9fFBJimxD6n1cCyYWSLNTWSgKhjZeVWZOLxkbpTQGkh6WhQYbcXNtpWo9McxUVrXvANA0N8l5HwsIc34omIAAIDbWdFhEhSZ2W7DWfFhnZepqWCGrPBQfLcz17AsHBaKiORuTieFy79Xv84Q/AM8+wQgSRr2GPEpGPyMkB5s8Htm0DHnxQNvo8utMxH3wAPPSQ5GwrVgC33qp3i4jIXXgWIJGXa2gAnnsOGDJEzin+4QfgxReZJHXGrFlSgujGG2X8xhutxd2JyLsxUSLyYvv2yf2An35ahj17gCuu0LtVnikqCnj9dWDTJuDoUUk8X3xRDmcSkfdiokTkhWpqgL/8Re77GxoqCdPChUCPHnq3zPNNnix3v/n974EnngAmTZI6pETknZgoEXmZLVvkvqWvvw68+iqwebPcnYKcJzgYWLpUeujq64HhwyUxbX4RHhF5ByZKRF6itBR44AFgyhRJjDIz5eRtXy6L5GrDhwM7dgDLlgGvvCKHNXfu1LtVRORMTJSIvMAHH8jtuz77TMY//1xqFpLr+fsDjz4K7N8vBbQnTJCEVaumQESejYkSkQcrKABuuQWYPRuYOhU4dIiXruslJQXYuBFYswb4+GNJXD/+WO9WEVF3MVEi8kBKAW+8IRvjAweAb74B3n0XiI7Wu2WklRK44QZJWm+8UW7tR0SeiYkSkYfJyQGuvVYKIM6dK4d8rr1W71ZRc9HRcjL9V1/JuWIsJUDkuZgoEXkIFo70PNOny+HQBx6QUgKTJwPZ2Xq3iog6g4kSkQdg4UjPFRIipQR275Zb540cCTz1VKv77xKRQTFRIjIwFo70HiNGSC/g0qXA889Lovvjj3q3iojaw0SJyKBYONL7aKUEDhwA4uNZSoDIEzBRIjIYFo70fikpwNdfA6tXW0sJrFund6uIyB4mSkQGwsKRvmXWLEmEr71W6mHdfjtw7pzerSKi5pgoERkAC0f6rrg4qYH15ZfATz9JL+Ibb0itLCLSHxMlIh2xcCRpZswADh+Ww64PPiilBI4c0btVRMREiUgnLBxJLWmlBHbtAqqqWEqAyAiYKBG5GQtHUntGjpTSAc8+K6UExoyRw3JE5H5MlIjciIUjqaO0UgL79wOxscD48XJYrqpK75YR+RYmSkRuwMKR1FX9+0spgbffBj76CBg6FNiwQe9WEfkOJkpELsbCkdRdJhNw771yNeRVV8k95G6/HSgu1rtlRN6PiRKRi7BwJDmbVkrgiy/kHCaWEiByPSZKRC7AwpHkSjNnAllZkng/+KAk40eP6t0qIu/ERInIiVg4ktxFKyWwbRtQUiKHd596Sq6qJCLnYaJE5AQsHEl6GT9eLg7429+k7MSYMVKHiYicg4kSUTexcCTpLSBArqI8eBDo1QuYMEFKC7CUAFH3MVEi6iIWjiSjGTAA+PZb4K23gFWrgGHDgI0b9W4VkWdjokTUBSwcSUallRLIzAQmTgSmTWMpAaLuYKJE1AksHEmeIj5ezpP7/HNg506WEiDqKiZKRB3EwpHkiW64QXqX7rkH+MMfgGuuAY4d07tVRJ6DiRJRO8rKWDiSPFt4uJw/t22bHIIbPlzOr2tq0rtlRMZnUoodsUSOfPAB8PDDgJ8fsGIFcNttereIqHsaGoDly6WcwODBwJtv8vw6orawR4nIDnuFI5kkkTfQSglkZgJRUVKHiaUEiBxjokQ+pbS07edZOJJ8xYABwHffSSmBlSvlcNw337T/vooK17eNyEiYKJHPePFF4I47HD/PwpHka5qXEhg1Crj+eiklUFJi//WNjcDkycD69W5tJpGumCiRT8jIAJ54Avj6a+C992yfa2xk4UjybQkJcj7eZ5/ZlhJoaflyKYkxezaQm+v+dhLpgSdzk9crKpIKxb/8AlgscgXQ0aNAbKwE/fvukzux//nPwKJFcg4Hka8qLwf++lfg5Zfl/Lx//hO45BIgL09O/q6rk3VkwABg9265OS+RN2OiRF6tsRGYNEluEqrdVT0gAPjtb4H+/YHnnwfS02XvmTWRiKy2b5cyGHl5kjht2CDTtPXI318ucHj/fV2bSeRyTJTIqz3+OPDSS/brxYSGyiG2efNYE4nInvp64Jln5JBbdXXrqt4mk6xDf/yjPu0jcgcmSuS11q0Dbr3V/i0b/PzkSracHCAiwv1tI/IUJSXAwIFySM7eutSjB7BpE3D11e5vG5E78GRu8kpHjgB33+34eYtFAv+iRe5rE5Enevhh+71Jzd18M3D2rPvaRORO7FEir1NVJZc6nzgh5yi1xWQCtm6Vu6wTka0NG4Dp09t/XUCA3AcxIwMIDHR9u4jciT1K5FWUkpt/5uW1nyRp7r9fzsUgIquqqo7f07ChAdi7V0pwEHkbf70bQORM//VfUgvGYmn9nMkkV+o0NMh5FcOGSUHJq6+2/3oiX3bhAvD003Ij3S1bpG6SyQQEBUmJgJaamqSkwLhxbR/2JvI0PPTmK8rKpLulvh6oqbGdBkj3S2Wl4/c3NbV/74KQEImijgQHA2az9e/wcMlYAgOt1R21aV2webMkPlrSYzLJRzU2SrPGjgWuuUYSo3HjWFCSqDPOnZPyANu2ybp24ICEhaAg2fnQ1rugIODHH+WWKF3mA/GKPAcTJaOor5dAUFYmNySrqpLH2lrZfdPGa2vlNTU1Ml5ebjsOWANKXZ1M90QBAXL9PmANRj17SvAKD5fnzOaL42cb4zD8X3/ELzXB8pbgBkwcWoYpY6oxcYIFo9PNCOgdyep4RM5QX4/q/HL8uLUe2zJM2LK7J3YeDkftBUkakiIr8PMD/0SUOs94ZSdeITgYCAuTIThYpmnPRUbKEBXFeGUQTJScra5Orqc9d05KQpeUyHD+vG0i1PxRCyT2aHs1UVEdGwesK6q9ldfeNE1EhFw370h7z5eXt30Mq+Xz2h1qmwdIe0FTm1ZZKdMrK23GL1TU4a4jf0VAUx0mIgNXqy1Iq94FP9hpS2CgNQg1D0jaeHQ0EBMjQ+/eUr47Nta6zIi8iRPjVSP8sT9oLDJ6TEKG6SqEBdThX/2fhV9UBONVR8btYbwyBCZKHVFfDxQUAGfOyFBQ0DqwaH9XVdm+NyhIfsBRUdYfuL0ffctpoaHWQEJtslgcxMPKSmvPXMtAb2+8tFSG4mK5Hrq54GAJRlog6t1b/o6Lkxtl9ekDJCYC/frxmB7py0DxyuG6Sa0xXhkWE6X6erlEKi9PAsqpU62DTFGR9fU9esiPLTYWiI+3zea1v3v3liEuTrpWyfPU1koAOndOhpIS+buoSB6Li2VaYaEMzS+bi4iQQNS3rwSlpCR57NtXAlNyMqtcUtcwXpE9jFcu5RuJUmmpXLJhbzh50np/C7NZsuyEBNvHlBTreFKSXDpF1FxpKZCfLxsq7TE313ZaYaH1ZNSoKNvfVUqKdRg8mOcm+DLGK3I1xqtO8Z5EqbwcyM6W28A3f8zLk+tcAQksycnyz01Oth0uvVS6kYlcpaZGNnQnTkhQOnHCdtBObvXzk725yy6TIDR4MJCaKo/x8fp+B3IOxisyOsarizwvUSorA/btk8By6JDcqyIrSzJgQIJLaqrcCn7wYLlFvBZsEhL0bTtRW86ftwah3Fz5bR8+LBvQsjJ5TVSU/LbT0uR3npYmJZH79NG37WQf4xV5Kx+KV8ZOlPLzZcEfOgTs2SNDVpZ0B0ZGSlBJSwMuv1wCi/bPYF0L8jalpbIeHD4sQUkbz8uTM2YjI2U9GD3aOgwezDNp3Ynxikh4WbwyTqJUXg7s2CEVzXbtAn7+WU5KAySojBwpmejIkTIkJurbXiIjKC+XdWXfPuuQlSUF+UJDperf6NHAhAlyQzsP25MzLMYros7z0HilX6J0+rSUeN2xQx4zMyXTHDRISihrAWbECB6LJ+qMujpZn/bulaCkbcgbG+WwzsSJQHq6PKaldexmXr6O8YrINTwgXrkvUSotBb7+Gli/Hti0SQJPQIA1e7zqKnmMjXVLc4h8SlWV3FciI0N6QXbulLot0dGy7k2bJreJv+QSvVtqDIxXRPoxWLxyXaKklGSF69cDX30lX9RkkszwN7+R7HDsWK+/rJDIkJqagP37JRBt2gR8950Ep7Q0YMYMCUITJ0plYF/AeEVkXDrHK+cnSj/8AKxcCaxbJ/UYEhLkS0yfDlx3nc8XriIypAsX5JDS+vUyHD4sxQenTZNbwU+b5p1JE+MVkedxc7xyTqJ0/LgEm5UrgZwcYMgQ4M47JdMbPpznQBB5mrw8YMMGYO1aYMsWucz3jjuAu+4Cxo/Xu3Xdw3hF5F1cHK+6nihduACsWQO89prslcXFSbC59145oZGIvMPp08CqVZJYHDoEDBgA3HcfMH++59yPkPGKyDe4IF51PlGqqgJeeQV48UW5d8wttwBz50o3NeuBEHm3vXuBd98F3nlHrkqZNw9YuFAq8xoR4xWR73JWvFIddeGCUv/930rFxioVFqbUwoVKnT7d4be7Q1NTk1q+fLkaP358l94/ZswYderUKZfMY9u2bWrChAkqODhYxcfHqz//+c+qrq7Oa1/XlvaWc3fm0ZH3Pv3002rw4MEqLCxMBQYGqv79+6sFCxaoysrKLrfFiMvZpSoqlHrxRaUuuUQps1mpRx9V6pdf9G6VFeNVt+Zh9N+9L8UrpZRatWqVuuKKK1RoaKhKSkpSc+fOVQUFBV3+PCMuZ5fqZrzqWKK0fbtSQ4fKDBYsUKq4uIutdZ2jR4+q9PR0BUANHz680+/Pzc1tN5h0dR6ZmZkqODhYLVmyRFVVVakdO3aomJgYNW/ePK98XVvaW87dmUdH3ztp0iT1yiuvqF9++UVVVFSoNWvWqICAADVt2jSXLhd3Lme3qa9X6uWXlYqPV6p3b6XefVfvFjFedXMeRv/d+1q8Wr16tQKgnnvuOVVWVqb27dunUlJS1IgRI1RDQ4PLlgvjlVXbiZLFotTSpUr5+ys1dapSx445o6lO9/PPP6tbbrlFrVy5Uo0YMaJLgefZZ59Vy5cvd8k8Zs+erZKTk5XFYrk4bdmyZcpkMqmsrCyve11b2lvO3ZlHR987c+ZM1djYaPPe22+/XQGw2XP05OXsdmVlSj38sFJ+fkrNmaOUnd45l2O8cso8jP6797V4NWXKFJWYmGjzupdffu8UzkcAAAvgSURBVFkBUBkZGZ3+PCMuZ7frZLxynCg1NSn17/8uQWfpUglCHmDcuHFdCjyjR49WpzvYNd+ZeTQ0NKjQ0FA1d+5cm+mZmZkKgFq6dKlXva49bS3n7syju+178MEHFQCVnZ3dqc8z6nLWzaZNsrc2apRSJSXumy/jlVPmYfTfvS/GqwEDBqjRo0fbvO7TTz9VANSqVas69XlGXc666WC8cnwHuscfB/7v/4BPP5WTn7z4ktmcnByYzWb0dcEJqbm5uaiqqkJSUpLN9P79+wMADhw44FWva0t7y7k78+hu+86ePYvg4GAkJyd36vOMuJx1NWWKFIUrKQFuvBFoaHDPfBmvnMLov3tfjFcpKSk4p91H8FeFhYUXn+vM5xlxOeuqg/HKfqL07bfASy/JmeIzZriwlcawdu1azJo1yyWfrf2gw8LCbKabzWYEBwejqKjIq17XlvaWc3fm0Z331tTUYNOmTbj//vsR+GuRMk9ezrrr3x/YuBE4cAB45hnXz4/xymmM/rv3xXj15JNPorCwECtWrEBlZSUOHTqEF154AVOnTsWVV17Zqc8z4nLWXQfilf1E6dlnJeDMnu3K5hnGhx9+iNtuu80ln11fXw8A6GHnUuSAgADU1tZ61eva0t5y7s48uvPeZ555BgkJCfj73//e6c8z4nI2hNRUYNEiuSy/utq182K8chqj/+59MV5NmjQJCxcuxCOPPILw8HAMGTIElZWV+Ne//tXpzzPicjaEduJV60SpoQHYuhW45x53NE93R48eRc+ePdGnTx+XfL7ZbAYANDY2tnruwoULCA4O9qrXOdKR5dydeXT1vR9//DHWrl2LjRs32uwVeepyNpR775Wby+7d67p5MF45ldF/974YrxYtWoQ33ngD3333HaqqqpCbm4sJEyZg/PjxOH36dKc+z2jL2VDaiFetE6WyMinM5CN3xV6zZo3LurEBID4+HgBQUVFhM72mpgZ1dXVISEjwqtc50pHl3J15dOW9q1evxtKlS7F582ZceumlXfo8oy1nQ4mNlXOFiotdNw/GK6cy+u/e1+JVQUEBnnvuOcyfPx/XXHMNevbsieTkZLz55pvIz8/HsmXLOvV5RlvOhtJGvGqdKMXEyI0gjX4SlpN89NFHLuvGBoDk5GSEhYXh5MmTNtNzcnIAAMOGDfOq1znSkeXcnXl09r0rVqzAypUrsWnTJiQmJnb584y2nA1l/35AKbmFgKswXjmV0X/3vhavjh07hqamplYxKjw8HNHR0Th06FCnPs9oy9lQ2ohXrRMlkwmYMwd4+WXAU44vdlF2djYiIiLsbiidxd/fHzNmzMDWrVthsVguTl+/fj1MJhNuuukmr3qdPR1dzt2ZR0ffq5TCwoULcfDgQXzyyScIDQ3t1ucZaTkbzrJlwNChgCuDJeOVUxn9d+9r8Uq74q6goMDm/ZWVlTh//jz69evnkuXCeNWC3aIBp08rFR2t1Ny5HlOPRNOZmiFPPfWUWrFihVPnsWTJEhUeHq42btx4cVpmZqYym81q8eLFFyuX9urVy26FU294XUudWc4dnUdXl7NW38PRsGzZMt2XX1eXs6G88YZSJpNSGza4fl6MV12eB+NVa0aKVxaLRU2ZMkXFx8erLVu2qJqaGnXq1Cl15513Kj8/P7V161bdl58vxCvHBSe//FKpwECl7rtP7ptkYD/88INKT09XCQkJFzd48fHxasKECWrLli0O3zd06FCVn5/v1HksWbJEhYWF2awQSim1ZcsWNXbsWBUUFKQSEhLUggUL7N4Lx1te11xnlnNH59HV5Xzw4MEOJ0quWC6uXM6G8frrUvH2b39z3zwZr7o0D8ar1owUr5RSqqSkRD322GNqwIABKigoSIWGhqr09HS1bt26Ln9fIyxnw+hAvDIppZTDrqgvv5RLbocPl2Jul1zilB4uIvJC1dXAI48Ab78NPP00sGSJe+fPeEVEHdWJeOW4MjcAzJwJ/PQTUF4OXH65HMNzV6VdIvIc69YBaWnAJ59IdWx3J0kA4xURdUwn41XbiRIgH7ZvH/CPf0jWNWAA8MYbckkuEfm2jAy5DcAttwDjxgFZWXIrAL0wXhGRI12MV+0nSgAQEAA8+ihw+DBw/fXAQw8Bl10GvPACUFnZ3aYTkSdpagI++AAYPx646iogMBDYuRNYu9YY9YwYr4hI44R41fY5So4cPy5B55135PLcW2+VyriTJwN+Hcu9iMjDHDwIrFwp5//k5wO/+x3wxBPAhAl6t6xtjFdEvseJ8apriZKmtBR47z1pzK5dQN++UtPknnuAIUO6/LFEZBD5+cD778t6vn8/cOmlwF13AfPmyc0kPQnjFZF3c1G86l6i1Fx2NrBqlQShvDwJPDNmANOnA+np0h1ORMa3fz+wfr0M27cD4eHArFnA3XcDEydKr4ynY7wi8g5uiFfOS5Q0SskJU+vWAV99BRw5Ig2/7joJQtOnAy6sLEtEnVRRAXz7rTXYnD0LxMXJunrTTZJABAXp3UrXYLwi8iw6xCvnJ0ot5ebKl/nqK+D774G6OrkyZeJE2XObOBFITnZpE4iomZISYMcOYNs2edy1C7BYgLFjrb0qo0Z5R89RZzFeERmLAeKV6xOl5mprgS1bJABlZAB79gD19bLH1jwQDRsG+Pu7rVlEXu3YMemSzsiQxyNHJKhoCcDVV8vVYb166d1SY2G8InI/A8Yr9yZKLTU2yvFFbYF8/71kjwEBwMCBwOjR1mHUKCAkRLemEhleUxNw8iRw6JBs1PfsAX78ESgulnVq2DDrxv2aa5gYdRbjFZHzeFC80jdRaslikQJQu3ZJ0bh9+4Cff5baJ/7+QGoqMHKkDEOHAoMGAb/ePZnIp5w/L+vK4cPWdeXAAaCmRuqEDBliXVdGjZKNd2Cg3q32LoxXRB3j4fHKWImSPUoBOTnWhasN587J82FhEoAGD5Zh0CDpouvfn1eukGdTSva4jhyRAJOdbR0vLpbXhIXJnpcWZEaOlKDD374+GK/IV3lxvDJ+ouRISYlkqNnZMhw+LP+UkydlTy8gAEhJkVsYJCfLkJJiHQ8P1/sbEMnJwnl5wIkTciLxiRPW8aNHZY8LkKs6Bg+WXorUVOtGNinJN0+69jSMV+QNfDReeW6i5EhtrTWTzc6Wf6D2D83Pt74uJsY2IF1yCdCnjxShS0iQf7QH/kPJYEpL5fLVM2eAggJrkNGCS0GB7IkBQHS07cbxssuktyE1FYiK0vVrkIswXpGRMF7Z5X2JUlvq6qz/9OZDbi5w6pQcR9UEBgLx8XJOQWKiDFpQSkqSwNW7tzyS76msBIqK5JBKQYFtcDl1Sh7PnJENoSYkRH47LXsLtPGICP2+DxkP4xU5C+NVt/hWotSe2lr7P56zZ63TioqAhgbre/z9rQEoNlb27LSgFBcn02JiJPuOjJQhOFi/70itNTQAZWUynD8vh0mKi2UoLLT+fe6c/P9LSmQjpjGZ5H+dmGi7l9+vnzz27SvTIyP1+47kfRivfBPjldsxUeosi8X649N+iMXF8reWsWs/1KIioLy89WcEBUnXpBaItKHltNBQCVJhYbbjYWGA2SyPvqy2VgJAaamM19ZK8KipkellZUBVlTyWllqDizZo06qrW392SIhsPOLjrRuSlhsW7e/YWENdoUF0EeOVcTBeeSwmSq5WXy+BqOUPv60VQRuqq4ELF9r+/LAwCUihoTLu7y+BTavhEhkpexDNp0VEyF3Tm0/ThIcDPXrYn1dgINCzp+PvqZ3IZ09ZmfXYNiDfS1vhy8sloDefVlEhdTaaTystlYBSWyvjbfHzk+8ZGmo/qLc1rXdv1sAh38R4JRivqBkmSkbX1CQrYVWVrHCVlTLU1sq0igoZr662rsA1NRIIlJIVHrDuzdibprFY7O9RatoKhNqK7kjPnrZ7Mf7+1j3M0FC56sfetB49rFf8RERIkA0JsR4SCA6WYKGNR0bK8956bzIiI2O8YrzyQkyUiIiIiBzw07sBREREREbFRImIiIjIASZKRERERA74A/hA70YQERERGdH/B6+HsFgMcmdtAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 33
}
],
"source": [
"import numpy as np\n",
"from itertools import product\n",
"\n",
"\n",
"# EUROPEAN\n",
"F0 = 0.04\n",
"u = 2\n",
"d = 0.5\n",
"payoffE = lambda F: np.maximum(F-F0,0.)\n",
"\n",
"timesteps = 1\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):F0 for omega in trajectories}\n",
"numeraire = {(omega,0):0.9 for omega in trajectories}\n",
"discountedprocess = {(omega,0):F0 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 / %f / %f'% (time-1,numeraire[(omega,time-1)],process[(omega,time-1)]),\n",
" '%d / %f / %f'% (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": 34,
"metadata": {
"id": "iF294x6oH6hR",
"outputId": "bd5c4284-e6c4-4051-ac48-c05cf7929719",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 172
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 34
}
],
"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 / %f'% (time-1,discountedprocess[(omega,time-1)]),'%d / %f'% (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": 35,
"metadata": {
"id": "znIzWsbeH6hS"
},
"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": "code",
"execution_count": 36,
"metadata": {
"id": "rfcRmU-8H6hS",
"outputId": "fe2b9f58-af38-4b54-d432-7dacd582e748",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 172
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"execution_count": 36
}
],
"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": {
"id": "0cHccwhRH6hS"
},
"source": [
"In order to get prices back one has to multiply this tree with the corresponding numeraire prices, hence the actual caplet price will be $ 0.016296 * 0.9 $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CK8n14XsH6hS"
},
"source": [
"## Caps"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fHLqlaikH6hT"
},
"source": [
"In the sequel, we fix a number of future dates \n",
"\\begin{align*}\n",
"T_0 < T_1 < \\ldots < T_n \n",
"\\end{align*}\n",
"with $T_i - T_{i-1} \\equiv \\delta$.\n",
"\n",
"Fix a rate $\\kappa > 0$. At time $T_i$ the holder of the cap receives\n",
"\\begin{align*}\n",
"\\delta (F(T_{i-1},T_i) - \\kappa)^+.\n",
"\\end{align*}\n",
"Let $t \\leq T_0$. We write\n",
"\\begin{align*}\n",
"{\\rm Cpl}(t;T_{i-1},T_i), \\quad i=1,\\ldots,n\n",
"\\end{align*}\n",
"for the time $t$ price of the $i$th caplet, and\n",
"\\begin{align*}\n",
"{\\rm Cp}(t) = \\sum_{i=1}^n {\\rm Cpl}(t;T_{i-1},T_i)\n",
"\\end{align*}\n",
"for the time $t$ price of the cap."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "d1u2R5pbH6hT"
},
"source": [
"## Floors "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZIN9mX-5H6hU"
},
"source": [
"At time $T_i$ the holder of the floor receives\n",
"\\begin{align*}\n",
"\\delta (\\kappa - F(T_{i-1},T_i))^+.\n",
"\\end{align*}\n",
"Let $t \\leq T_0$. We write\n",
"\\begin{align*}\n",
"{\\rm Fll}(t;T_{i-1},T_i), \\quad i=1,\\ldots,n\n",
"\\end{align*}\n",
"for the time $t$ price of the $i$th floorlet, and\n",
"\\begin{align*}\n",
"{\\rm Fl}(t) = \\sum_{i=1}^n {\\rm Fll}(t;T_{i-1},T_i)\n",
"\\end{align*}\n",
"for the time $t$ price of the floor."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7SVn1fgzH6hU"
},
"source": [
"## Swaps"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zAto8qOKH6hV"
},
"source": [
"Fix a rate $K$ and a nominal $N$. The cash flow of a payer swap at $T_i$ is\n",
"\\begin{align*}\n",
"(F(T_{i-1},T_i) - K) \\delta N.\n",
"\\end{align*}\n",
"The total value $\\Pi_p(t)$ of the payer swap at time $t \\leq T_0$ is\n",
"\\begin{align*}\n",
"\\Pi_p(t) = N \\bigg( P(t,T_0) - P(t,T_n) - K \\delta \\sum_{i=1}^n P(t,T_i) \\bigg).\n",
"\\end{align*}\n",
"The value of a receiver swap at $t \\leq T_0$ is\n",
"\\begin{align*}\n",
"\\Pi_r(t) = -\\Pi_p(t).\n",
"\\end{align*}\n",
"The swap rate $R_{\\rm swap}(t)$ is the fixed rate $K$ which gives $\\Pi_p(t) = \\Pi_r(t) = 0$. Hence\n",
"\\begin{align*}\n",
"R_{\\rm swap}(t) = \\frac{P(t,T_0) - P(t,T_n)}{\\delta \\sum_{i=1}^n P(t,T_i)}, \\quad t \\in [0,T_0].\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "E9SN74gQH6hV"
},
"source": [
"## Swaptions"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KNVoH_sQH6hV"
},
"source": [
"A payer (receiver) swaption is an option to enter a payer (receiver) swap at $T_0$.\n",
"The payoff of a payer swaption at $T_0$ is\n",
"\\begin{align*}\n",
"N \\delta (R_{\\rm swap}(T_0) - K)^+ \\sum_{i=1}^n P(T_0,T_i),\n",
"\\end{align*}\n",
"and of a receiver swaption\n",
"\\begin{align*}\n",
"N \\delta (K - R_{\\rm swap}(T_0))^+ \\sum_{i=1}^n P(T_0,T_i).\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QkgFQMuxH6hW"
},
"source": [
"## Spot measure"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_auJSD5EH6hW"
},
"source": [
"From now on, let $P$ be a martingale measure in the bond market $(P(t,T))_{t \\leq T}$, i.e. for each $T > 0$ the discounted bond price process\n",
"\\begin{align*}\n",
"\\frac{P(t,T)}{B(t)}\n",
"\\end{align*}\n",
"is a martingale. This leads to the following fundamental formula of interest rate theory\n",
"$$\n",
"P(t,T) = E(\\exp(-\\int_t^T R_s ds)) | \\mathcal{F}_t )\n",
"$$\n",
"for $ 0 \\leq t \\leq T $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7HfXt0cOH6hW"
},
"source": [
"## Forward measures"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "B9Q0jKqaH6hX"
},
"source": [
"For $T^{\\ast} > 0$ define the $T^{\\ast}$-forward measure ${P}^{T^{\\ast}} $ such that for any $T > 0$ the discounted bond price process\n",
"\\begin{align*}\n",
"\\frac{P(t,T)}{P(t,T^{\\ast})}, \\quad t \\in [0,T]\n",
"\\end{align*}\n",
"is a ${P}^{T^{\\ast}}$-martingale.\n",
"\n",
"\n",
"For any $T < T^{\\ast}$ the simple forward rate\n",
"\\begin{align*}\n",
"F(t;T,T^{\\ast}) = \\frac{1}{T^{\\ast} - T} \\bigg( \\frac{P(t,T)}{P(t,T^{\\ast})} - 1 \\bigg)\n",
"\\end{align*}\n",
"is a $\\mathbb{P}^{T^{\\ast}}$-martingale.\n",
"\n",
"For any time derivative $X \\in \\mathcal{F}_{T^*}$ paid at $ T^* $ we have that the fair value via ``martingale pricing'' is given through\n",
"\\begin{align*}\n",
"P(t,T^*) \\mathbb{E}^{T^*}[X | \\mathcal{F}_t].\n",
"\\end{align*}\n",
"The fair price of the $i$th caplet is therefore given by\n",
"\\begin{align*}\n",
"{\\rm Cpl}(t;T_{i-1},T_i) = \\delta P(t,T_i) \\mathbb{E}^{T_i} [ (F(T_{i-1},T_i) - \\kappa)^+ | \\mathcal{F}_t].\n",
"\\end{align*}\n",
"By the martingale property we obtain therefore\n",
"\\begin{align*}\n",
"\\mathbb{E}^{T_i}[F(T_{i-1},T_i) | \\mathcal{F}_t] = F(t;T_{i-1},T_i),\n",
"\\end{align*}\n",
"what was proved by trading arguments before."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "0W90M8OcH6hX"
},
"source": [
"## Black's formula"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ekb4Wk2YH6hX"
},
"source": [
"Let $X \\sim N(\\mu,\\sigma^2)$ and $K \\in \\mathbb{R}_{> 0}$. Then we have\n",
"\\begin{align*}\n",
"\\mathbb{E}[ (e^X - K)^+ ] &= e^{\\mu + \\frac{\\sigma^2}{2}} \\Phi \\bigg( -\\frac{\\log K - (\\mu + \\sigma^2)}{\\sigma} \\bigg)\n",
"- K \\Phi \\bigg( -\\frac{\\log K - \\mu}{\\sigma} \\bigg),\n",
"\\\\ \\mathbb{E}[ (K - e^X)^+ ] &= K \\Phi \\bigg( \\frac{\\log K - \\mu}{\\sigma} \\bigg) - e^{\\mu + \\frac{\\sigma^2}{2}} \\Phi \\bigg( \\frac{\\log K - (\\mu + \\sigma^2)}{\\sigma} \\bigg).\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CYfsYhmbH6hX"
},
"source": [
"## Black's formula for caps and floors"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tx2fpG2tH6hY"
},
"source": [
"\n",
"Let $t \\leq T_0$. From our previous results we know that \n",
"\\begin{align*}\n",
"{\\rm Cpl}(t;T_{i-1},T_i) &= \\delta P(t,T_i) \\mathbb{E}_t^{{T_i}} [ (F(T_{i-1},T_i) - \\kappa)^+ ],\n",
"\\\\ {\\rm Fll}(t;T_{i-1},T_i) &= \\delta P(t,T_i) \\mathbb{E}_t^{{T_i}} [ (\\kappa - F(T_{i-1},T_i))^+ ],\n",
"\\end{align*}\n",
"and that $F(t;T_{i-1},T_i)$ is an $P^{T_i}$-martingale.\n",
"\n",
"We assume that under ${P}^{T_i}$ the forward rate $F(t;T_{i-1},T_i)$ is an exponential Brownian motion\n",
"\\begin{align*}\n",
"F(t;T_{i-1},T_i) & = F(s;T_{i-1},T_i) \\\\\n",
"& \\exp \\bigg( -\\frac{1}{2} \\int_s^t \\lambda(u,T_{i-1})^2 du + \\int_s^t \\lambda(u,T_{i-1}) dW_u^{T_i} \\bigg)\n",
"\\end{align*}\n",
"for $s \\leq t \\leq T_{i-1}$,\n",
"with a function $\\lambda(u,T_{i-1})$. \n",
"\n",
"We define the variance $\\sigma^2(t)$ as\n",
"\\begin{align*}\n",
"\\sigma^2(t) := \\frac{1}{T_{i-1} - t} \\int_t^{T_{i-1}} \\lambda(s,T_{i-1})^2 ds.\n",
"\\end{align*}\n",
"The $P^{T_i}$-distribution of $\\log F(T_{i-1},T_i)$ conditional on $\\mathcal{F}_t$ is\n",
"$N(\\mu,\\sigma^2)$ with\n",
"\\begin{align*}\n",
"\\mu &= \\log F(t;T_{i-1},T_i) - \\frac{\\sigma^2(t)}{2} (T_{i-1} - t),\n",
"\\\\ \\sigma^2 &= \\sigma^2(t) (T_{i-1} - t).\n",
"\\end{align*}\n",
"In particular\n",
"\\begin{align*}\n",
"\\mu + \\frac{\\sigma^2}{2} &= \\log F(t;T_{i-1},T_i),\n",
"\\\\ \\mu + \\sigma^2 &= \\log F(t;T_{i-1},T_i) + \\frac{\\sigma^2(t)}{2} (T_{i-1} - t).\n",
"\\end{align*}\n",
"\n",
"We have\n",
"\\begin{align*}\n",
"{\\rm Cpl}(t;T_{i-1},T_i) &= \\delta P(t,T_i) (F(t;T_{i-1},T_i) \\Phi(d_1(i;t)) - \\kappa \\Phi(d_2(i;t))),\n",
"\\\\ {\\rm Fll}(t;T_{i-1},T_i) &= \\delta P(t,T_i) ( \\kappa \\Phi(-d_2(i;t)) - F(t;T_{i-1},T_i) \\Phi(-d_1(i;t)) ),\n",
"\\end{align*}\n",
"where\n",
"\\begin{align*}\n",
"d_{1,2}(i;t) = \\frac{\\log \\big( \\frac{F(t;T_{i-1},T_i)}{\\kappa} \\big) \\pm \\frac{1}{2} \\sigma(t)^2 (T_{i-1} - t)}{\\sigma(t) \\sqrt{T_{i-1} - t}}.\n",
"\\end{align*}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "mttsBAWcH6hY"
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"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
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"outputs": [],
"source": [
""
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