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Worldquant_Nov2022.ipynb
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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"colab": {
"name": "Worldquant_Nov2022.ipynb",
"provenance": [],
"include_colab_link": true
}
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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/29ffd4566e1f4349ce5f6a9c87bbbda1/worldquant_nov2022.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e2AxQWQN59kC"
},
"source": [
"# Deep Hedging"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "B2w3cfW159kK"
},
"source": [
"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": "xdUMvkQp59kM"
},
"source": [
"# Deep Hedging exemplified by means of the Black Scholes model"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "XmfNvCFo59kN"
},
"source": [
"Let $T$ be a finite time horizon and consider on a filtered probability space $(\\Omega, {(\\mathcal{F}_t)}_{0\\leq t\\leq T}), \\mathcal{F}_T, P)$ 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",
"$$\n",
"\\inf_{\\pi \\text{ premium}, \\, H \\text{ predictable }}\\mathbb{E}[( f(S_T)- \\pi- (H\\bullet S)_T)^2],\n",
"$$\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 predictable 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 $(S_t(\\omega_i))_{0 \\leq t \\leq T}$, the output $y_i$ should be $0$ and the\n",
"the loss function is given by\n",
"\n",
"$$\n",
"\\mathcal{L}= \\frac{1}{K}\\sum_i \\left(f(S_T(\\omega_i))- \\pi- \\int_0^T g_t(S_t (\\omega_i)) dS_t(\\omega_i)\\right)^2.\n",
"$$\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": "markdown",
"metadata": {
"id": "s9v41vm059kN"
},
"source": [
"In contrast to the original deep hedging approach we consider two training data sets here (xtrain and xtrain_red), where the second one is not a random sample Ktrain trajectories, but rather a set of trajectories, where R initial steps coincide for sets of N_red trajectories."
]
},
{
"cell_type": "code",
"metadata": {
"id": "wIUAEhkA59kO"
},
"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\n",
"\n",
"import copy"
],
"execution_count": 1,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "EMjoD9lb59kR"
},
"source": [
"N=100 # time disrectization\n",
"S0=1 # initial value of the asset\n",
"T=1 # maturity\n",
"strike = 1.0 # f(S)=(S-1)_+ European Call Contract\n",
"sigma=0.2 # volatility in Black Scholes"
],
"execution_count": 2,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "EHEx7CI559kR",
"outputId": "ca756e75-ba26-4286-b5fe-febec7ec2c92"
},
"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))"
],
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Price of a Call option in the Black scholes model with initial price 1 strike 1.0 maturity 1 and volatility 0.2 is equal to 0.07965567455405798\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "JoZA9Wze59kS"
},
"source": [
"#Definition of neural networks for heding strategies\n",
"\n",
"m = 1 # dimension of price\n",
"d = 3 # 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='tanh',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(0,0.1),#kernel_initializer='random_normal',\n",
" bias_initializer='random_normal',\n",
" name=str(i)+str(j))\n",
" layers = layers + [layer]"
],
"execution_count": 4,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "vY8NG7QV59kS"
},
"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",
"hedgeeval = Input(shape=(m,))\n",
"premium = Input(shape=(m,))\n",
"\n",
"inputs = [price]+[hedge]+[hedgeeval]+[premium]\n",
"outputhelper=[]\n",
"\n",
"premium = Dense(m, activation='linear', trainable=True,\n",
" kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',\n",
" bias_initializer=initializers.RandomNormal(0,1))(premium)\n",
"\n",
"for j in range(N):\n",
" strategy = price\n",
" strategyeval=hedgeeval\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",
" strategyeval=layers[k+(j)*d](strategyeval)\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",
" outputhelper = outputhelper + [strategyeval]\n",
" price=pricenew\n",
"payoff= Lambda(lambda x : 0.5*(K.abs(x-strike)+x-strike))(price)\n",
"outputs = Subtract()([payoff,hedge])\n",
"outputs = Subtract()([outputs,premium]) # payoff minus price minus hedge\n",
"outputs= [outputs] + outputhelper +[premium]\n",
"outputs = Concatenate()(outputs)\n",
"\n",
"model_hedge_strat = Model(inputs=inputs, outputs=outputs)"
],
"execution_count": 5,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "XTEFOl4F59kV"
},
"source": [
"gamma = 1.0\n",
"grid = [(i/N)**gamma*T for i in range(N+1)]\n",
"\n",
"Ktrain = 10**5\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.ones((Ktrain,m))] +\n",
" [priceBS*np.ones((Ktrain,m))]+\n",
" [np.random.normal(-(sigma)**2/2*(grid[i+1]-grid[i]),sigma*np.sqrt(grid[i+1]-grid[i]),(Ktrain,m)) for i in range(N)])\n",
"\n",
"ytrain=np.zeros((Ktrain,1+N))"
],
"execution_count": 6,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "b7W-7isT59kV"
},
"source": [
"#import keras\n",
"from keras import losses\n",
"def custom_loss(y_true,y_pred):\n",
" #return losses.mean_squared_error(y_true[0], y_pred[0])\n",
" z = y_pred[:,0]-y_true[:,0]\n",
" z=K.mean(K.square(z))\n",
" return z"
],
"execution_count": 7,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "cnTJ7DX559kW"
},
"source": [
"model_hedge_strat.compile(optimizer='adam',loss=custom_loss)"
],
"execution_count": 8,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "8Qbx4kJk59kW",
"outputId": "93863989-335c-409a-8837-acf2d1d656d0"
},
"source": [
"for i in range(10):\n",
" model_hedge_strat.fit(x=xtrain,y=ytrain, epochs=1,verbose=True,batch_size=100)"
],
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"1000/1000 [==============================] - 108s 57ms/step - loss: 0.1415\n",
"1000/1000 [==============================] - 58s 58ms/step - loss: 0.0058\n",
"1000/1000 [==============================] - 56s 56ms/step - loss: 4.6421e-04\n",
"1000/1000 [==============================] - 57s 57ms/step - loss: 3.5647e-04\n",
"1000/1000 [==============================] - 56s 56ms/step - loss: 3.1297e-04\n",
"1000/1000 [==============================] - 55s 55ms/step - loss: 2.6383e-04\n",
"1000/1000 [==============================] - 56s 56ms/step - loss: 2.0747e-04\n",
"1000/1000 [==============================] - 56s 56ms/step - loss: 1.6580e-04\n",
"1000/1000 [==============================] - 55s 55ms/step - loss: 1.3650e-04\n",
"1000/1000 [==============================] - 56s 56ms/step - loss: 1.2233e-04\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 482
},
"id": "inPlO-7r59kW",
"outputId": "8ba89751-0a71-40ca-9ac8-e94bf651ab2c"
},
"source": [
"a = model_hedge_strat.predict(xtrain)\n",
"plt.hist(a[:,0])\n",
"plt.show()\n",
"print(np.std(a[:,0]))\n",
"print(np.mean(a[:,N+1]))"
],
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"3125/3125 [==============================] - 47s 15ms/step\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.011505407\n",
"0.07953531\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "JeeOPzE659kX",
"outputId": "bd4804f0-a23f-4dd3-9e82-196247e0176d"
},
"source": [
"Ktest=50\n",
"xtest = ([initialprice*np.ones((Ktest,m))] +\n",
" [np.zeros((Ktest,m))]+\n",
" [0.5*np.ones((Ktest,m))+np.cumsum(np.ones((Ktest,m))*(1.5-0.5)/Ktest,axis=0)] +#change this if you go to higher dimensions\n",
" [priceBS*np.ones((Ktest,m))]+\n",
" [np.random.normal(-(sigma)**2/2*(grid[i+1]-grid[i]),sigma*np.sqrt(grid[i+1]-grid[i]),(Ktest,m)) for i in range(N)])\n",
"\n",
"y=model_hedge_strat.predict(xtest)[:,10]\n",
"print(y)"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"2/2 [==============================] - 0s 21ms/step\n",
"[-0.57985127 -0.53752154 -0.49442008 -0.45056757 -0.4059934 -0.36073688\n",
" -0.31484535 -0.26837465 -0.22138822 -0.17395711 -0.12615968 -0.07808271\n",
" -0.02981855 0.0185323 0.06686342 0.11506271 0.16301256 0.21059223\n",
" 0.25767916 0.30415234 0.34989136 0.3947824 0.43871737 0.48159787\n",
" 0.52333593 0.56385595 0.60309446 0.6410021 0.67754227 0.7126903\n",
" 0.7464343 0.7787739 0.80971724 0.8392822 0.8674932 0.8943817\n",
" 0.91998297 0.94433767 0.9674881 0.98947936 1.0103571 1.0301685\n",
" 1.0489607 1.0667793 1.0836715 1.0996807 1.1148515 1.1292259\n",
" 1.1428446 1.1557463 ]\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 300
},
"id": "lwbk07zw59kY",
"outputId": "c588ff2b-f2fc-48fa-baff-14564b3119ad"
},
"source": [
"logincrements = xtrain[4:4+N]\n",
"hedge = np.zeros(Ktrain)\n",
"price = S0*np.ones((Ktrain,N))\n",
"for k in range(N-1):\n",
" helper = logincrements[k][:,]\n",
" helper = helper.transpose()\n",
" price[:,k+1] = price[:,k]*np.exp(helper[:])\n",
" hedge[:] = hedge[:] + scipy.norm.cdf((np.log(price[:,k]/strike)+0.5*(T-grid[k+1])*sigma**2)/(np.sqrt(T-grid[k+1])*sigma))*(price[:,k+1]-price[:,k])\n",
"hedge[:]= hedge[:]-0.5*(np.abs(price[:,N-1]-strike)+(price[:,N-1]-strike))+priceBS\n",
"plt.hist(hedge)\n",
"plt.show()\n",
"print(np.std(hedge))\n",
"print(np.mean(hedge))"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.006893723736473796\n",
"0.00035899673848748833\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "X15OQqi559kY",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"outputId": "7686281a-3401-474c-e7a9-9ab3b8987c95"
},
"source": [
"l =20\n",
"s=np.linspace(0.5,1.5,Ktest)\n",
"z=scipy.norm.cdf((np.log(s/strike)+0.5*(T-grid[l])*sigma**2)/(np.sqrt(T-grid[l])*sigma))\n",
"#plt.plot(s,z)\n",
"#plt.plot(s,y)\n",
"y=model_hedge_strat.predict(xtest)[:,l]\n",
"plt.plot(s,y,s,z)\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"2/2 [==============================] - 0s 22ms/step\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
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"needs_background": "light"
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]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9bzImsl0p4Aq"
},
"source": [
"# Deep Simulation"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "P12RKZE5p4At"
},
"source": [
"We have understood controlled neural differential equations as structural roof of many sorts of neural networks. So far we have abstractly considered the initial value as input, even though it became clear in applications as Deep Portfolio Optimization or Deep Hedging that the dependence on control variable is equally interesting. In the sequel we shall investigate this further."
]
},
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"cell_type": "markdown",
"metadata": {
"id": "92lqTQOAp4At"
},
"source": [
"Consider a controlled differential equation\n",
"$$\n",
"dX_t = \\sum_{i=0}^d V_i(X_t) d u^i(t) \\, , \\; X_0 = x \\in \\mathbb{R}^m\n",
"$$\n",
"for neural networks $ V_i : \\mathbb{R}^m \\to \\mathbb{R}^m $, $ i = 1,\\ldots,d$ and $ d $ continuous, finite variation controls $ u^i $. We are interested in the behaviour of the map\n",
"$$\n",
"\\text{ control $u$ } \\mapsto \\text{ solution process } X \\, .\n",
"$$\n",
"Taylor expansion along controls gives a satisfying answer to this question. Let us study this in some detail.\n",
"\n",
"By the fundamental theorem of calculus we obtain for every smooth test function $ f $ that\n",
"$$\n",
"f(X_t) = f(x) + \\sum_{i=0}^d \\int_0^t V_i f(X_s) du^i(s)\n",
"$$\n",
"for $ 0 \\leq t $. This equation can be inserted into itself which leads to a generalized version of Taylor expansion for controlled ODEs\n",
"$$\n",
"\\sum_{k=0}^M \\sum_{(i_1,\\ldots,i_k) \\in {\\{0,\\ldots,d\\}}^k} V_{i_1} \\ldots V_{i_k} f(x) \\int_{0 \\leq t_1 \\leq \\ldots \\leq t_k \\leq t} du^{i_1}(t_1) \\dots du^{i_k}(t_k) + R_M(f,t) \\, ,\n",
"$$\n",
"for $ M \\geq 0 $, with the remainder satisfying\n",
"$$\n",
"R_M(f,t) = \\sum_{(i_1,\\ldots,i_{M+1}) \\in {\\{0,\\ldots,d\\}}^{M+1}}\n",
"\\int_{0 \\leq t_1 \\leq \\ldots \\leq t_{M+1} \\leq t}\n",
"V_{i_1} \\ldots V_{i_{M+1}} f(X_{t_{1}}) du^{i_1}(t_1) \\dots du^{i_k}(t_{M+1}) \\, .\n",
"$$\n",
"Notice that the vector field $ V $ acts on test function $ f $ as transport operator, i.e.\n",
"$$\n",
"Vf(x) : = df(x)(V(x))\n",
"$$\n",
"for $ x \\in \\mathbb{R}^m $.\n",
"\n",
"Let us put this into an algebraic setup to understand better the structure of iterated integrals. Consider an algebra of non-commutative power series generated from $ d +1 $ non-commuting (free) indeterminates $ e_0,\\ldots,e_d $ (this mimicks the action of the vector fields, which generically do not commute). Every element of this algebra can be written as\n",
"$$\n",
"Z_t = \\sum_{k=0}^\\infty \\sum_{(i_1,\\ldots,i_k) \\in {\\{0,\\ldots,d\\}}^k} a_{i_1,\\ldots,i_k} e_{i_1} \\dots e_{i_k} \\, ,\n",
"$$\n",
"without any further convergence assumption. This algebra is denoted by $ \\mathbb{A}_{d+1} $. Dually we can consider the free vector space on finite words in letters $ \\{ 0, \\ldots, d \\} $. As a subspace of $ \\mathbb{A}_{d+1} $ we distinguish the Lie algebra $ \\mathfrak{g} $ generated by $ e_0,\\ldots,e_d$. Its associated exponential image is denoted by $ G $ and is a group.\n",
"\n",
"By [Chow's theorem](https://en.wikipedia.org/wiki/Chow%E2%80%93Rashevskii_theorem) 'every' point in $G$ can be represented as\n",
"$$\n",
"\\sum_{k \\geq 0} \\sum_{(i_1,\\ldots,i_k) \\in {\\{0,\\ldots,d\\}}^k}\n",
" \\int_{0 \\leq t_1 \\leq \\dots \\leq t_k \\leq t}\n",
" d u^{i_1}(t_1)\\ldots d u^{i_k}(t_k) e_{i_1} \\ldots\n",
" e_{i_k}\n",
"$$\n",
"for some continuous finite variation paths $ u $ taking values in $ \\mathbb{R}^{d+1} $ and some time $ t > 0$. Of course each expression of the above type lies in $G$. This actually means that iterated integrals 'fill' the group $G$ and therefore $ G $ constitutes all algebraic relations among iterated integrals."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "I5enZpmlp4Au"
},
"source": [
"In order to apply the above theory to the actual calculation of controlled ODEs one has to make the calculation of iterated integrals tractable, which is non-trivial since they constitute an infinite dimensional system. In order to calculate iterated integrals up to order $M$ in dimension $ d $ actually $ \\frac{(d+1)^{M+1}-1}{d} $ quantities have to be calculated which is exponential in $ M $."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Y0MSRSkip4Av"
},
"source": [
"An elegant way out might be to consider lower dimensional representations of iterated integrals which share their properties. This will be achieved by an application of the [Johnson-Lindenstrauss Lemma](https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma) (take a look at the very informative Wikipedia entry) and at the [original work](http://stanford.edu/class/cs114/readings/JL-Johnson.pdf), whose proof we shall sketch in the sequel.\n",
"\n",
"Let us first state the formal assertion: for any $ 0 < \\epsilon < 1 $ and any integer $ N \\geq 1 $, any dimension $ k $ with\n",
"$$\n",
"k \\geq \\frac{24 \\log N}{3 \\epsilon^2 - 2 \\epsilon^3}\n",
"$$\n",
"and any set $ A $ of $ N $ points in some $ \\mathbb{R}^m $ there exists a map $ \\pi: \\mathbb{R}^m \\to \\mathbb{R}^k $ such that\n",
"$$\n",
"{|| x - y||}^2 (1-\\epsilon) \\leq{|| \\pi(x) -\\pi( y) ||}^2 \\leq {|| x - y ||}^2 (1+\\epsilon)\n",
"$$\n",
"for all point $ x,y \\in A $, i.e. the geometry of $ A $ is almost preserved after the projection. Norms are $ L^2$ norms here."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "X6I-tTtRp4Aw"
},
"source": [
"The proof consists of three steps: let $ R $ denote a random matrix with independent identically distributed standard normal entries of dimension $ k \\times m $.\n",
"1. For $ u \\in \\mathbb{R}^m $ and $ v := \\frac{1}{\\sqrt{k}} R u $ it holds that\n",
"$$\n",
"E[{||v||}^2] = {||u||}^2 \\, ,\n",
"$$\n",
"which is just a calculation with independent standard normals. Notice also that the entries of $ v $ are independent standard normal random variables with variance $ \\frac{{||u||}^2}{k} $.\n",
"2. It holds (for the particular $k$ from above!) that\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\big) \\leq \\frac{1}{N^2} \\, .\n",
"$$\n",
"Indeed\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\big) = P\\big (\\exp(\\lambda Z) \\geq \\exp(\\lambda (1+\\epsilon) k) \\big )\n",
"$$\n",
"with a $ \\chi^2 $ random variable of dimension $ k $. Notice that each summand in $ ||v||^2 $ has variance $ ||u||^2/k $, whence yield $ Z $ by rescaling. The formula holds for every positive $\\lambda$. By Markov's inequality we arrive at\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\big) \\leq {\\big( \\frac{1}{\\sqrt{1-2\\lambda}\\exp(\\lambda(1+\\epsilon))}\\big)}^k \\, .\n",
"$$\n",
"For $ \\lambda = \\frac{\\epsilon}{2(1+\\epsilon)} $ (this is our choice) we obtain\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\big) \\leq \\big( (1+\\epsilon)\\exp(-\\epsilon) \\big)^{k/2} \\, ,\n",
"$$\n",
"which yields by $ \\log (1+a) \\leq a - a^2/2 + a^3/3 $ that\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\big) \\leq \\frac{1}{N^2} \\, .\n",
"$$\n",
"In an completely analogous manner (replace $ \\lambda $ by $ - \\lambda $ and arrive for $ \\lambda = \\frac{\\epsilon}{2(1-\\epsilon)} $ at an upper bound\n",
"$$\n",
"\\big( (1-\\epsilon)\\exp(-\\epsilon) \\big)^{k/2} \\, ,\n",
"$$\n",
"which in turn can be estimated by $ \\log (1-a) \\leq -a - a^2/2 $. Whence the result\n",
"$$\n",
"P\\big( {||v||}^2 \\geq {||u||}^2 (1+\\epsilon) \\text{ or } {||v||}^2 \\leq {||u||}^2 (1-\\epsilon) \\big) \\leq \\frac{2}{N^2} \\, .\n",
"$$\n",
"3. Summing this up over all possible combination of two points yields that\n",
"$$\n",
"P\\big(\\text{ The ratio of norms of distances lies in } [1-\\epsilon,1+\\epsilon] \\big) \\geq \\frac{1}{N} ,\n",
"$$\n",
"whence there exists a matrix $ R $ which does the job."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "b0f3OZDGp4Aw"
},
"source": [
"This result can now be applied to the differential equation in $ \\mathbb{A}_{d+1} $ which generates the iterated integrals, namely\n",
"$$\n",
"d Z_t = \\sum_{i=0}^d Z_t e_i du^i(t) \\, .\n",
"$$\n",
"The random projection of $ Z_t $ will almost preserve the geometry of the iterated integrals (which is necessary for the quality of the regression), and the random projection can be calculated by means of a *random* controlled differential equation, which facilitates calculations tremendously.\n",
"\n",
"There are two ways how one can see this result:\n",
"\n",
"1. We consider a space $ \\mathbb{R}^k $, where we mimick the 'geometry' of iterated integrals, i.e. we consider the controlled differential equation with independent random matrices $ A_1, \\ldots, A_d $ and independent random vectors $ b_1, \\ldots, b_d $ and activation function $ \\sigma $ (applied componentwise)\n",
"$$\n",
"d X_t = \\sum_{i=1}^d \\sigma (A_i X_t + b_i) d u^i(t)\n",
"$$\n",
"as a sufficiently close replica of the vector of iteraated integrals. Following rough path literature and the notions introduced by Terry Lyons we call $ Z $ signature and $ X $ random signature.\n",
"\n",
"2. We consider a space $ \\mathbb{R}^k $ and vector fields\n",
"$$\n",
"V_i (x) = \\sigma (A_i x + b_i)\n",
"$$\n",
"for again with random matrices $ A_i $ and $ b_i $ and define a representation $ e_i \\mapsto V_i $. This representation is faithful under mild assumptions on $ \\sigma $ and $ k $, whence again a solution of\n",
"$$\n",
"d X_t = \\sum_{i=1}^d \\sigma (A_i X_t + b_i) d u^i(t)\n",
"$$\n",
"inserted into functions $ f_1, \\ldots, f_N $ mimicks the geometry of signature."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "FQ7yhE7mp4Ax"
},
"source": [
"In the sequel we shall see two instances where this is applied: first we learn an unknown stochastic differential equation."
]
},
{
"cell_type": "code",
"metadata": {
"id": "8Ij6j_mLp4Ax"
},
"source": [
"import numpy as np\n",
"import scipy as sp\n",
"from matplotlib import pyplot as plt\n",
"from scipy import linalg"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"outputId": "bf29227d-b603-405e-bbd0-6b21e07da26a",
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "qMcmdaA1Bq3X"
},
"source": [
"import pandas as pd\n",
"import pandas_datareader.data as web\n",
"!pip install --upgrade pandas-datareader"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
"Requirement already satisfied: pandas-datareader in /usr/local/lib/python3.7/dist-packages (0.10.0)\n",
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"Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.23->pandas-datareader) (2022.6)\n",
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"Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests>=2.19.0->pandas-datareader) (1.24.3)\n",
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]
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "pGrCYv60p4Ay"
},
"source": [
"class SDE:\n",
" def __init__(self,timehorizon,initialvalue,dimension,dimensionBM,dimensionR,vectorfield,timesteps):\n",
" self.timehorizon = timehorizon\n",
" self.initialvalue = initialvalue # np array\n",
" self.dimension = dimension\n",
" self.dimensionBM = dimensionBM\n",
" self.dimensionR = dimensionR\n",
" self.vectorfield = vectorfield\n",
" self.timesteps = timesteps\n",
"\n",
" def path(self):\n",
" BMpath = [np.zeros(self.dimensionBM)]\n",
" SDEpath = [np.array([1.0, self.initialvalue])]\n",
" for i in range(self.timesteps):\n",
" helper = np.random.normal(0,np.sqrt(self.timehorizon/self.timesteps),self.dimensionBM)\n",
" BMpath = BMpath + [BMpath[-1]+helper]\n",
" SDEpath = SDEpath + [np.exp(-1.0*self.timehorizon/self.timesteps)*(SDEpath[-1]+self.vectorfield(SDEpath[-1],helper))]\n",
"\n",
" return [BMpath, SDEpath]\n",
"\n",
" def anypath(self):\n",
" BMpath = [np.zeros(self.dimensionBM)]\n",
" SDEpath = [np.array([1.0, self.initialvalue])]#[np.ones((self.dimension,1))*self.initialvalue]\n",
"\n",
" for i in range(self.timesteps):\n",
" helper = np.cos(BMpath[-1]*50)*self.timehorizon/self.timesteps#np.random.normal(0,np.sqrt(self.timehorizon/self.timesteps),self.dimensionBM)\n",
" BMpath = BMpath + [BMpath[-1]+helper]\n",
" SDEpath = SDEpath + [np.exp(-0.0*self.timehorizon/self.timesteps)*(SDEpath[-1]+self.vectorfield(SDEpath[-1],helper))]\n",
"\n",
" return [BMpath, SDEpath]\n",
"\n",
" def reservoir(self,BMpath,scaling,k):\n",
" reservoirpath = [canonical(k,self.dimensionR)*self.initialvalue]\n",
" for i in range(self.timesteps):\n",
" increment = scaling*(BMpath[i+1]-BMpath[i])\n",
" reservoirpath = reservoirpath + [np.exp(-1.0*self.timehorizon/self.timesteps)*(reservoirpath[-1]+reservoirfield(reservoirpath[-1],increment))]\n",
" return reservoirpath\n",
""
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "KFIeex1Up4A0"
},
"source": [
"Here we use the methodology introduced above under 2.: we solve an equation with vector fields\n",
"$$\n",
"V_i(x) = A_i x + b_i\n",
"$$\n",
"with random vectors and matrices on some $ \\mathbb{R}^M $. Then we insert the resulting vector in several (non-)linear functions $ \\operatorname{id}, \\operatorname{arctan}, \\operatorname{arctan}(2.)$ yielding a high dimensional regression basis (in the case below in $ \\mathbb{R}^{3M} $)."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IWPtloNzp4A2"
},
"source": [
"An very interesting strand of applications is to build econometric models, i.e. data-driven scenario generators which are estimated by regression."
]
},
{
"cell_type": "code",
"metadata": {
"id": "CY4DoJGpp4A3"
},
"source": [
"end = '2019-01-01'\n",
"start = '2014-01-01'\n",
"get_px = lambda x: web.DataReader(x, 'yahoo', start=start, end=end)['Adj Close']\n",
"\n",
"symbols = ['MSFT','GOOG', 'BAC','AMZN','AAPL','INTC','PBR','JPM']\n",
"# raw adjusted close prices\n",
"data = pd.DataFrame({sym:get_px(sym) for sym in symbols})\n",
"# log returns\n",
"lrets = np.log(data/data.shift(1)).dropna()"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "SGxLudXnp4A3",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "8107a180-56b8-41f0-be30-e2c56371ad05"
},
"source": [
"#data\n",
"lrets.loc['2014-01-07'].values"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([ 0.00772013, 0.01909475, -0.00965007, 0.01111606, -0.00717692,\n",
" 0.00509305, -0.01995481, -0.01159205])"
]
},
"metadata": {},
"execution_count": 97
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "P4aaimTBp4A3"
},
"source": [
"Omega = (lrets\n",
" .rolling(30)\n",
" .cov()\n",
" .dropna())"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "Tb9qcXqpp4A4"
},
"source": [
"dates = lrets.index"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "P0lwvNmOp4A4"
},
"source": [
"dates = dates[30:]"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "flVJn2g9p4A4"
},
"source": [
"covdata = dict(zip(dates, [Omega.loc[date].values for date in dates]))"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "wIB6cXUXp4A5"
},
"source": [
"marketBM = dict(zip(dates, [np.matmul(np.linalg.inv(linalg.sqrtm(Omega.loc[date].values)),lrets.loc[date].values) for date in dates]))\n",
"#marketBM = dict(zip(dates, [np.matmul(np.linalg.inv(np.eye(9)),lrets.loc[date].values) for date in dates]))"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "tzMMFgRYp4A5",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 300
},
"outputId": "bb0c288d-d7ec-4303-fd84-07902f274ebd"
},
"source": [
"plt.plot([marketBM[date][0] for date in dates])\n",
"plt.show()\n",
"print(np.std(np.array([marketBM[date][0] for date in dates])))\n",
"print(np.mean(np.array([marketBM[date][0] for date in dates])))"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"1.0073383455829792\n",
"0.09940040781880508\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "snP8rbJIp4A5"
},
"source": [
"K=8\n",
"BMmarketpath = 1/250*np.ones((len(dates),K))\n",
"mean=np.zeros(K)\n",
"for k in range(K):\n",
" mean[k] = np.mean([marketBM[l][k] for l in dates])"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "yfVETTwGp4A5",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
},
"outputId": "a4902882-95ff-438d-a8a9-c0f40b9c683d"
},
"source": [
"for i in range(K):\n",
" BMmarketpath[:,i] = np.cumsum([np.sqrt(1/250)*(marketBM[date][i]-0.*mean[i])\n",
" for date in dates])\n",
"#BMmarketpath[:,K]= np.cumsum(BMmarketpath[:,K])\n",
"plt.plot(BMmarketpath)\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "SSAtqS-xp4A6"
},
"source": [
"Kmarket = 8\n",
"Ymarket = np.zeros((len(dates),Kmarket))\n",
"for i in range(Kmarket):\n",
" Ymarket[:,i]=np.cumsum([lrets.loc[date].values[i] for date in dates])\n",
"Ymarket = np.exp(Ymarket)"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "NnkgM4ZCp4A6",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
},
"outputId": "839c0d59-a498-4569-8cf4-06d53ea08a4c"
},
"source": [
"plt.plot(Ymarket)\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Jj7lBoc5p4A6",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "2c9d2cf5-b3c2-4930-cc4c-89cd1a0a7e8d"
},
"source": [
"Ymarketdiff = np.diff(Ymarket,axis=0)\n",
"Ymarkettrain = np.concatenate((Ymarket[:500],Ymarketdiff[:500:1]),axis=0)\n",
"np.shape(Ymarkettrain)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(1000, 8)"
]
},
"metadata": {},
"execution_count": 108
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "L_uwtTBxp4A7"
},
"source": [
"d=K\n",
"M=200\n",
"\n",
"def nilpotent(M):\n",
" B = np.zeros((M,M))\n",
" for i in range(2,M):\n",
" B[i,i-1]=1.0\n",
" return B\n",
"\n",
"def canonical(i,M):\n",
" e = np.zeros((M,1))\n",
" e[i,0]=1.0\n",
" return e\n",
"\n",
"def randomAbeta(d,M):\n",
" A = []\n",
" beta = []\n",
" for i in range(d):\n",
" #B = 0.1*np.identity(M)+np.random.normal(0.0,.5,size=(M,M))\n",
" B = np.random.normal(0.0,0.02,size=(M,M)) # 0.1 for scen-gen, 1.5 for SABR\n",
" #B = np.random.permutation(B)\n",
" #B = np.identity(M)\n",
" #B = sp.linalg.sqrtm(np.matmul(B,np.transpose(B)))\n",
" A = A + [B]\n",
" beta = beta + [0.*canonical(i,M)+np.random.normal(0.0,0.03,size=(M,1))]\n",
" return [A,beta]\n",
"\n",
"Abeta = randomAbeta(d,M)\n",
"A = Abeta[0]\n",
"beta = Abeta[1]\n",
"\n",
"def sigmoid(x):\n",
" return np.tanh(x)\n",
"\n",
"def reservoirfield(state,increment):\n",
" value = np.zeros((M,1))\n",
" for i in range(d):\n",
" value = value + sigmoid(np.matmul(A[i],state) + beta[i])*increment[i]\n",
" return value"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "KrP2MYhcp4A7",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "376c9193-f1b0-48ac-f66e-2e7c17b1cbb2"
},
"source": [
"BMmarketpathlist = [BMmarketpath[i,:] for i in range(len(dates))]\n",
"Reservoir = SDE(1,1.5,2,K,M,reservoirfield,len(dates)-1)\n",
"X=Reservoir.reservoir(BMmarketpathlist,1.0,0)\n",
"np.shape(X)\n",
"Xdata = np.squeeze(X)\n",
"Xdatadiff = np.diff(Xdata,axis=0)\n",
"Xtrain=np.concatenate((Xdata[:500],Xdatadiff[:500:1]),axis=0)\n",
"np.shape(Xtrain)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(1000, 200)"
]
},
"metadata": {},
"execution_count": 110
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "9-j7nB9Vp4A7",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 491
},
"outputId": "a2b2a68f-86c3-495d-a687-5786b7d4001e"
},
"source": [
"from sklearn import linear_model\n",
"import pandas as pd\n",
"lm = linear_model.Ridge(alpha=0.05)#LinearRegression()\n",
"model = lm.fit(Xtrain,Ymarkettrain)\n",
"plt.plot(model.predict(Xtrain),'r')\n",
"plt.plot(Ymarkettrain,'b')\n",
"plt.show()\n",
"model.score(Xtrain,Ymarkettrain)\n",
"model.coef_"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 6.76819663e-01, 8.00645651e-02, -8.46241106e-03, ...,\n",
" -1.65317448e-02, 5.17566872e-02, -1.38114328e-03],\n",
" [ 6.75252818e-01, 2.26037829e-02, 3.12547021e-03, ...,\n",
" -4.09801612e-02, 1.91642630e-02, -2.47702740e-02],\n",
" [ 6.59604043e-01, 2.54387981e-02, -3.84346764e-02, ...,\n",
" -3.20453123e-03, 1.88364305e-02, 1.00939039e-02],\n",
" ...,\n",
" [ 6.64680785e-01, 6.09945314e-02, 2.39698198e-02, ...,\n",
" -1.94186452e-02, 1.41000333e-01, -3.93311491e-02],\n",
" [ 6.50189528e-01, -3.75533270e-02, -1.15263809e-01, ...,\n",
" 3.07669260e-02, -1.47639088e-01, 1.23709129e-01],\n",
" [ 6.69360594e-01, 5.67693052e-02, -7.71573942e-02, ...,\n",
" -1.17631274e-02, 5.25420936e-02, -4.29592369e-04]])"
]
},
"metadata": {},
"execution_count": 111
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "2WUCmMuMp4A7",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 374
},
"outputId": "cee40184-bf24-4af4-8028-6a81be630997"
},
"source": [
"f,p=plt.subplots(Kmarket,1,figsize=(6,6),sharey=False)\n",
"\n",
"for i in range(Kmarket):\n",
" p[i].plot(model.predict(Xdata[401:600])[:,i],'b')\n",
" p[i].plot(Ymarket[401:600][:,i],'g')\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x432 with 8 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "71445Ed8p4A7",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 266
},
"outputId": "eb265f4c-32b7-468e-f102-b5e2a2fb6d38"
},
"source": [
"BMmarketpathlistrandom = [np.zeros(K)]\n",
"for i in range(len(dates)):\n",
" BMmarketpathlistrandom = BMmarketpathlistrandom + [BMmarketpathlistrandom[-1] + np.random.normal(0,1/np.sqrt(250),K)]\n",
"Reservoir = SDE(1,1.5,2,K,M,reservoirfield,len(dates)-1)\n",
"Xtest=Reservoir.reservoir(BMmarketpathlistrandom,1.0,0)\n",
"np.shape(Xtest)\n",
"Xtestdata = np.squeeze(Xtest)\n",
"\n",
"plt.plot(model.predict(Xtestdata[:100]))\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "B9Dkh3hkp4A7"
},
"source": [],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "dcfm7Ro6p4A8"
},
"source": [],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "VZwy9FGDFgwl"
},
"execution_count": null,
"outputs": []
}
]
}
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