{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Deep Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a controlled neural differential equation\n", "$$\n", "dX_t = \\sum_{i=0}^d V_i(X_t) d u^i(t) \\, , \\; X_0 = y \\in \\mathbb{R}^m\n", "$$\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", "$$\n", "f(X_t) = x + \\sum_{i=0}^d \\int_0^t V_i f(X_s) du^i(s)\n", "$$\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": {}, "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": {}, "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 Theorem, 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": {}, "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 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 $. 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)} $ 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": {}, "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the sequel we shall see two instances where this is applied: first we learn an unknown stochastic differential equation." ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d=2\n", "M=30 \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 vectorfieldoperator(state,increment):\n", " d = np.shape(increment)[0]\n", " N = np.shape(state)[0]\n", " direction = np.zeros((N,1))\n", " for i in range(d):\n", " helper = np.zeros((N,1))\n", " for j in range(N):\n", " helper[j]=np.sin((j+1)*state[j,0])\n", " direction=direction + helper*increment[i]\n", " return direction\n", "\n", "def vectorfield2d(state,increment):\n", " return np.array([(2.0*np.sqrt(state[1]**2))**0.7,1.0*state[1]])*increment[0]+np.array([(2.0*np.sqrt(state[1]**2))**0.7,0.0*state[1]])*increment[1]\n", "\n", "def vectorfield3d(state,increment):\n", " return np.array([np.sin(state[0])*np.exp(-state[2]),np.cos(state[1]),-state[2]*state[1]])*increment[0]+np.array([np.sin(state[1]),np.cos(state[0]),-state[0]*state[1]])*increment[1]\n", "def vectorfield(state,increment):\n", " return 5*np.exp(-state)*increment[0] + 5*np.cos(state)*increment[1]\n", "def randomAbeta(d,M):\n", " A = []\n", " beta = []\n", " for i in range(d):\n", " B = 0.0*nilpotent(M) + np.random.normal(0.0,0.5,size=(M,M)) \n", " B = np.random.permutation(B)\n", " A = A + [B]\n", " beta = beta + [canonical(i,M)+np.random.normal(0.0,0.1,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" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": true }, "outputs": [], "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(-0.0*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):\n", " reservoirpath = [canonical(0,self.dimensionR)*self.initialvalue]\n", " for i in range(self.timesteps):\n", " increment = BMpath[i+1]-BMpath[i]\n", " reservoirpath = reservoirpath + [np.exp(-0.0*self.timehorizon/self.timesteps)*(reservoirpath[-1]+reservoirfield(reservoirpath[-1],increment))]\n", " return reservoirpath \n", " " ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Sabr = SDE(1,1.0,2,d,M,vectorfield2d,10000)\n", "training = Sabr.path()" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "image/png": 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GRYmmldLDVaVBg8QxlDgXI1cGBIj6/qtXxVAJblBX77SHp4yxfwCs5ZyvtJaX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\nb85j1vumQxNIfjnxi6HzVNX8VZ1yTkfFJ8Xj9EM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f1,p1=plt.subplots(2,1,figsize=(6,6),sharey=True)\n", "p1[0].plot(training[0][:10000],'r')\n", "p1[1].plot(training[1][:10000],'g')\n", "#plt.savefig('trainingpath.pdf')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2000, 2)" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BMpath=training[0]\n", "Y = training[1]\n", "Ydata = np.squeeze(Y)\n", "Ydatadiff = np.diff(Ydata,axis=0)\n", "Ytrain = np.concatenate((Ydata[:1000],Ydatadiff[:1000:1]),axis=0)\n", "np.shape(Ytrain)" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2000, 30)" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X=Sabr.reservoir(BMpath)\n", "np.shape(X)\n", "Xdata = np.squeeze(X)\n", "Xdatadiff = np.diff(Xdata,axis=0)\n", "Xtrain=np.concatenate((Xdata[:1000],Xdatadiff[:1000:1]),axis=0)\n", "np.shape(Xtrain)" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "image/png": 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OtXv8xTtOAgCi4tVCrdMJy29Aa2NummX5ve117QsP7QlwbhnGX/BJcQeAxHgz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\n87xxwAZ6fPJaumXQemvZx3dvcnrP9yz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "array([[ 1.00012792, 0.55387202, -0.97116232, 0.92713923, 1.56673332,\n", " -0.43665076, -1.29558234, -0.24080606, -0.5466374 , -0.33390654,\n", " -0.38413194, -0.33618094, -1.33634164, 0.02514181, -0.31821885,\n", " -0.72255828, -0.24063695, -0.10196031, -0.46445299, 0.14928589,\n", " -0.9466267 , 0.34732252, -0.46316145, -1.40821566, 0.07139127,\n", " -0.38030789, -0.44398579, 0.27376517, 0.8513087 , -0.52421979],\n", " [ 1.00040623, 0.73596326, -0.78360438, 0.40981875, 0.24787034,\n", " 0.07532344, -0.4046941 , 0.19191621, -0.1745398 , 0.25490734,\n", " 0.63030905, -0.57391784, -0.39330352, -0.19727881, -0.30068266,\n", " -0.50753692, -0.20748391, 0.09986918, -0.36194681, -0.03092786,\n", " -0.47247133, 0.38407192, -0.02708139, -0.16990073, 0.26360567,\n", " -0.46333975, -0.44003509, 0.48343491, 0.24871577, -0.02894263]])" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn import linear_model\n", "import pandas as pd\n", "lm = linear_model.LinearRegression()\n", "model = lm.fit(Xtrain,Ytrain)\n", "plt.plot(model.predict(Xtrain),'r')\n", "plt.plot(Ytrain,'b')\n", "plt.show()\n", "model.score(Xtrain,Ytrain)\n", "model.coef_" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "image/png": 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ylRYC+On19gOPOSLuXDa37RbcNscaQE6YV29rhQXR0cu6E/jr278mdXIqmc+k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\nvBGTefkFxN/thcaYdq9zynEdq2SvHbyeMDM//IYrPy99CoJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f,p=plt.subplots(2,1,figsize=(6,6),sharey=True)\n", "\n", "N=2\n", "\n", "for i in range(N):\n", " p[i].plot(model.predict(Xdata[:2000])[:,i],'b')\n", " p[i].plot(Ydata[:2000][:,i],'g')\n", "plt.savefig('training.pdf')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": true }, "outputs": [], "source": [ "generalization = Sabr.path()\n", "BMpath = generalization[0]\n", "Y = generalization[1]\n", "Ydata = np.squeeze(Y)" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "image/png": 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DnZHxcETdhdw56GXjwvCPXGWmjGhDcLeaLfdQayhHjzI+RNKTEgkOaJC+ILb7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\nVtKWlcNUIK/mVapC+YNQMIzRVT7J0tb6NlXrqYL7UWPd8UL/ZfJn16C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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = Sabr.reservoir(BMpath)\n", "Xdata = np.squeeze(X)\n", "\n", "N=2\n", "\n", "fig,p=plt.subplots(N, 1, figsize=(6,6),sharex=True, sharey=True)\n", "for i in range(N):\n", " p[i].plot(model.predict(Xdata[:1000])[:,i],'b')\n", " p[i].plot(Ydata[:1000][:,i],'g')\n", "#plt.savefig('generalization.pdf')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An second very interesting strand of applications is to build econometric models, i.e. data-driven scenario generators which are estimated by regression." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from scipy import linalg\n", "from matplotlib import pyplot as plt\n", "import pandas as pd\n", "import pandas_datareader.data as web" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "end = '2015-01-01'\n", "start = '2007-01-01'\n", "get_px = lambda x: web.DataReader(x, 'yahoo', start=start, end=end)['Adj Close']\n", "\n", "symbols = ['GOOG', 'AAPL','TLT','MSFT']\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()" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.02195283, 0.032963 , -0.00167618, 0.00604542])" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lrets.loc['2007-01-04'].values" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Omega = (lrets\n", " .rolling(30)\n", " .cov()\n", " .dropna()) # this will get you to 66 windows instead of 125 with NaNs" ] }, { "cell_type": "code", "execution_count": 123, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dates = lrets.index#Omega.index.get_level_values(0) # or just the index of your base returns" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dates = dates[30:]" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": true }, "outputs": [], "source": [ "covdata = dict(zip(dates, [Omega.loc[date].values for date in dates]))" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": true }, "outputs": [], "source": [ "marketBM = dict(zip(dates, [np.matmul(np.linalg.inv(linalg.sqrtm(Omega.loc[date].values)),lrets.loc[date].values) for date in dates]))" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "image/png": 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KSfeNF4b8/SM89El233BlsQsOeXK6c1+W6QJvLPjW+SCNSwxzd5k6DJXofRmIZn4tcStP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\nSSJrzYv6QVQDlLxV7LefWe0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot([marketBM[date][0] for date in dates])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "collapsed": true }, "outputs": [], "source": [ "K=4\n", "BMmarketpath = np.zeros((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])" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "image/png": 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S8dSF/cAWFkLkOFw4uF3dB/TumcCBxWTZGW807FX5KrOEDUTXNv/iCuttH00yrrv4PeDW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(K):\n", " BMmarketpath[:,i] = np.cumsum([np.sqrt(1/250)*(marketBM[date][i]-mean[i])\n", " for date in dates])\n", "plt.plot(BMmarketpath)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 141, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Kmarket = 4\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)" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [ { "data": { "image/png": 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Eh1SW/KpMWfbDL28ZTXhpP7gQHY200EWHYnM4eX3JPnKKjHHiKx+cyImCEgZG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\nAqKL8R48lKA7XqTkQDLbtidzV0YEkw9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(Ymarket)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2000, 4)" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ymarketdiff = np.diff(Ymarket,axis=0)\n", "Ymarkettrain = np.concatenate((Ymarket[:1000],Ymarketdiff[:1000:1]),axis=0)\n", "np.shape(Ymarkettrain)" ] }, { "cell_type": "code", "execution_count": 133, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d=K\n", "M=150\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(0.0,0.5,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 + [canonical(i,M)+np.random.normal(0.0,0.5,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" ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2000, 150)" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BMmarketpathlist = [BMmarketpath[i,:] for i in range(len(dates))]\n", "Reservoir = SDE(1,0.5,2,K,M,vectorfield2d,len(dates)-1)\n", "X=Reservoir.reservoir(BMmarketpathlist)\n", "np.shape(X)\n", "Xdata = np.squeeze(X)\n", "Xdatadiff = np.diff(Xdata,axis=0)\n", "Xtrain=np.concatenate((Xdata[:1000],Xdatadiff[:1000:1]),axis=0)\n", "np.shape(Xtrain)" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "image/png": 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0+bftfovMS9uH+Tq/zsqSsdNgKGGAFQpQYyuecG/fruv5TiAdpLE0bZr09tuS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\nqBnztnu7neUXyKK2/POIRF9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" -1.27352155e-01, -1.04085331e-01, -2.87760786e-02,\n", " 1.04159797e-01, -9.86291263e-02, 9.09029735e-02,\n", " -1.42546410e-01, 9.38539734e-02, 1.04217374e-01,\n", " 5.79736116e-02, 7.98731873e-02, 1.93039972e-02,\n", " 7.08583735e-02, -1.02833442e-02, -1.27377595e-02,\n", " -7.11248674e-02, 4.56246432e-02, -1.55930630e-01,\n", " 1.93303461e-02, -6.62468032e-02, -7.89725182e-02,\n", " 6.29326863e-02, 9.04316318e-02, -1.08852262e-01,\n", " 1.05923711e-01, 1.46391662e-02, 1.37881153e-01,\n", " 1.25539018e-01, -2.70825675e-03, -3.40100804e-02,\n", " 8.68870140e-02, -7.69915674e-02, 7.20164191e-02,\n", " 1.16653993e-01, 1.86228764e-02, -9.23331327e-02,\n", " 9.42758264e-02, -6.02543933e-02, -3.83338388e-03,\n", " 1.19286469e-02, -5.95492915e-02, -4.26503979e-03,\n", " -3.12865092e-02, -1.34487444e-02, 2.37362262e-01,\n", " 1.33825851e-02, 4.57456339e-02, -6.34220955e-02,\n", " 9.69300313e-02, 9.78532393e-02, 7.27899209e-02,\n", " -1.92108100e-01, 1.88422629e-01, -8.30514579e-02,\n", " 8.21034275e-02, -4.76077310e-02, -8.18529064e-02,\n", " 2.09567599e-02, 1.36311413e-02, -6.49621273e-02,\n", " 6.30175289e-02, -1.38291892e-02, -3.86323678e-02,\n", " -1.36641356e-01, -9.10860822e-03, 5.31535709e-02,\n", " 1.32625102e-01, -1.17540869e-01, -3.33742301e-02,\n", " -2.68216848e-02, -1.23394804e-01, 1.58725485e-01]])" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn import linear_model\n", "import pandas as pd\n", "lm = linear_model.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_" ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "image/png": 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Z1rpZPzB93PcDXQEvYAvQy4n7bwsMsk4HYEaY7AVMAR6ponwva4zeQBdr7O6N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\nIS1NEQx30VDjo6hIt+0FXYratk3HVb1e6OhQ9ETi1NZHOFEf5YLVLtq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f,p=plt.subplots(Kmarket,1,figsize=(6,6),sharey=True)\n", "\n", "for i in range(Kmarket):\n", " p[i].plot(model.predict(Xdata[:2000])[:,i],'b')\n", " p[i].plot(Ymarket[:2000][:,i],'g')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "data": { "image/png": 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bqLxuvYtrLW+qYYbRpOYW2da6jXM/OZf31qe1oZMktvkrqfCJyIQnfniC+xbc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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "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(1,0.5,2,K,M,vectorfield2d,len(dates)-1)\n", "Xtest=Reservoir.reservoir(BMmarketpathlistrandom)\n", "np.shape(Xtest)\n", "Xtestdata = np.squeeze(Xtest)\n", "\n", "plt.plot(model.predict(Xtestdata[:1000]))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A third example goes for learning high dimensional or even infinite dimensional SDEs, like, e.g., HJM type equations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d = 2 # number of driving Brownian motions\n", "M = 50 # dimension of the reservoir driven by the same number of Brownian motions by\n", " # the reservoir vector field which uses random matrices defined below" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sigmoid(x):\n", " return np.tanh(x)\n", "\n", "def grid(dimension):\n", " B = np.zeros((dimension,1))\n", " for i in range(dimension):\n", " B[i,0]= i + 1.0\n", " return B\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" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def randomAbeta(d,M):\n", " A = []\n", " beta = []\n", " for i in range(d):\n", " B = 0.0*nilpotent(M) + np.random.normal(0.0,1.5,size=(M,M))\n", " A = A + [B]\n", " beta = beta + [canonical(i,M)+np.random.normal(0.0,0.5,size=(M,1))]\n", " return [A,beta]\n", "\n", "Abeta = randomAbeta(d,M)\n", "A = Abeta[0]\n", "beta = Abeta[1]\n", "\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now a HJM like vector field driven by $d$ Brownian motions is introduced. Maturity discretization is given by 'dimension' and vectorized by the function grid." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dimension = 500\n", "\n", "def hjmfield(state,increment):\n", " value = np.zeros((dimension,1))\n", " for i in range(d):\n", " value = value + (0.5*((0.01*grid(dimension))**i)*\n", " np.exp(-0.005*i*grid(dimension))*increment[i])\n", " return value\n", "\n", "initialvalue = np.exp(-0.005*grid(dimension))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the essential class is defined. SDE chooses a random reservoir when instantiated. Then one can generate paths from it by method path (output: one trajectory and the corresponding Brownian motion). The second method reservoir allows to calculate the values of the reservoir given the Brownian path (which has to be given as argument). Packing everything in efficient arrays is not done well :-)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "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 = [self.initialvalue]\n", " \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 + [SDEpath[-1]+np.matmul(nilpotent(dimension)-np.identity(dimension),SDEpath[-1])*self.timehorizon/self.timesteps+self.vectorfield(SDEpath[-1],helper)]\n", " return [BMpath, SDEpath]\n", " \n", " def reservoir(self,BMpath):\n", " reservoirpath = [canonical(1,self.dimensionR)]\n", " for i in range(self.timesteps):\n", " increment = BMpath[i+1]-BMpath[i]\n", " reservoirpath = reservoirpath + [reservoirpath[-1]+np.matmul(nilpotent(self.dimensionR)-np.identity(self.dimensionR),reservoirpath[-1])*self.timehorizon/self.timesteps+reservoirfield(reservoirpath[-1],increment)]\n", " return reservoirpath \n", " " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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VXZNa8cMBqUDtHn5hSXlt4G/ew/Ite1i6eQ/Tv9l68OfaxETQMyWOHh1a1z6m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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(initialvalue)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The class object is called HJM with the above initial value. One path is stored in training, which is then fed into a simple regression." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "HJM = SDE(1,initialvalue,dimension,d,M,hjmfield,10000)\n", "training = HJM.path()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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fDL8sLsHKPdTof2gXXKCt/NOH0dP7lFHxprT17mifeMK3DPpgy7t2eS/bsaO2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\nCZncJSmhH8PieGRlQgXbAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f1,p1=plt.subplots(2,1,figsize=(6,6),sharey=True)\n", "p1[0].plot(training[0][:10000],'r')\n", "Yplot = training[1]\n", "Yplot = np.squeeze(Yplot)\n", "p1[1].plot(Yplot[:10000],'g')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the Brownian path is extracted which is then fed into the reservoir." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6000, 500)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BMpath=training[0]\n", "Y = training[1]\n", "Ydata = np.squeeze(Y)\n", "Ydatadiff = np.diff(Ydata,axis=0)\n", "Ytrain = np.concatenate((Ydata[:3000],Ydatadiff[:3000:1]),axis=0)\n", "np.shape(Ytrain)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6000, 50)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X=HJM.reservoir(BMpath)\n", "np.shape(X)\n", "Xdata = np.squeeze(X)\n", "Xdatadiff = np.diff(Xdata,axis=0)\n", "Xtrain=np.concatenate((Xdata[:3000],Xdatadiff[:3000:1]),axis=0)\n", "np.shape(Xtrain)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "array([[ 6.18111345e-03, 9.86496322e-01, 1.43285029e-02, ...,\n", " 4.01697973e-02, 2.35281795e-01, -6.75035313e-03],\n", " [ 6.12089073e-03, 9.81579424e-01, 1.42832878e-02, ...,\n", " 3.99536851e-02, 2.34069736e-01, -6.78774164e-03],\n", " [ 7.86811456e-04, 9.72573983e-01, 4.78589461e-02, ...,\n", " 5.64196652e-02, 2.08432295e-01, -9.45880887e-03],\n", " ...,\n", " [-2.61377562e-03, 8.18831190e-02, 6.63718725e-03, ...,\n", " 3.28503386e-03, 1.23161894e-02, -1.28382365e-02],\n", " [-2.61425597e-03, 8.14752239e-02, 6.62040471e-03, ...,\n", " 3.27059459e-03, 1.22280024e-02, -1.28294225e-02],\n", " [-2.61473026e-03, 8.10693636e-02, 6.60370824e-03, ...,\n", " 3.25625512e-03, 1.21402663e-02, -1.28206292e-02]])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn import linear_model\n", "import pandas as pd\n", "lm = linear_model.LinearRegression()\n", "model = lm.fit(Xtrain,Ytrain)\n", "plt.plot(model.predict(Xtrain),'r')\n", "plt.plot(Ytrain,'b')\n", "plt.show()\n", "model.score(Xtrain,Ytrain)\n", "model.coef_" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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5U4hdN4PORfNoZTsA2Bzdmi0tepFw4kW0zbqMuCYtPU4bHlTuIuI7xSVlLF2Y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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(model.predict(Xdata[:6000])[3000,:])\n", "plt.plot(Ydata[:6000][3000,:])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now generalizations are considered." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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eloM81/m27rfMbDYz1T5JV19aTfdN3RlSewi/n/4dgFxSinwXp+Jo2wzr8GwMGeGPVXgW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "generalization = HJM.path()\n", "BMpathgen = generalization[0]\n", "Ygen = generalization[1]\n", "Ygendata = np.squeeze(Ygen)\n", "\n", "Xgen = HJM.reservoir(BMpathgen)\n", "Xgendata = np.squeeze(Xgen)\n", "\n", "N=4\n", "\n", "fig,p=plt.subplots(N, 1, figsize=(6,6), sharey=True)\n", "for i in range(N):\n", " j = np.random.randint(0,dimension)\n", " p[i].plot(model.predict(Xgendata[:1000])[:,j],'b')\n", " p[i].plot(Ygendata[:1000][:,j],'g')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }