Example-2-GP-BS-Derivatives.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import Random\n",
    "from numpy import *\n",
    "from time import *\n",
    "from datetime import *\n",
    "from BlackScholes import *\n",
    "import math\n",
    "import scipy as sp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import gaussian_process\n",
    "from sklearn.gaussian_process.kernels import Matern, WhiteKernel, ConstantKernel, RBF\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "KC = 130\n",
    "KP = 70\n",
    "r = 0.002\n",
    "sigma = 0.4\n",
    "T = 2.0\n",
    "S0 = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lb = 0\n",
    "ub = 300\n",
    "training_number = 100\n",
    "testing_number = 50\n",
    "sigma_n = 1e-8 # additive noise in GP\n",
    "\n",
    "call = lambda x,y: bsformula(1, lb+(ub-lb)*x, KC, r, T, y, 0)[0]\n",
    "put = lambda x,y: bsformula(-1, lb+(ub-lb)*x, KP, r, T, y, 0)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    }
   ],
   "source": [
    "x_train = np.array(np.linspace(0.01,1.2, training_number), dtype='float32').reshape(training_number, 1)\n",
    "x_test = np.array(np.linspace(0.01,1.0, testing_number), dtype='float32').reshape(testing_number, 1)\n",
    "\n",
    "y_train = []\n",
    "    \n",
    "for idx in range(len(x_train)):\n",
    "    y_train.append(call(x_train[idx], sigma))\n",
    "y_train = np.array(y_train)\n",
    "\n",
    "sk_kernel = RBF(length_scale=1.0, length_scale_bounds=(0.01, 10000.0)) #+ WhiteKernel(noise_level = 1e-12) #100000.0\n",
    "gp = gaussian_process.GaussianProcessRegressor(kernel=sk_kernel, n_restarts_optimizer=20)\n",
    "gp.fit(x_train,y_train)\n",
    "y_pred, sigma_hat = gp.predict(x_test, return_std=True)\n",
    "    \n",
    "l = gp.kernel_.length_scale\n",
    "rbf= gaussian_process.kernels.RBF(length_scale=l)\n",
    " \n",
    "Kernel= rbf(x_train, x_train)\n",
    "K_y = Kernel + np.eye(training_number) * sigma_n\n",
    "L = sp.linalg.cho_factor(K_y)\n",
    "alpha_p = sp.linalg.cho_solve(np.transpose(L), y_train)\n",
    "    \n",
    "k_s = rbf(x_test, x_train)\n",
    "k_s_prime = (x_train.T - x_test) * k_s / l**2\n",
    "f_prime = np.dot(k_s_prime, alpha_p)/(ub-lb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.75439240e-04],\n",
       "       [-1.22950533e-04],\n",
       "       [-4.13244370e-05],\n",
       "       [ 7.62267220e-05],\n",
       "       [ 2.59931975e-05],\n",
       "       [-3.20261712e-05],\n",
       "       [-5.60893810e-05],\n",
       "       [ 3.92175627e-06],\n",
       "       [ 1.24009995e-05],\n",
       "       [-1.41266671e-05],\n",
       "       [-5.15623565e-05],\n",
       "       [ 5.50146309e-06],\n",
       "       [-6.24555213e-05],\n",
       "       [-3.24606615e-05],\n",
       "       [-3.21306438e-05],\n",
       "       [-4.67498265e-05],\n",
       "       [-5.41750483e-05],\n",
       "       [-5.11845138e-05],\n",
       "       [-3.96970271e-05],\n",
       "       [-3.14215275e-05],\n",
       "       [-3.20850439e-05],\n",
       "       [-3.67832295e-05],\n",
       "       [-3.48736588e-05],\n",
       "       [-2.09163407e-05],\n",
       "       [-3.50899221e-06],\n",
       "       [ 1.29739586e-05],\n",
       "       [ 1.79270090e-05],\n",
       "       [ 1.74317894e-05],\n",
       "       [ 2.30325727e-05],\n",
       "       [ 4.25660578e-05],\n",
       "       [ 7.14531684e-05],\n",
       "       [ 9.32059144e-05],\n",
       "       [ 9.46861846e-05],\n",
       "       [ 8.18726819e-05],\n",
       "       [ 7.15811727e-05],\n",
       "       [ 8.46553615e-05],\n",
       "       [ 1.20697355e-04],\n",
       "       [ 1.63547822e-04],\n",
       "       [ 1.89437720e-04],\n",
       "       [ 1.94171750e-04],\n",
       "       [ 2.06500908e-04],\n",
       "       [ 2.62071462e-04],\n",
       "       [ 3.84215004e-04],\n",
       "       [ 5.53598418e-04],\n",
       "       [ 7.26134105e-04],\n",
       "       [ 8.77633701e-04],\n",
       "       [ 1.02643517e-03],\n",
       "       [ 1.23845614e-03],\n",
       "       [ 1.56074760e-03],\n",
       "       [ 1.97563339e-03]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = lambda x,y: bsformula(1, lb+(ub-lb)*x, KC, r, T, y, 0)[1]\n",
    "delta(x_test, sigma) - f_prime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2768b0b8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6),facecolor='white', edgecolor='black')\n",
    "plt.plot(lb+(ub-lb)*x_test, delta(x_test,sigma), color = 'black', label = 'Exact')\n",
    "plt.plot(lb+(ub-lb)*x_test, f_prime, color = 'red', label = 'GP')\n",
    "plt.grid(True)\n",
    "plt.xlabel('S')\n",
    "plt.ylabel('$\\Delta$')\n",
    "plt.legend(loc = 'best', prop={'size':10})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a27770f60>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6),facecolor='white', edgecolor='black')\n",
    "plt.plot(lb+(ub-lb)*x_test, delta(x_test,sigma) - f_prime, color = 'black', label = 'GP Error')\n",
    "plt.grid(True)\n",
    "plt.xlabel('S')\n",
    "plt.ylabel('Error in $\\Delta$')\n",
    "plt.legend(loc = 'best', prop={'size':10})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## vega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    }
   ],
   "source": [
    "x_train = np.array(np.linspace(0.01,1.2, training_number), dtype='float32').reshape(training_number, 1)\n",
    "x_test = np.array(np.linspace(0.01,1.0, testing_number), dtype='float32').reshape(testing_number, 1)\n",
    "\n",
    "y_train = []\n",
    "    \n",
    "for idx in range(len(x_train)):\n",
    "    y_train.append(call((S0-lb)/(ub-lb), x_train[idx]))\n",
    "y_train = np.array(y_train)\n",
    "\n",
    "sk_kernel = RBF(length_scale=1.0, length_scale_bounds=(0.01, 10000.0)) #+ WhiteKernel(noise_level = 1e-12) #100000.0\n",
    "gp = gaussian_process.GaussianProcessRegressor(kernel=sk_kernel, n_restarts_optimizer=20)\n",
    "gp.fit(x_train,y_train)\n",
    "y_pred, sigma_hat = gp.predict(x_test, return_std=True)\n",
    "    \n",
    "l = gp.kernel_.length_scale\n",
    "rbf= gaussian_process.kernels.RBF(length_scale=l)\n",
    " \n",
    "Kernel= rbf(x_train, x_train)\n",
    "K_y = Kernel + np.eye(training_number) * sigma_n\n",
    "L = sp.linalg.cho_factor(K_y)\n",
    "alpha_p = sp.linalg.cho_solve(np.transpose(L), y_train)\n",
    "    \n",
    "k_s = rbf(x_test, x_train)\n",
    "\n",
    "k_s_prime = np.zeros([len(x_test), len(x_train)])\n",
    "for i in range(len(x_test)):\n",
    "    for j in range(len(x_train)):\n",
    "        k_s_prime[i,j]=(1.0/l**2)*(x_train[j]-x_test[i])*k_s[i,j]\n",
    "        \n",
    "f_prime = np.dot(k_s_prime, alpha_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.03042599],\n",
       "       [-0.03417824],\n",
       "       [ 0.04813572],\n",
       "       [-0.02066425],\n",
       "       [ 0.00078639],\n",
       "       [-0.02449945],\n",
       "       [-0.00979741],\n",
       "       [ 0.00720845],\n",
       "       [-0.00084125],\n",
       "       [-0.00923278],\n",
       "       [ 0.02570014],\n",
       "       [-0.01109279],\n",
       "       [-0.00459649],\n",
       "       [-0.01045877],\n",
       "       [-0.00890098],\n",
       "       [-0.0122505 ],\n",
       "       [-0.00843964],\n",
       "       [-0.00497917],\n",
       "       [-0.01303292],\n",
       "       [-0.00153103],\n",
       "       [ 0.00095914],\n",
       "       [ 0.00080953],\n",
       "       [ 0.00808772],\n",
       "       [ 0.00748916],\n",
       "       [ 0.00914164],\n",
       "       [ 0.00981196],\n",
       "       [ 0.00930099],\n",
       "       [ 0.00777037],\n",
       "       [ 0.00491814],\n",
       "       [ 0.00155685],\n",
       "       [-0.00102143],\n",
       "       [-0.00163249],\n",
       "       [-0.00316678],\n",
       "       [ 0.00079119],\n",
       "       [ 0.00363495],\n",
       "       [ 0.0017962 ],\n",
       "       [ 0.00741908],\n",
       "       [ 0.00859901],\n",
       "       [ 0.00773113],\n",
       "       [ 0.01086757],\n",
       "       [ 0.0114922 ],\n",
       "       [ 0.01150779],\n",
       "       [ 0.00659299],\n",
       "       [-0.00650103],\n",
       "       [-0.0189475 ],\n",
       "       [-0.04155439],\n",
       "       [-0.04968136],\n",
       "       [-0.08426404],\n",
       "       [-0.09294605],\n",
       "       [-0.08197963]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vega = lambda x,y: bsformula(1, lb+(ub-lb)*x, KC, r, T, y, 0)[2]\n",
    "vega((S0-lb)/(ub-lb), x_test) - f_prime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2c084d30>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6),facecolor='white', edgecolor='black')\n",
    "plt.plot(x_test, vega((S0-lb)/(ub-lb), x_test), color = 'black', label = 'Exact')\n",
    "plt.plot(x_test, f_prime, color = 'red', label = 'GP')\n",
    "plt.grid(True)\n",
    "plt.xlabel('$\\\\sigma$')\n",
    "plt.ylabel('$\\\\nu$')\n",
    "plt.legend(loc = 'best', prop={'size':10})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2c2c39b0>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,6),facecolor='white', edgecolor='black')\n",
    "plt.plot(x_test, vega((S0-lb)/(ub-lb), x_test)-f_prime, color = 'black', label = 'GP Error')\n",
    "plt.grid(True)\n",
    "plt.xlabel('$\\\\sigma$')\n",
    "plt.ylabel('Error in $\\\\nu$')\n",
    "plt.legend(loc = 'best', prop={'size':10})"
   ]
  }
 ],
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