Example-1-MGP-BS-Pricing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import torch\n",
    "import gpytorch\n",
    "import numpy as np\n",
    "from scipy import *\n",
    "from BlackScholes import *\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats  \n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### set BS model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.0  # risk-free rate\n",
    "S= 100      # Underlying spot\n",
    "KC = 110    # Call strike\n",
    "KP = 90     # Put strike\n",
    "sigma = 0.3 # implied volatility\n",
    "T = 2.0     # Time to maturity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the call and put prices using the BS model\n",
    "call = lambda x: bsformula(1, lb+(ub-lb)*x, KC, r, T, sigma, 0)[0]\n",
    "put = lambda x: bsformula(-1, lb+(ub-lb)*x, KP, r, T, sigma, 0)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "lb = 0.001             # lower bound on domain\n",
    "ub = 300               # upper bound on domain\n",
    "training_number = 50   # Number of training samples\n",
    "testing_number =  100  # Number of testing samples\n",
    "\n",
    "train_x = torch.linspace(0, 1.0, training_number)\n",
    "train_y1 = torch.FloatTensor(call(np.array(train_x)))\n",
    "train_y2 = torch.FloatTensor(put(np.array(train_x)))\n",
    "\n",
    "#Create a train_y which interleaves the two\n",
    "train_y = torch.stack([train_y1, train_y2], -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## define multi-GP class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MultitaskGPModel(gpytorch.models.ExactGP):\n",
    "    def __init__(self, train_x, train_y, likelihood):\n",
    "        super(MultitaskGPModel, self).__init__(train_x, train_y, likelihood)\n",
    "        self.mean_module = gpytorch.means.MultitaskMean(\n",
    "            gpytorch.means.ConstantMean(), num_tasks=2\n",
    "        )\n",
    "        \n",
    "        self.covar_module = gpytorch.kernels.MultitaskKernel(gpytorch.kernels.ScaleKernel(\n",
    "            gpytorch.kernels.MaternKernel(nu=2.5)), num_tasks=2, rank=1\n",
    "        )\n",
    "              \n",
    "    def forward(self, x):\n",
    "        mean_x = self.mean_module(x)\n",
    "        covar_x = self.covar_module(x)\n",
    "        return gpytorch.distributions.MultitaskMultivariateNormal(mean_x, covar_x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_x = torch.linspace(0, 1.0, testing_number)\n",
    "test_y1 = torch.FloatTensor(call(np.array(test_x)))\n",
    "test_y2 = torch.FloatTensor(put(np.array(test_x)))\n",
    "test_y = torch.stack([test_y1, test_y2], -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Iter 245/300 - Loss: 235.833 lengthscale: 0.211 noise: 1.927\n",
      "Iter 246/300 - Loss: 233.863 lengthscale: 0.211 noise: 1.926\n",
      "Iter 247/300 - Loss: 232.550 lengthscale: 0.211 noise: 1.924\n",
      "Iter 248/300 - Loss: 233.138 lengthscale: 0.211 noise: 1.923\n",
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      "Iter 267/300 - Loss: 227.045 lengthscale: 0.210 noise: 1.896\n",
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      "Iter 272/300 - Loss: 224.190 lengthscale: 0.210 noise: 1.888\n",
      "Iter 273/300 - Loss: 224.634 lengthscale: 0.209 noise: 1.887\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter 274/300 - Loss: 223.161 lengthscale: 0.209 noise: 1.885\n",
      "Iter 275/300 - Loss: 222.477 lengthscale: 0.209 noise: 1.884\n",
      "Iter 276/300 - Loss: 221.840 lengthscale: 0.209 noise: 1.882\n",
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      "Iter 279/300 - Loss: 221.752 lengthscale: 0.209 noise: 1.877\n",
      "Iter 280/300 - Loss: 220.667 lengthscale: 0.209 noise: 1.876\n",
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      "Iter 283/300 - Loss: 218.572 lengthscale: 0.209 noise: 1.871\n",
      "Iter 284/300 - Loss: 220.025 lengthscale: 0.209 noise: 1.869\n",
      "Iter 285/300 - Loss: 219.337 lengthscale: 0.209 noise: 1.867\n",
      "Iter 286/300 - Loss: 217.826 lengthscale: 0.209 noise: 1.866\n",
      "Iter 287/300 - Loss: 218.546 lengthscale: 0.209 noise: 1.864\n",
      "Iter 288/300 - Loss: 217.763 lengthscale: 0.209 noise: 1.862\n",
      "Iter 289/300 - Loss: 216.194 lengthscale: 0.209 noise: 1.861\n",
      "Iter 290/300 - Loss: 217.983 lengthscale: 0.209 noise: 1.859\n",
      "Iter 291/300 - Loss: 216.478 lengthscale: 0.209 noise: 1.857\n",
      "Iter 292/300 - Loss: 215.424 lengthscale: 0.209 noise: 1.856\n",
      "Iter 293/300 - Loss: 215.866 lengthscale: 0.209 noise: 1.854\n",
      "Iter 294/300 - Loss: 215.758 lengthscale: 0.209 noise: 1.852\n",
      "Iter 295/300 - Loss: 214.833 lengthscale: 0.209 noise: 1.850\n",
      "Iter 296/300 - Loss: 216.421 lengthscale: 0.208 noise: 1.849\n",
      "Iter 297/300 - Loss: 217.069 lengthscale: 0.208 noise: 1.847\n",
      "Iter 298/300 - Loss: 214.724 lengthscale: 0.208 noise: 1.845\n",
      "Iter 299/300 - Loss: 216.433 lengthscale: 0.208 noise: 1.843\n",
      "Iter 300/300 - Loss: 212.881 lengthscale: 0.208 noise: 1.842\n"
     ]
    }
   ],
   "source": [
    "likelihood = gpytorch.likelihoods.MultitaskGaussianLikelihood(num_tasks=2)\n",
    "model = MultitaskGPModel(train_x, train_y, likelihood)\n",
    "\n",
    "model.train()\n",
    "likelihood.train()\n",
    "\n",
    "# Use the adam optimizer\n",
    "optimizer = torch.optim.Adam([\n",
    "    {'params': model.parameters()},  # Includes GaussianLikelihood parameters\n",
    "], lr=0.1)\n",
    "\n",
    "# \"Loss\" for GPs - the marginal log likelihood\n",
    "mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)\n",
    "\n",
    "n_iter = 300\n",
    "for i in range(n_iter):\n",
    "    optimizer.zero_grad()\n",
    "    output = model(train_x)\n",
    "    loss = -mll(output, train_y)\n",
    "    loss.backward()\n",
    "    print('Iter %d/%d - Loss: %.3f lengthscale: %.3f noise: %.3f' % (i + 1, n_iter, loss.item(), model.covar_module.data_covar_module.base_kernel.lengthscale, likelihood.noise))\n",
    "    \n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make predictions\n",
    "model.eval()\n",
    "likelihood.eval()\n",
    "with torch.no_grad(), gpytorch.settings.fast_pred_var():\n",
    "    y_hat= likelihood(model(test_x))\n",
    "lower, upper = y_hat.confidence_region()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[[0.2084]]], grad_fn=<ClampBackward>) tensor([[1.8397]], grad_fn=<SoftplusBackward>) 2.5 [[36.977943  -1.1028435]\n",
      " [-1.1028435  3.068603 ]]\n"
     ]
    }
   ],
   "source": [
    "# Print fitted parameters\n",
    "a = model.covar_module.task_covar_module.covar_factor.clone().detach()\n",
    "v = model.covar_module.task_covar_module.var.clone().detach()\n",
    "Omega = np.outer(a,a) + np.diag(v)\n",
    "#lengthscale=model.covar_module.data_covar_module.lengthscale\n",
    "lengthscale = model.covar_module.data_covar_module.base_kernel.lengthscale\n",
    "sigma_2_n = likelihood.noise\n",
    "nu = model.covar_module.data_covar_module.base_kernel.nu\n",
    "print(lengthscale, sigma_2_n, nu, Omega)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$\\\\pi$')"
      ]
     },
     "execution_count": 26,
     "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# predictionn plot with var band \n",
    "plt.figure(figsize = (10, 6), facecolor='white', edgecolor='black')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), np.array(y_hat.mean[:,0]), color = 'red', label = 'GP Prediction')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), np.array(test_y[:,0]), color = 'black', label = 'Analytical Model')\n",
    "plt.scatter(lb+(ub-lb)*train_x, train_y[:,0], color = 'black', marker = '+', s = 100) \n",
    "plt.fill_between(lb+(ub-lb)*np.array(test_x.flatten()), lower[:,0].detach().numpy(), upper[:,0].detach().numpy(), color = 'grey', alpha=0.3)\n",
    "plt.legend(loc = 'best', prop={'size':10})\n",
    "plt.xlim([KC/2.0,2*KC])\n",
    "plt.xlabel('S')\n",
    "plt.ylabel('V')\n",
    "\n",
    "\n",
    "plt.figure(figsize = (10, 6), facecolor='white', edgecolor='black')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), np.array(y_hat.mean[:,1]), color = 'red', label = 'GP Prediction')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), np.array(test_y[:,1]), color = 'black', label = 'Analytical Model')\n",
    "plt.scatter(lb+(ub-lb)*train_x, train_y[:,1], color = 'black', marker = '+', s = 100) \n",
    "plt.fill_between(lb+(ub-lb)*np.array(test_x.flatten()), lower[:,1].detach().numpy(), upper[:,1].detach().numpy(), color = 'grey', alpha=0.3)\n",
    "plt.legend(loc = 'best', prop={'size':10})\n",
    "plt.xlim([KP/2.0,2*KP])\n",
    "plt.xlabel('S')\n",
    "plt.ylabel('V')\n",
    "\n",
    "\n",
    "plt.figure(figsize = (10, 6), facecolor='white', edgecolor='black')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), 2.0*np.array(y_hat.mean[:,0])- np.array(y_hat.mean[:,1]), color = 'red', label = 'GP Prediction')\n",
    "plt.plot(lb+(ub-lb)*np.array(test_x.flatten()), 2.0*np.array(test_y[:,0])-np.array(test_y[:,1]) , color = 'black', label = 'Analytical Model')\n",
    "plt.scatter(lb+(ub-lb)*train_x, 2*train_y[:,0]-train_y[:,1], color = 'black', marker = '+', s = 100) \n",
    "\n",
    "plt.fill_between(lb+(ub-lb)*np.array(test_x.flatten()), 2.0*lower[:,0].detach().numpy()-upper[:,1].detach().numpy() , 2.0*upper[:,0].detach().numpy()-lower[:,1].detach().numpy(), color = 'grey', alpha=0.3)\n",
    "plt.legend(loc = 'best', prop={'size':10})\n",
    "plt.xlim([KP/2.0,2*KC])\n",
    "plt.xlabel('S')\n",
    "plt.ylabel('$\\pi$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# covariance of posterior\n",
    "var_1=np.diag(np.array(y_hat.covariance_matrix.detach().numpy()),0)[0:199:2]\n",
    "var_2=np.diag(np.array(y_hat.covariance_matrix.detach().numpy()),0)[1:199:2]\n",
    "covar_12=np.diag(np.array(y_hat.covariance_matrix.detach().numpy()),1)[0:199:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/scipy/stats/_continuous_distns.py:437: RuntimeWarning: invalid value encountered in sqrt\n",
      "  sk = 2*(b-a)*np.sqrt(a + b + 1) / (a + b + 2) / np.sqrt(a*b)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py:163: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lnspc = np.linspace(-5.0, 30, 100)\n",
    "\n",
    "ab,bb,cb,db = stats.beta.fit(var_1)  \n",
    "pdf_beta = stats.beta.pdf(lnspc, ab, bb,cb, db)  \n",
    "plt.plot(lnspc, pdf_beta, label='var($f_{*1}$ $\\|$ $X,Y,X_*$)', color='r')\n",
    "\n",
    "ab,bb,cb,db = stats.beta.fit(var_2)  \n",
    "pdf_beta = stats.beta.pdf(lnspc, ab, bb,cb, db)  \n",
    "plt.plot(lnspc, pdf_beta, label='var($f_{*2}$ $\\|$ $X,Y,X_*$)', color='k')\n",
    "\n",
    "ab,bb,cb,db = stats.beta.fit(covar_12)  \n",
    "pdf_beta = stats.beta.pdf(lnspc, ab, bb,cb, db)  \n",
    "plt.plot(lnspc, pdf_beta, label='covar($f_{*1}f_{*2}$ $\\|$ $X,Y,X_*$)', color=\"grey\", linestyle='--')\n",
    "\n",
    "#ab,bb,cb,db = stats.beta.fit(CVA_1_yr_tilde_down-CVA_tilde_down)  \n",
    "#pdf_beta = stats.beta.pdf(lnspc, ab, bb,cb, db)  \n",
    "#plt.plot(lnspc, pdf_beta, label='MC-GP (upper)', color='grey', linestyle='-.')\n",
    "\n",
    "plt.xlabel('uncertainty')\n",
    "plt.ylabel('density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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
}