3.3 Pricing with the NIG Process.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normal Inverse Gaussian Process\n",
    "\n",
    "\n",
    "## Contents\n",
    "   - [Numerical methods for option pricing](#sec1)\n",
    "   - [The NIG PIDE method](#sec2)\n",
    "     - [The Lévy measure](#sec2.1)\n",
    "     - [The PIDE](#sec2.2) \n",
    "\n",
    "The methods used in this notebook are basically the same presented in the notebook **3.2**.     \n",
    "As you probably have noticed when reading the notebook **1.5**, the NIG process is very similar to the VG process.      They are both obtained by Brownian subordination. They both depend on three variables. Their distribution is quite similar.   \n",
    "\n",
    "And of course, the numerical methods for option pricing are quite similar as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "import scipy.special as scps\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import partial\n",
    "from scipy.integrate import quad\n",
    "\n",
    "from FMNM.probabilities import Q1, Q2\n",
    "from FMNM.CF import cf_NIG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 1  # terminal time\n",
    "N = 10000000  # number of generated random variables\n",
    "S0 = 100.0  # initial price\n",
    "K = 100.0  # strike\n",
    "k = np.log(K / S0)  # log moneyness\n",
    "\n",
    "r = 0.1\n",
    "theta = -0.11  # drift of the Brownian motion\n",
    "sigma = 0.2  # volatility of the Brownian motion\n",
    "kappa = 0.3  # variance of the IG process\n",
    "lam = T**2 / kappa  # scale\n",
    "mu_s = T / lam  # scaled mu\n",
    "\n",
    "w = (1 - np.sqrt(1 - 2 * theta * kappa - kappa * sigma**2)) / kappa  # Martingale correction\n",
    "dev_X = np.sqrt(sigma**2 + theta**2 * kappa)  # std dev NIG process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let me recall the derivation of some formulas:\n",
    "\n",
    "##### Mean and Variance: \n",
    "Using the Brownian subordination expression for the NIG process (where $T_t \\sim IG(t,\\kappa t)$), we get\n",
    "\n",
    "$$ \\mathbb{E}[X_t] = \\mathbb{E}[\\theta T_t + \\sigma W_{T_t}] = \\theta \\mathbb{E}[T_t] + 0 = \\theta t.$$\n",
    "\n",
    "where I used the [Tower property](https://en.wikipedia.org/wiki/Law_of_total_expectation), and\n",
    "\n",
    "$$ \\text{Var}[X_t] = \\text{Var}[\\theta T_t + \\sigma W_{T_t}] = \\theta^2 \\text{Var}[T_t] + \n",
    "\\sigma^2 \\text{Var}[W_{T_t}] = (\\theta^2 \\kappa + \\sigma^2) t. $$\n",
    "\n",
    "where for the term $\\text{Var}[W_{T_t}]$ I used the [conditional variance](https://en.wikipedia.org/wiki/Law_of_total_variance) formula.\n",
    "\n",
    "##### Martingale correction:\n",
    "\n",
    "The idea is to find the correction term $w$ such that the process $e^{-rt}S_t$ is a martingale. The stock process has dynamics $S_t = S_0 e^{rt - wt + X_t}$.     \n",
    "We have that\n",
    "\n",
    "$$ \\mathbb{E}[ e^{-rt} S_0 e^{rt - wt + X_t} ] = S_0$$\n",
    "\n",
    "$$ \\mathbb{E}[ e^{-wt + X_t}] = 1$$\n",
    "\n",
    "$$ e^{wt} = \\mathbb{E}[ e^{X_t}] $$\n",
    "\n",
    "$$ w = \\log( \\phi(-i) ) \\quad \\quad \\text{for} \\quad t=1  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The martingale correction w=-0.088817 can be computed from the CF as: \n",
      "(-0.088817+0j)\n"
     ]
    }
   ],
   "source": [
    "print(\"The martingale correction w={0:.6f} can be computed from the CF as: \".format(w))\n",
    "print(np.log(cf_NIG(-1j, t=1, mu=0, theta=theta, sigma=sigma, kappa=kappa)).round(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "\n",
    "# Numerical methods\n",
    "\n",
    "##### Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monte Carlo, call: 13.429721691441594, std err: 0.0049326098983063895\n",
      "Monte Carlo, put: 3.915092184682041, std_err: 0.0025466749195472587\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=42)\n",
    "IG = ss.invgauss.rvs(mu=mu_s, scale=lam, size=N)  # The IG RV\n",
    "Norm = ss.norm.rvs(0, 1, N)  # The normal RV\n",
    "X = theta * IG + sigma * np.sqrt(IG) * Norm  # NIG random vector\n",
    "S_T = S0 * np.exp((r - w) * T + X)  # exponential dynamics\n",
    "\n",
    "call_payoff = np.maximum(S_T - K, 0)\n",
    "put_payoff = np.maximum(K - S_T, 0)\n",
    "call = np.exp(-r * T) * np.mean(call_payoff)\n",
    "put = np.exp(-r * T) * np.mean(put_payoff)\n",
    "call_err = np.exp(-r * T) * ss.sem(call_payoff)\n",
    "put_err = np.exp(-r * T) * ss.sem(put_payoff)\n",
    "print(\"Monte Carlo, call: {}, std err: {}\".format(call, call_err))\n",
    "print(\"Monte Carlo, put: {}, std_err: {}\".format(put, put_err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Fourier inversion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fourier inversion call:  13.427965\n",
      "Fourier inversion put:  3.911707\n"
     ]
    }
   ],
   "source": [
    "# function binding\n",
    "cf_NIG_b = partial(cf_NIG, t=T, mu=r - w, theta=theta, sigma=sigma, kappa=kappa)\n",
    "\n",
    "# price\n",
    "call_F = S0 * Q1(k, cf_NIG_b, np.inf) - K * np.exp(-r * T) * Q2(k, cf_NIG_b, np.inf)\n",
    "put_F = -S0 * (1 - Q1(k, cf_NIG_b, np.inf)) + K * np.exp(-r * T) * (1 - Q2(k, cf_NIG_b, np.inf))\n",
    "\n",
    "print(\"Fourier inversion call: \", call_F.round(6))\n",
    "print(\"Fourier inversion put: \", put_F.round(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "\n",
    "# The NIG PIDE method \n",
    "\n",
    "<a id='sec2.1'></a>\n",
    "## Curiosities about the NIG Lévy measure\n",
    "\n",
    "The NIG process is a pure jump process with triplet $(b,0,\\nu)$. (For more information on the Lévy triplet see Appendix **A.3**)\n",
    "\n",
    "The expression of the drift $b$ in [2] and [3] is given for the parameters:\n",
    "\n",
    "$$ \\beta = \\frac{\\theta}{\\sigma^2}, \\quad \\quad \\alpha = \\sqrt{ \\beta^2 + \\frac{1}{\\kappa \\sigma^2} } \\quad \\quad\n",
    " \\delta = \\frac{T \\sigma}{\\sqrt{\\kappa}} $$\n",
    "\n",
    "and is:\n",
    "\n",
    "$$ b = \\frac{2 \\delta \\alpha}{\\pi} \\int_0^1 \\sinh(\\beta x) K_1(\\alpha x) dx $$\n",
    "\n",
    "The Lévy measure is:\n",
    "\n",
    "$$ \\nu(x) = \\frac{C}{|x|} e^{A x} K_1(B|x|) $$\n",
    "\n",
    "with\n",
    "\n",
    "$$ A = \\frac{\\theta}{\\sigma^2} \\quad B = \\frac{\\sqrt{\\theta^2 + \\sigma^2/\\kappa}}{\\sigma^2} \n",
    "\\quad C = \\frac{\\sqrt{\\theta^2 + \\sigma^2/\\kappa}}{\\sigma \\pi \\sqrt{\\kappa}} $$\n",
    "\n",
    "The function $K_1$ is a Bessel function of second kind with 1 degree of freedom.\n",
    "\n",
    "Let us recall from the Levy processes theory that:\n",
    "\n",
    "$$ \\mathbb{E}[X_t] = t \\biggl( b +  \\int_{|x|>1} x \\nu(dx) \\biggr)$$\n",
    "\n",
    "$$ \\text{Var}[X_t] = t \\int_{\\mathbb{R}} x^2 \\nu(dx) $$\n",
    "\n",
    "Let's verify it is correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NIG_measure(x):\n",
    "    A = theta / (sigma**2)\n",
    "    B = np.sqrt(theta**2 + sigma**2 / kappa) / sigma**2\n",
    "    C = np.sqrt(theta**2 + sigma**2 / kappa) / (np.pi * sigma * np.sqrt(kappa))\n",
    "    return C / np.abs(x) * np.exp(A * (x)) * scps.kv(1, B * np.abs(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.concatenate((np.linspace(-0.1, -0.001, 200), np.linspace(0.001, 0.1, 200)))\n",
    "plt.plot(x, NIG_measure(x))\n",
    "plt.title(\"NIG Lévy measure\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The theoretical mean is theta:  -0.11\n",
      "The drift component is:  -0.10992734491736125\n",
      "The mean is the sum of the drift and the integration over |x>1| i.e. :  -0.11000000000015915\n"
     ]
    }
   ],
   "source": [
    "beta = theta / (sigma**2)\n",
    "alpha = np.sqrt(beta**2 + 1 / (kappa * sigma**2))\n",
    "delta = sigma / np.sqrt(kappa)\n",
    "int_b = lambda y: 2 / np.pi * delta * alpha * np.sinh(beta * y) * scps.kv(1, alpha * np.abs(y))\n",
    "drift = quad(int_b, 0, 1, points=0, limit=2000)[0]\n",
    "\n",
    "print(\"The theoretical mean is theta: \", theta)\n",
    "print(\"The drift component is: \", drift)\n",
    "\n",
    "int_m = lambda y: y * NIG_measure(y)\n",
    "mean_greater1 = quad(int_m, -10, -1, limit=2000)[0] + quad(int_m, 1, 10, limit=2000)[0]\n",
    "\n",
    "print(\"The mean is the sum of the drift and the integration over |x>1| i.e. : \", drift + mean_greater1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variance obtained from integration of Lévy mesure is:  0.04363\n",
      "The theoretical variance is:  0.04363\n"
     ]
    }
   ],
   "source": [
    "int_s = lambda y: y**2 * NIG_measure(y)\n",
    "var_int = quad(int_s, -2, 2, points=0)[0]  # I inform that the point 0 has a singularity\n",
    "var_th = dev_X**2\n",
    "print(\"The variance obtained from integration of Lévy mesure is: \", round(var_int, 6))\n",
    "print(\"The theoretical variance is: \", var_th.round(7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Martingale correction:\n",
    "\n",
    "The martingale correction can be computed from the Lévy measure as well:\n",
    "\n",
    "$$ w = \\int_{\\mathbb{R} \\backslash [-\\epsilon,\\epsilon]} (e^z-1) \\nu(dz). $$\n",
    "\n",
    "we have to choose an $\\epsilon > 0$ very small, but it cannot be zero. The reason is that the NIG process has infinite variation (see **A.3** for the definition) and this means that the integral above does not converge for $\\epsilon = 0$. \n",
    "\n",
    "**Comment:**     \n",
    "For infinite variation processes we have that:\n",
    "\n",
    "$ \\int_{[-\\epsilon,\\epsilon]} (e^z-1) \\nu(dz) \\approx \\int_{[-\\epsilon,\\epsilon]} z \\nu(dz) = \\infty. $\n",
    "\n",
    "This is the main difference with the VG process, which instead has finite variation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Martingale correction:  -0.088817\n",
      "Martingale correction from integration:  -0.088817\n"
     ]
    }
   ],
   "source": [
    "epsilon = 0.0000001\n",
    "int_w = lambda y: (np.exp(y) - 1) * NIG_measure(y)\n",
    "w2 = quad(int_w, -10, -epsilon)[0] + quad(int_w, epsilon, 10)[0]\n",
    "print(\"Martingale correction: \", w.round(6))\n",
    "print(\"Martingale correction from integration: \", round(w2, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2.2'></a>\n",
    "## The NIG PIDE\n",
    "\n",
    "The NIG PIDE is \n",
    "\n",
    "$$\n",
    "\\frac{\\partial V(t,x)}{\\partial t} \n",
    "          + \\biggl( r - \\int_{\\mathbb{R}} \\bigl( e^z-1-z \\mathbb{1}_{|z|<\\epsilon} \\bigr) \\nu(dz) \\biggr) \\frac{\\partial V(t,x)}{\\partial x} $$\n",
    "$$          + \\int_{\\mathbb{R}} \\bigl( V(t,x+z)- V(t,x) - z \\frac{\\partial V(t,x) }{\\partial x} \\mathbb{1}_{|z|<\\epsilon} \\bigr) \\nu(dz)  = r V(t,x).\n",
    "$$\n",
    "\n",
    "for a small value of $\\epsilon$ we can use the Brownian approximation described in **3.2** and **A.3**.      \n",
    "The jump-diffusion type PIDE is:\n",
    "\n",
    "$$\n",
    "  \\frac{\\partial V(t,x)}{\\partial t} +\n",
    " \\bigl( r-\\frac{1}{2}\\sigma_{\\epsilon}^2 - w_{\\epsilon} \\bigr) \\frac{\\partial V(t,x)}{\\partial x} \n",
    " + \\frac{1}{2}\\sigma_{\\epsilon}^2 \\frac{\\partial^2 V(t,x)}{\\partial x^2}\n",
    " + \\int_{|z| \\geq \\epsilon} V(t,x+z) \\nu(dz) = (\\lambda_{\\epsilon} + r) V(t,x).\n",
    "$$\n",
    "\n",
    "with parameters   \n",
    "\n",
    "$$\n",
    "  \\sigma_{\\epsilon}^2 :=  \\int_{|z| < \\epsilon} z^2 \\nu(dz), \\quad \\quad w_{\\epsilon} := \\int_{|z| \\geq \\epsilon} (e^z-1) \\nu(dz), \\quad \\quad\n",
    " \\lambda_{\\epsilon} :=  \\int_{|z| \\geq \\epsilon} \\nu(dz) .\n",
    "$$\n",
    "\n",
    "The previous approximated equation is identical to the VG equation.     \n",
    "I'm not repeating the calculation. I'm just going to present some numerical values and some plots.\n",
    "\n",
    "**Comment:**      \n",
    "I would like to point out that the convergence to the right price is quite slow, in particular for small values of $\\kappa$.     \n",
    "We have seen a similar behavior for the VG PIDE, but in the NIG PIDE is a bit worse.      \n",
    "The algorithm works very well for PUT options, while for CALL options it is hard to obtain good results under our grid resolution.    \n",
    "In order to improve the performances I also used a big computational domain $[A_1,A_2]$, but the improvements are still not satisfactory. \n",
    "I expect that for a higher grid resolution (in particular for more time steps), we can achieve better performances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from FMNM.Parameters import Option_param\n",
    "from FMNM.Processes import NIG_process\n",
    "import FMNM.NIG_pricer as NIG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_param = Option_param(S0=S0, K=K, T=T, exercise=\"European\", payoff=\"call\")\n",
    "opt_param2 = Option_param(S0=S0, K=K, T=T, exercise=\"European\", payoff=\"put\")\n",
    "NIG_param = NIG_process(r=r, sigma=sigma, theta=theta, kappa=kappa)\n",
    "\n",
    "NIG_c = NIG.NIG_pricer(opt_param, NIG_param)\n",
    "NIG_p = NIG.NIG_pricer(opt_param2, NIG_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### European Call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13.387236700090668, 46.138726234436035)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NIG_c.PIDE_price((22000, 50000), Time=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NIG_c.plot([50, 200, 0, 100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### European Put"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.9110477337160687, 25.69834804534912)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NIG_p.PIDE_price((20000, 30000), Time=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NIG_p.plot([20, 150, 0, 80])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### American Put"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_param3 = Option_param(S0=S0, K=K, T=T, exercise=\"American\", payoff=\"put\")\n",
    "NIG_am = NIG.NIG_pricer(opt_param3, NIG_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.064476059362546, 4.531420946121216)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NIG_am.PIDE_price((10000, 10000), Time=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NIG_am.plot([50, 150, 0, 60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Rama Cont and Peter Tankov (2003) \"Financial Modelling with Jump Processes\", Chapman and Hall/CRC; 1 edition.  \n",
    "\n",
    "[2] Rydberg Tina (1997) \"The Normal Inverse Gaussian Lévy Process:\n",
    "Simulation and Approximation\",  Communications in Statistics. Stochastic Models. 13:4, 887-910\n",
    "\n",
    "[3] Barndorff-Nielsen, Ole E. (1998) \"Processes of Normal Inverse Gaussian type\" Finance and Stochastics 2, 41-68."
   ]
  }
 ],
 "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}