Day 2/Part_2_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Black-Scholes Model\n",
    "\n",
    "\n",
    "The purpose of this notebooks is to review the Black-Scholes model in the context of equity derivatives without dividends.\n",
    "\n",
    "#### Contents\n",
    "\n",
    "- European Option definition\n",
    "- B-S Model Assumptions\n",
    "- BS-Equation Derivation and Solution\n",
    "- Put-Call Parity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optional Configuration\n",
    "import seaborn as sns \n",
    "sns.set(style=\"whitegrid\")\n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "%config Completer.use_jedi = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## European Option\n",
    "\n",
    "An option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy (Call) or sell (Put) an underlying asset or instrument at a specified strike price $K$ on or before a specified expiry date $T$, depending on the style of the option. \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "The key difference between American and European options relates to when the options can be exercised:\n",
    "\n",
    "- A European option may be exercised only at the expiration date of the option $T$.\n",
    "- An American option on the other hand may be exercised at any time before the expiration date.\n",
    "\n",
    "For European options, the payoff—when it occurs—is given by\n",
    "\n",
    "$$Call \\ \\ Payoff = (S_T - K)^{+}$$\n",
    "\n",
    "$$Put \\ \\  Payoff = (K - S_T)^{+},$$\n",
    "\n",
    "where $K$ is the strike price and $S_T$ is the price of the underlying asset at the time of exercise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider an European option with strike given by $K$. Then, its payoff as a function of the the underlying price at the expiry $S_T$ is illustrated by the following function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_payoff(K):\n",
    "\n",
    "    S = K\n",
    "    underlying_prices = np.linspace(.0,  2*S, 100)\n",
    "    values_call = [np.maximum(s - K, 0) for s in underlying_prices]\n",
    "    values_put = [np.maximum(K-s, 0) for s in underlying_prices]\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(underlying_prices, values_call, lw=1.,\n",
    "             color=\"maroon\", label=\"European Call\")\n",
    "    plt.plot(underlying_prices, values_put, lw=1.,\n",
    "             color=\"cornflowerblue\", label=\"European Put\")\n",
    "    plt.xlabel('$S_T$')\n",
    "    plt.ylabel('Payoff')\n",
    "    plt.title(f'European Option with strike $K$={K}')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $K=100$, then we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 284,
       "width": 392
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_payoff(K=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $K=50$, then we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 284,
       "width": 386
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_payoff(K=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Black-Scholes Model Assumptions\n",
    "\n",
    "#### Assumptions\n",
    "\n",
    "- (A1) The risk-free interest rate $r$ is known and constant through time\n",
    "- (A2) The underlying asset/stock price $S$ follows a Geometric Brownian motion with constant parameters $\\mu$ and $\\sigma$, under a certain probability measure $\\mathbb{P}$\n",
    "- (A3) Stock pays no dividends\n",
    "- (A4) The option can only be exercised at expiration i.e. it is a European type\n",
    "- (A5) There are no transaction costs\n",
    "- (A6) Fractional trading is possible\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Black-Scholes Equation Derivation\n",
    "To derive the famous equation, the idea is to construct a self-financing portfolio with one option and $\\Delta$ units of the underlying stock. So, the value of the portfolio at a given time $t$ is given by\n",
    "$$\\Pi_t = V_t + \\Delta S_t,$$\n",
    "and must satisfy the following two conditions:\n",
    "- (C1) The portfolio is riskless\n",
    "- (C2) The portfolio earns the risk free rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using assumption (A2)\n",
    "$$dS_t = \\mu S_t dt + \\sigma S_t dW_t^{\\mathbb{P}},$$\n",
    "and Ito's formula applied to the function $V(t, S)$, we obtain\n",
    "\\begin{align*}\n",
    "d \\Pi_t &= dV_t + \\Delta dS_t\\\\\n",
    "&= \\left[ \\frac{\\partial V}{\\partial t} + \\frac{\\partial V}{\\partial S} \\mu S  + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2 \\right] dt +  \\frac{\\partial V}{\\partial S} \\sigma SdW_t^{\\mathbb{P}} +    \\Delta  dS_t\\\\\n",
    "&= \\left[ \\frac{\\partial V}{\\partial t} + \\frac{\\partial V}{\\partial S} \\mu S  + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2 \\right] dt +  \\frac{\\partial V}{\\partial S} \\sigma SdW_t^{\\mathbb{P}} +    \\Delta  \\mu S dt + \\Delta \\sigma SdW_t^{\\mathbb{P}}\\\\\n",
    "&= \\left[ \\frac{\\partial V}{\\partial t} + \\frac{\\partial V}{\\partial S} \\mu S  + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2 +  \\Delta  \\mu S \\right] dt +  \\left[ \\frac{\\partial V}{\\partial S} \\sigma S +  \\Delta \\sigma S \\right] dW_t^{\\mathbb{P}}\\\\\n",
    "&= \\left[ \\frac{\\partial V}{\\partial t} + \\frac{\\partial V}{\\partial S} \\mu S  + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2  + \\Delta  \\mu S \\right] dt +  \\left[ \\frac{\\partial V}{\\partial S}  +  \\Delta \\right] \\sigma S dW_t^{\\mathbb{P}}.\\\\\n",
    "\\end{align*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Condition (C1) implies that the second term in the last expression should be equal zero. \n",
    "\n",
    "Thus, taking $\\Delta = -\\frac{\\partial V}{\\partial S}$ we obtain\n",
    "\n",
    "\\begin{align*}\n",
    "d\\Pi_t &= \\left[ \\frac{\\partial V}{\\partial t} + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2 \\right] dt.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, condition (C2) implies\n",
    "\\begin{align*}\n",
    "d\\Pi_t &= r \\Pi_t dt = r \\left[  V_t -\\frac{\\partial V}{\\partial S} S_t \\right].\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combining the last two equations we obtain\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial V}{\\partial t} + \\frac{1}{2}\\frac{\\partial^2 V}{\\partial S^2} \\sigma^2 S^2  = r\\left[  V_t -\\frac{\\partial V}{\\partial S} S_t \\right]dt,\n",
    "\\end{align*}\n",
    "\n",
    "from which we can derive the following partial differential equation (PDE)\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial V}{\\partial t} + \\frac{1}{2} \\sigma^2 S^2  \\frac{\\partial^2 V}{\\partial S^2} + r S_t\\frac{\\partial V}{\\partial S}     - r  V_t  = 0 .\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding the final condition, which comes from (A4), we obtain the famous second order parabollic partial differential equation with boundary condition\n",
    "\\begin{align*}\n",
    "\\frac{\\partial V}{\\partial t}  + r^d S_t\\frac{\\partial V}{\\partial S} + \\frac{1}{2} \\sigma^2 S^2  \\frac{\\partial^2 V}{\\partial S^2}    - r V_t  &= 0, \\qquad \\qquad t \\in [0,T]\\\\\n",
    "V_T =  (S_T - &  K)^{+} .\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution\n",
    "\n",
    "The solution to this PDE with boundary condition is given by\n",
    "\\begin{align*}\n",
    "V(S_t, t) = \\Phi(d_1) S_t - \\Phi(d_2)K e^{-r(T-t)},\n",
    "\\end{align*}\n",
    "where\n",
    "\\begin{align*}\n",
    "d_1 & = \\dfrac{1}{\\sigma \\sqrt{T-t}} \\left[ \\ln \\left(\\frac{S_t}{K} \\right) + \\left( r + \\dfrac{\\sigma^2}{2}\\right) (T-t)  \\right]\\\\\n",
    "d_2 & = d_1 - \\sigma\\sqrt{T-t},\n",
    "\\end{align*}\n",
    "and $\\Phi$ denotes the cumulative distribution function (cdf) of a standard normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution via the Heat Equation\n",
    "\n",
    "See the original paper: [The Pricing of Options and Corporate Liabilities\n",
    "Author(s): Fischer Black and Myron Scholes](https://www.cs.princeton.edu/courses/archive/fall09/cos323/papers/black_scholes73.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution via Feynman-Kac"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Feynman-Kac formula](https://en.wikipedia.org/wiki/Feynman–Kac_formula) guarantess that the solution to the PDE can be written as the following conditional expectation\n",
    "\\begin{align*}\n",
    "V(S_t, t) &= \\mathbb{E}^{\\mathbb{Q}}\\left[ e^{-r(T-t)} (S_T- K)^{+} | S_t \\right], \n",
    "\\end{align*}\n",
    "where $S$ is a stochastic process \n",
    "under the [probability measure](https://en.wikipedia.org/wiki/Probability_measure) $\\mathbb{Q}$ which satisfies the following stochastic differential equation (SDE)\n",
    "\\begin{align*}\n",
    "dS_t = r S_t dt + \\sigma S_t dW^{\\mathbb{Q}}_t. \n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the last expression, we can see that $S$ is a geometric Brownian motion! So, from yesterday's class we know its properties."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le'ts calculate the expectation that we obtained from the [Feynman-Kac formula](https://en.wikipedia.org/wiki/Feynman–Kac_formula)\n",
    "\n",
    "\\begin{align*}\n",
    "V(S_t, t) &= \\mathbb{E}_t^{\\mathbb{Q}}\\left[ e^{-r(T-t)} (S_T- K)^{+} \\right ]\\\\\n",
    " &= e^{-r(T-t)} \\mathbb{E}_t^{\\mathbb{Q}}\\left[  (S_T- K)^{+} \\right ]\\\\\n",
    " &= e^{-r(T-t)} \\mathbb{E}_t^{\\mathbb{Q}}\\left[ 1_{[K,\\infty)} (S_T) (S_T- K) \\right ]\\\\\n",
    " &= e^{-r(T-t)} \\left\\{   \\mathbb{E}_t^{\\mathbb{Q}}\\left[ 1_{[K,\\infty)} (S_T)S_T \\right ] - K \\mathbb{Q}\\left(S_T|S_t \\geq K \\right ) \\right\\}.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we can write it like\n",
    "$$V(S_t, t) = e^{-r(T-t)} \\left( E_1 - K E_2  \\right),$$\n",
    "\n",
    "where \n",
    "\n",
    "$$E_1 = \\mathbb{E}_t^{\\mathbb{Q}}\\left[ 1_{[K,\\infty)} (S_T)S_T \\right ]$$\n",
    "\n",
    "$$E_2 =  \\mathbb{Q}\\left(S_T|S_t \\geq K \\right ).$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate $E_1$ and $E_2$ let's make some observations:\n",
    " \n",
    "(1) Under the probability measure $\\mathbb{Q}$ the process $S$ is also a geometric Brownian motion. So, Ito's formula implies that\n",
    "\n",
    "$$\\ln(S_T)  = \\ln (S_t) +  \\left( r-\\frac{1}{2}\\sigma^2 \\right)(T-t)  + \\sigma (W_T^{\\mathbb{Q}} - W_t^{\\mathbb{Q}}).$$\n",
    "Hence\n",
    "$$\\ln(S_T) |S_t \\sim \\mathcal{N}\\left( \\ln(S_t) +  \\left( r-\\frac{1}{2}\\sigma^2 \\right)(T-t),\\sigma^2(T-t) \\right),$$ \n",
    "or equivalently\n",
    "$$S_T |S_t \\sim LogNormal\\left(\\ln(S_t) +  \\left( r-\\frac{1}{2}\\sigma^2 \\right)(T-t),\\sigma^2(T-t)\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) Recall that the probability density function (pdf) of a [log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_distribution) $Lognorma(\\mu, \\sigma^2)$ is given by\n",
    "$$\n",
    "p(x) = {\\displaystyle {\\frac {1}{x\\sigma {\\sqrt {2\\pi }}}}\\ \\exp \\left(-{\\frac {\\left(\\ln \\left(x\\right)-\\mu \\right)^{2}}{2\\sigma ^{2}}}\\right)}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these observations, we have all the tools to calculate $E_1$ and $E_2$. Let's start with $E_2$ for being the simplests one:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "E_2 &= \\mathbb{Q}\\left(S_T \\geq K \\right ) \\\\ \n",
    "&= \\mathbb{Q}\\left(\\ln (S_T) \\geq \\ln(K) \\right ) \\\\\n",
    "&= 1 - \\mathbb{Q}\\left(\\log (S_T) \\leq \\ln(K) \\right ) \\\\\n",
    "&= 1 - \\Phi \\left(  \\frac{ \\log(K)  - \\ln(S_t) -  \\left( r - \\frac{1}{2}\\sigma^2 \\right) }{\\sigma \\sqrt{(T-t)}} \\right) \\\\\n",
    "&= \\Phi \\left(  \\frac{1}{\\sigma \\sqrt{(T-t)}} \\left[ \\ln(S_t/K)  +  \\left( r - \\frac{1}{2}\\sigma^2 \\right) \\right] \\right) \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's calculate $E_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "E_1 &= \\mathbb{E}_t^{\\mathbb{Q}}\\left[ 1_{[K,\\infty)} (S_T)S_T \\right ] \\\\ \n",
    "& = \\int_K^{\\infty} s {\\frac {1}{s \\sigma\\sqrt{T-t} {\\sqrt {2\\pi }}}}\\ \\exp \\left(-{\\frac {\\left(\\ln \\left(s\\right)-\\ln(S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t)  \\right)^{2}}{2\\sigma ^{2}(T-t)  }}\\right) ds\\\\\n",
    "& = \\int_K^{\\infty}  {\\frac {1}{ \\sigma\\sqrt{T-t} {\\sqrt {2\\pi }}}}\\ \\exp \\left(-{\\frac {\\left(\\ln \\left(s\\right)-\\ln(S_t) -(r-\\frac{1}{2}\\sigma^2) \\right)^{2}(T-t)}{2\\sigma ^{2}(T-t)  }}\\right) ds \\\\\n",
    "& =\\frac {1}{\\sigma \\sqrt {2\\pi }  \\sqrt{T-t} } \\int_K^{\\infty}   \\exp \\left(-{\\frac {\\left[\\ln (s/S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t) \\right]^{2}}{2\\sigma ^{2}(T-t)  }}\\right) ds \\\\\n",
    "& =\\frac {1}{\\sigma\\sqrt{T-t} \\sqrt {2\\pi }   } \\int_K^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {\\left[\\frac{ \\ln (s/S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t)}{\\sigma\\sqrt{T-t}}\\right]^{2}} \\right) ds \n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need a change of variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$z = \\left[\\frac{ \\ln (s/S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t)}{\\sigma\\sqrt{T-t}}\\right] - \\sigma\\sqrt{T-t}$\n",
    "\n",
    "\n",
    "$z = \\frac{\\ln (s/S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t)-\\sigma^2(T-t) }{\\sigma\\sqrt{T-t}}= \\frac{\\ln (s/S_t) -(r+\\frac{1}{2}\\sigma^2)(T-t) }{\\sigma\\sqrt{T-t}}$\n",
    "\n",
    "If $s=K$, then\n",
    "$z =  \\frac{\\ln (K/S_t) -(r+\\frac{1}{2}\\sigma^2)(T-t) }{\\sigma\\sqrt{T-t}}$\n",
    "\n",
    "\n",
    "$s = S_t\\exp\\left[ z\\sigma\\sqrt{T-t}  +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right] $\n",
    "\n",
    "\n",
    "\n",
    "$dz =  \\frac{1}{{\\sigma\\sqrt{T-t}}} \\frac{ds}{s}$\n",
    "\n",
    "$  {\\sigma\\sqrt{T-t}} S_t\\exp\\left[ z\\sigma\\sqrt{T-t}  +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right]  dz = ds$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "E_1 \n",
    "& =\\frac {1}{\\sigma\\sqrt{T-t} \\sqrt {2\\pi }   } \\int_K^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {\\left[\\frac{ \\ln (s/S_t) -(r-\\frac{1}{2}\\sigma^2)(T-t)}{\\sigma\\sqrt{T-t}}\\right]^{2}} \\right) ds \\\\\n",
    "& = \\frac {1}{\\sigma\\sqrt{T-t} \\sqrt {2\\pi }   } \\int_{K^*}^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {\\left[z+\\sigma\\sqrt{T-t}\\right]^{2}} \\right) {\\sigma\\sqrt{T-t}} S_t\\exp\\left[ z\\sigma\\sqrt{T-t}  +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right]  dz \\\\\n",
    "& = \\frac {1}{\\sqrt {2\\pi }   } \\int_{K^*}^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {\\left[z+\\sigma\\sqrt{T-t}\\right]^{2}} \\right)  S_t\\exp\\left[ z\\sigma\\sqrt{T-t}  +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right]  dz \\\\\n",
    "& =S_t\\exp\\left[ (r+\\frac{1}{2}\\sigma^2)(T-t) \\right]  \\frac {1}{\\sqrt {2\\pi }   } \\int_{K^*}^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {\\left[z+\\sigma\\sqrt{T-t}\\right]^{2}} \\right)  \\exp\\left[ z\\sigma\\sqrt{T-t}\\right]  dz \\\\\n",
    "& =S_t\\exp\\left[ (r+\\frac{1}{2}\\sigma^2)(T-t) \\right] \\exp\\left[ -\\frac{1}{2} \\sigma^2 (T-t)\\right] \\frac {1}{\\sqrt {2\\pi }   } \\int_{K^*}^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {z^{2}} \\right)    dz \\\\\n",
    "& =S_t\\exp\\left[ r(T-t) \\right]  \\frac {1}{\\sqrt {2\\pi }   } \\int_{K^*}^{\\infty}   \\exp \\left(  -\\frac{1}{2}  {z^{2}} \\right)    dz \\\\\n",
    "& = S_t\\exp\\left[ r(T-t) \\right]   (1 - \\Phi(K^{*}))    \\\\\n",
    "& = S_t\\exp\\left[ r(T-t) \\right]     \\Phi(-K^{*})   \\\\\n",
    "& =S_t\\exp\\left[ r(T-t) \\right]   \\Phi \\left( \\frac{1}{\\sigma\\sqrt{T-t}} \\left[ \\ln (S_t/K) +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right] \\right)\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we have\n",
    "\n",
    "\\begin{align*}\n",
    "V(S_t, t) & = e^{-r(T-t)} \\left( E_1 - K E_2  \\right) \\\\\n",
    "& =  e^{-r(T-t)} \\left\\{   S_t e^{r(T-t)}  \\Phi \\left( \\frac{1}{\\sigma\\sqrt{T-t}} \\left[ \\ln (S_t/K) +(r+\\frac{1}{2}\\sigma^2)(T-t) \\right] \\right) - K \\Phi \\left(  \\frac{1}{\\sigma \\sqrt{(T-t)}} \\left[ \\ln(S_t/K)  +  \\left( r - \\frac{1}{2}\\sigma^2 \\right) \\right] \\right)   \\right\\}\\\\\n",
    "& = S_t \\Phi(d_1) - e^{-r(T-t)} K\\Phi(d_2)\\\\\n",
    "& = \\Phi(d_1) S_T - \\Phi(d_2) e^{-r(T-t)} K\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we have arrived to the Black-Scholes formula!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put-Call Parity\n",
    "\n",
    "In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.\n",
    "\n",
    "\n",
    "$$Call - Put = S - Ke^{-r(T-t)}.$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def BS_formula(payoff=\"call\", S=100., K=100., tau=1., r=0.1, sigma=0.2):\n",
    "    # Here tau = T-t Time to expiration\n",
    "\n",
    "    d1 = (np.log(S/K) + (r + 0.5*sigma**2)*(tau))/(sigma*np.sqrt(tau))\n",
    "    d2 = d1 - sigma*np.sqrt(tau)\n",
    "\n",
    "    if payoff == \"call\":\n",
    "        price = norm.cdf(d1)*S - norm.cdf(d2)*K*np.exp(-r*tau)\n",
    "    elif payoff==\"put\":\n",
    "        price = -norm.cdf(-d1)*S + norm.cdf(-d2)*K*np.exp(-r*tau)\n",
    "    else:\n",
    "        raise ValueError(\"Payoff not implemented. Set 'call' or 'put'\")\n",
    "\n",
    "    return price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call Price 13.269676584660886\n",
      "Put price 3.753418388256833\n"
     ]
    }
   ],
   "source": [
    "S=100.0     # St spot stock price\n",
    "K=100.0     # strike\n",
    "tau=1.0     # T-t\n",
    "r=0.1       # risk free rate \n",
    "sigma=0.2   # diffusion coefficient or volatility\n",
    "\n",
    "call = BS_formula(\"call\", S, K, tau, r, sigma)\n",
    "put = BS_formula(\"put\", S, K, tau, r, sigma)\n",
    "\n",
    "print(f'Call Price {call}')\n",
    "print(f'Put price {put}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert( call - put == S - K*np.exp(-r*tau) )"
   ]
  }
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