equity-options-pricing-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "inside-enemy",
   "metadata": {},
   "source": [
    "# Pricing equity options\n",
    "In this notebook I price American equity options using volatility tracking, riskless yield curve construction, and options pricing code from this package. I ensure that all market and economic data required for pricing is obtained from [FRED](https://fred.stlouisfed.org) and [Yahoo-finance](https://finance.yahoo.com) using [pandas-datareader](https://pydata.github.io/pandas-datareader/). Since the lifetime of an option is usually measured using trading\n",
    "days rather than calendar days, I make use of [the pandas-market-calendars library](https://pandas-market-calendars.readthedocs.io/en/latest/index.html) to get correct trading calendars.\n",
    "\n",
    "This notebook can also be used as a tutorial to using the `pricing.curves`, `pricing.options`, `volatility.parameter_estimators`, and `volatility.volatility_trackers` packages in this repository."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "decreased-lending",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uncomment if running in Google Colaboratory, otherwise the import of the curves module in the cell below will fail\n",
    "#!git clone -l -s https://github.com/ilchen/options-pricing.git cloned-repo\n",
    "#%cd cloned-repo\n",
    "\n",
    "# Install the latest version of pandas-datareader, yfinance, and pandas-market-calendars\n",
    "# !pip install pandas-datareader -U\n",
    "# !pip install yfinance -U\n",
    "# !pip install pandas-market-calendars -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fancy-spanking",
   "metadata": {},
   "source": [
    "## Constructing a riskless rate curve for USD\n",
    "Since I already covered it in a separate notebook, I will simply import it (along with all imports that this notebook needs). The resultant YieldCurve object is assigned to the `curve` variable.\n",
    "\n",
    "I prepared two alternative rislless rate/yield curves &mdash; one based on US Treasury Yields (you can use it for pricing options maturing up to 30 years in the future) and another based on AMERIBOR rates (you can use it for pricing options maturing up to 2 years in the future). Since AMERIBOR term structure is no longer published by the Federal Reserve Bank of St. Louis, it cannot be used anymore unfortunately..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "personalized-reviewer",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Uncomment the below line if you want to price with a yield curve based on US Treasury Yields\n",
    "%run riskless-yield-construction-example.ipynb\n",
    "\n",
    "# Uncomment the below line if you want to price with a yield curve based on AMERIBOR rates\n",
    "#%run riskless-rate-curve-construction-ameribor.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "encouraging-economics",
   "metadata": {},
   "source": [
    "## Estimating and forecasting volatility of the stock, options on which we want to price\n",
    "Now that the riskless curve has been constructed, the next thing to do is obtain an accurate volatility estimate for the stock whose options we want to price. There are various methods for doing it. The most common are the Exponentially Weighted Moving Average (EWMA) and GARCH(1, 1) methods. You can read about them on the Internet or delve into John C. Hull's [Risk Management and Financial Institutions](http://www-2.rotman.utoronto.ca/~hull/riskman/index.html) or [Options, Futures, and Other Derivatives](http://www-2.rotman.utoronto.ca/~hull/ofod/index.html). For the purposes of pricing options GARCH(1, 1) is preferred because it supports volatility forecasting for future maturities by incorporating mean reversion (and volatility of equities lends itself to mean reversion). In this notebook I therefore use GARCH(1, 1).\n",
    "\n",
    "### GARCH(1, 1)\n",
    "In order to use GARCH(1, 1) one first needs to estimate its parameters based on the historical data for the equity whose options you want to price. GARCH(1, 1) has three parameters &mdash; ω, α, and β. I use the maximum likelihood method to estimate them, which is an optimization task. The `volatility.parameter_estimators.GARCHParameterEstimator` class comes to rescure. _Implementation detail_: In that class I use [SciPy](https://docs.scipy.org/doc/scipy/tutorial/optimize.html) to optimize for maximum likelihood. Alternatively I could've used Google's TensorFlow 2.x.\n",
    "\n",
    "Constraint optimization for three variables is not fast. If you are not content with the speed of `volatility.parameter_estimators.GARCHParameterEstimator`, you can use its `volatility.parameter_estimators.GARCHVarianceTargetingParameterEstimator` counterpart. This latter class is \n",
    "faster because it uses the so-called _variance targeting_ method whereby it sets ω based on the sample variance of price changes. Then it optimises for only two variables instead of three as GARCHParameterEstimator does. It's marginally less accurate.\n",
    "\n",
    "*NB* When estimating ω, α, and β it's vital to use _adjusted closing_ prices, i.e. prices that have been adjusted for dividends and stock splits. Failing to do that will result in too high an estimate. Yahoo Finance provides such prices in the `Adj Close` column.\n",
    "\n",
    "#### Estimating GARCH(1, 1) parameters for Apple\n",
    "Since volatility tends to change with time, it's recommended to estimate it based on the most recent 90 or 180 days, or on the same number of days as the duration of the option being priced. In this notebook I use date from the past two years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "continuing-sensitivity",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 3740.49376 after 107 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000011477039, α=0.00096, β=0.93736\n"
     ]
    }
   ],
   "source": [
    "TICKER = 'AAPL'\n",
    "\n",
    "# I'll use price changes over the past two years to estimate GARCH(1, 1) ω, α, and β parameters\n",
    "start = BDay(1).rollback(date.today() - relativedelta(years=+2))\n",
    "ticker = yfin.Ticker(TICKER)\n",
    "\n",
    "data = ticker.history(start=start, actions=False, auto_adjust=False).tz_localize(None)\n",
    "\n",
    "asset_prices = data['Adj Close']\n",
    "\n",
    "vol_estimator = parameter_estimators.GARCHParameterEstimator(asset_prices)\n",
    "print('Optimal values for GARCH(1, 1) parameters:\\n\\tω=%.12f, α=%.5f, β=%.5f'\n",
    "      % (vol_estimator.omega, vol_estimator.alpha, vol_estimator.beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "turkish-carter",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "sunset-project",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 3734.56650 after 89 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000014691563, α=0.01197, β=0.92247\n"
     ]
    }
   ],
   "source": [
    "var_target_vol_estimator = parameter_estimators.GARCHVarianceTargetingParameterEstimator(asset_prices)\n",
    "print('Optimal values for GARCH(1, 1) parameters:\\n\\tω=%.12f, α=%.5f, β=%.5f'\n",
    "      % (var_target_vol_estimator.omega, var_target_vol_estimator.alpha, var_target_vol_estimator.beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "common-projector",
   "metadata": {},
   "source": [
    "As you can see, `GARCHParameterEstimator` is able to achieve a slightly higher value of the objective function than `GARCHVarianceTargetingParameterEstimator`. The higher, the more accurate as we are solving for the maximum value."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "literary-compensation",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for Apple\n",
    "Now that we have obtained optimal values for GARCH(1, 1) parameters ω, α, and β, we can proceed to forecast the volatility of AAPL stock. I created class `volatility.parameter_estimators.GARCHVolatilityTracker` to assist in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "unlimited-photographer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of AAPL for term 0.2027 years: 0.21649\n"
     ]
    }
   ],
   "source": [
    "vol_tracker = volatility_trackers.GARCHVolatilityTracker(vol_estimator.omega, vol_estimator.alpha,\n",
    "                                                         vol_estimator.beta, asset_prices)\n",
    "\n",
    "# Let's get volatility forecast for next January options, i.e. maturity on the 3rd Friday of next January\n",
    "from dateutil.relativedelta import FR\n",
    "maturity_date = curve.date + relativedelta(years=1, month=1, day=1, weekday=FR(3))\n",
    "vol = vol_tracker.get_annual_term_volatility_forecast(curve.to_years(maturity_date))\n",
    "print('Volatility of %s for term %.4f years: %.5f' % (TICKER, curve.to_years(maturity_date), vol))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "technological-camel",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing historical and future volatility of Apple stock for 200 business days into the future"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "surprised-seattle",
   "metadata": {},
   "outputs": [
    {
     "data": {
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akuLee+81EyZMOGr8H484CDQ7duwwN9xwg3UxSO+prTNnzjQXXHCBMaZ050mgTH/iS1XrqbJN9EC3cOFC43A4rCN7vHnxeDxm0qRJJjo62vz222/GmNIdcqeddlpAHOFz8OBBc9ddd5l3333XGPN7MT537lwzePBg43K5KvwMld0RFcj8qRUCfRmkPvBPdeuE7OxsM2/evIBbFqkPqofvM5WjNqgYtUHlqL/9U53t/44dO8wDDzxgtmzZYkeoNaq62/vffvvNtGzZ0qxbt65G47RLdbZbXoGw7tm1a5d5/vnnTXJysvXcjBkzTFBQkOncubPp3bu3ad++vXUgidvtNqtWrbK2YYGK5gpOiiVLlhx1BkthYWFAFInH66OPPrJW7N7TeQsLC635nQNt/uY/Sk9PN4MGDTIPPPDAUXOFLl261Jxyyinmv//9rzEmMHc0eTyectNVeHPw+OOPm8svv7zc2Ly8vBqNrbYqO0+6dyfJrFmzzJlnnlnuuT/OMRrIfK2nvEexBLKSkhIzfPhwc8UVV1hH0HmXwz179pjhw4ebRx55xNqpG0jr9LJzxnuXq6+++sr06dPHFBUVWc8dPnzYlvjqEpbBo1Ef+Kc6dUJOTk6NxlbbUB8cO77PlEdt4Bu1gf/Y9lesOtt/YwKnBqjO9t67HSsoKKi5AGsZlq/fHThwwLr/+uuvm+DgYPPRRx+Z9PR0s2rVKjNixAhz00031fvrFVWH098L3wP+8Hg8kqShQ4fqjjvuUNeuXXXHHXfou+++07333quzzjpLOTk5NkdZO7ndbknSuHHjdPPNNys/P1/Tpk3TL7/8orvuukunnHKKioqKFBwcbHOk9mrevLnOOOMMzZs3T5988okKCwut10477TS53W799NNPkiSnM7BWcR6PRw6HQ5deeqkkyRhj5SAvL08ZGRnW2CeffFJ/+9vfrM9dIDLGSJJGjRplPXY4HJKk3NxcHT582HpuxowZuvHGG1VSUmJbvLVBVeupAQMGqKioyMptIAoKCtIVV1yhHTt26Pnnn1d2dra1HLZs2VINGzbUli1brHV5aGioneHWqFNOOUVS+WUtLy9Pubm5CgoKksPh0EMPPaRzzjlHxcXFdoZaa7EM+kZ9ULXq1gmPPPKI3G53wH2eqA+OHd9nKkZt4Bu1QdXY9leuOtt/KTBqgOpu76dPn66SkpKAWvd4sXwdrUmTJtb9888/X4sXL9a4cePUvHlz9evXT9HR0Tpy5IhCQkJsjLJ2CayqBieNtxhyOp1yuVwKCQnR0KFDJUkvvPCCxowZo6ioKM2bN09RUVE2R1u7eHMXFBRk5e6yyy6Tw+HQq6++qnPPPVdut1vz5s1TWFiY3eHayuPxyOl06oknntDll1+u//u//1NBQYGuu+46hYeHS5LatWunFi1a2BypPbwFk/cz5XA4VFJSouDgYEVFRSkmJkaS9PDDD+uxxx7TmjVrFBQUZGfItvJ+gasoXzExMYqKipLD4dDDDz+sf/7zn1q+fHnA7QzwYj3lH2+ebr31VqWkpGjOnDkqKCjQgw8+qOjoaElSXFycYmNj5Xa75XQ6rc9hIPCuwx0Oh9xut4KCghQdHa2IiAgFBQXpoYce0jPPPKMff/wxIL/cVYZlsHLUB/6hTvAP9UH1sY7yjdqgctQGvrFcVY3tf8WOZXsfaNsxli/fvLnxeDxq1qyZmjVrZj3v8XgUExOjDh06WA2nQNpm+eIwgdR+w0nhLYIOHz6sxo0bSyp/5MkFF1ygJUuWaMmSJerRo4edodY63txlZWVZG7iyuRs5cqRWrVqlxYsXq2fPnnaGWit48+U1YcIErV27VnFxcTr77LO1efNm/e9//9OKFSvUtWtXGyO1jzdHubm5atiwofX8c889p3Xr1qlNmzZ6/PHHtWTJEg0YMMDGSGuHipZBSfrf//6nd999Vz179tTTTz+tn376KWDzxXrKf95ceb/ozZgxQ19++aUyMzN14YUXavfu3friiy+0bNmygNseVlQrSNKiRYv08MMP65RTTtHMmTP1888/B+yy5gvLYNWoD/xHneAf6gP/sY6qHLWBb9QGvrFc+Yftv29s731j+Srl3S6V5etz4x3/yCOP6M0339QPP/ygTp061WS4tdvJmm8M9dMfL9rovejcjh07TEJCQrm5LEtKSsw//vEPExkZac1ZGMj+OLdn2dz17t3bumCmMaUXWL333ntNSEiIWbNmTY3GWRt5PB5rDuIdO3aY4cOHm3Xr1hmPx2PeeustM378eHPqqaeaiy++2Kxdu9bmaGtGYWHhUc+VzdHIkSPN4sWLrdcee+wx43A4TIMGDcyvv/5aY3HWFjt37jzqs1HZMvjqq69a+Vq5cmWNxmqXkpKSo+ZNLfuZYj1VOW/uduzYYbp3725++OEHY0zpRWwnT55szjnnHPPnP/+53MUB66vq1AqzZ882DofDNGzYMGCWtcpQK1QP9YFv1An+oT7wH3VC9VEb/I7awDe2/dXH9v93bO99q+42PpCWr02bNplnnnmm3HOVfW6+++47M2nSJBMfH29WrVpVo7HWBTRX4BfvhfeMObow2rVrl2nRooW55ZZbjnrt66+/Nhs3bqyRGGurzMxM6/4fC6cdO3aYli1bmptvvvmo3H3wwQf1foVeke3bt5tnnnnGPPDAA2bu3LnlXktJSTGtWrUyEydOtFb8XoWFhQFzQa0NGzaYIUOGlNvYeZXNUVlvvPGGadu2bUAuj2vXrjVt27Y1t99+e7l1mTHGpKamVrgMzps3z5xyyikBk6/NmzebW265xYwePdo88sgj5fLEeqq8bdu2mSeeeMJMnTrVfPjhhyY3N9d6LSUlxcrVH9dRHo+n3l9A81hqhbVr15pzzz3XbNiwocbirI2oFapGfeA/6gT/UB/4jzqhctQGvlEb+Ma23z9s/31je+/bsWzjjQmM5WvdunUmLCzMOBwOs2zZsnKv+frcvP322+bWW2+t95+bY0VzBVXasGGDCQ4ONnfeeaf1XNkV0NSpU81dd9111EoJpbmLiYkxjz32mPVc2cLp+uuvNxMnTiyXu0DO49q1a01iYqI566yzzJAhQ4zD4TBz5syxXh89erS56qqrAjpHxpR+bhwOh+nQoYP5+eefjTGlnyuPx2NGjx5trrzyyqNy5PF4zN69e+0I11Zbt241TZo0MX/5y1+OOqrH4/GYG264wdxwww0VfqYOHDhQU2HaKjk52cTHx5vLL7/c3HbbbSYkJMQ8/vjj1uvXXXedufHGG1lPmdJcNWrUyAwfPtwMGzbMBAUFmcsuu8x88803xhhjJk6ceNTnKVBydTy1wpEjR2ogwtqLWqFq1AfVQ51QNeoD/1EnVI7awDdqA9/Y9vuH7X/l2N5X7Fi28YHyGVqzZo0JDw831157rRkxYoR56KGHjDG/n7Vy9tlnm/Hjx1eYj7y8vBqNtS6huYJKpaWlmUGDBpn+/fubBg0amClTpliveRe2Px4hgFK7d+82/fr1M507dzaNGzcu9yXEeypifT+Sojq2bNliEhMTzQMPPGCKiorM4cOHTVJSkpk5c6Y1pqJTXgPRm2++ae677z5zww03mLi4OPPjjz9ar3k/W2XV9yPiKvPss8+a8ePHG2NK11Uvv/yyue+++8zMmTPNvn37KiwaAilfR44cMaeddpp54IEHrOemTZtm7r77bmvdXtFnKhDl5+ebpKQkc/vtt1vPLV++3AwYMMCMHj3a/PDDDwFTlP/RsdYKgZqvsqgVqkZ9UH3UCVWjPvAPdULlqA18ozbwjW2/f9j+V43tfcWOZRsfCFatWmWioqLMgw8+aIwx5t577zVNmjQpdxZdUVFRhQ05VC7Y7mu+oPYyxuiHH35QmzZtNGXKFO3cuVPXX3+9HA6HnnnmGTkcDpWUlCg4mI/RH3k8Hs2ePVvt2rXT7bffrhUrVugf//iHJOn+++9XUFCQXC6XQkJCbI60diguLtajjz6qkSNHasaMGQoKClJoaKgiIiK0bNkyrVy5Ur1799a1116rsLAwu8O1XWRkpBYvXqwFCxZo//79GjdunBYuXKh33nlHffr00RVXXFFu/B8vUhZI1q1bZ31mzjrrLBUWFio6OlqvvPKK5syZoylTpujcc88t9zOBlK+CggIVFBRo+PDh1nO7d+/W1q1bdeqpp2rAgAEaO3bsUTkKRBERETpy5IiaNm0qqXQ9P2jQIL311lu67bbb9MQTT6hx48bq3bu3zZHWrOOpFbwXjQxU1ApVoz44NtQJVaM+8A91QuWoDSpGbeAb237/sP33D9v7ih3LNr6+O3DggIYOHapJkybp73//uyRp8uTJmjt3rp577jlNmzZNbrdboaGhR/1sfV8vnwjsFYdPDodDw4cPV1RUlIYMGaIhQ4bIGKMJEybIGKNnn31WwcHBMsawsP2B0+lUUlKSmjZtqjPPPFN9+/aVMUaPP/64pNLCKSQkRB6PJ2A2cJUJDQ3V1KlTtXfvXgUFBUmS/vGPf+jTTz/VVVddpfDwcN11113atm2bXnjhBZujtV///v2t4vLzzz/XlVdeqX79+qlhw4ZaunSp3eHVCt71UqtWrbRv3z599tlnCg8P1+zZs9WkSRNt3bpVEyZM0JtvvhlwhVVZxcXF2rp1q3766Se1aNFCc+fO1QcffKD7779fsbGxeuedd7R3717169dPzZs3tztc2xhjlJeXp9DQUB04cEBS6ZdjY4x69OihF198Ueecc47eeustPf300zZHW7OoFY4dtULVqA+ODXWCb9QH1UOd4Bu1gW/UBr6x7fcP23//sL0vj228byEhIfrmm2/KHSzRrFkz9evXT99++62mTZumoKCggFwvnxA1eJYM6oGSkhLz3nvvmbCwMHPXXXcZY0pPs/vvf/9rkpOTbY6u9il7+lxGRoZ54oknTHR0tHXqb0lJiZk7d67JyMiwK8Raad26dWbUqFHmq6++snL48ccfm+DgYLN582abo6sd+vTpY7Zs2WKMMWb8+PGmQYMGJjY21vzyyy82R1a7fPPNN8bhcJjTTz/d3HjjjeVeW758uXE4HGblypU2RVc7/Oc//zGRkZEmKSnJREVFmY8//th6LTk52TgcjqMuHhmoPvjgg3JzPbvdbmvahnfeecfExsaaXbt22RlirUCtUD3UCv6jPvAfdULlqA/8R51QOWoD/1AblMe2v3rY/vvG9v5obOOr5p0ibv369SYsLMy88cYbNkdUt3HmCsqp6hTUoKAgXXbZZZKk66+/XpLkdrv18ssva9u2bTUSY221d+9epaWl6dChQxo1apScTqecTqd1ynN8fLwmTJggqfSoC2OMDh06pOeee067du2yOfqa5ytfktSrVy+9/fbbSkhIsMY7nU51795d8fHxdoVc48rmaPTo0XI4HHI6nSooKFBsbKxycnJ0xx13aOHChfr+++/19NNP67TTTtPPP/+sQYMG2R1+jfvjZ0qSxowZo/vuu09PPvmkGjVqpLy8PDVo0ECSFBsbq379+ikmJsbOsGtU2RyNHDlSDodDf/7znzVy5EhJ0tixY9W3b1/ryMtGjRqpX79+ioqKsjnymld2e2iMkSSNGzdOS5Ys0RVXXKFPP/1U55xzjrXeio2NVUJCgvX5qs+oFY4dtULVqA/8R53gH+oD/1EnVI7awDdqA9/Y9vuH7b9vbO99Yxvvm69lyntmnDFG7dq10/nnn6+vv/5a48ePV1hYGGeuHAv7+jqobdavX28uvPBCs2HDhirHlpSUmHfeecc4HI6A74obY8zatWtNq1atTPfu3U1wcLDp16+fefnll01OTo4xpvzFxDIyMszjjz8e0LmrKl/GHH3RrHvvvdckJSWZ7Ozsmg7XFr5ylJWVZYwx5p577jERERGmRYsW1lEXRUVF5k9/+pN15EogqShfL730ksnLyzMZGRnm5ptvNkFBQeZvf/ubSUlJMbm5uWbatGmmW7duZv/+/XaHXyMqytHMmTOtZWr79u0mPj7eLFiwwPqZv/3tb6Zjx44mLS3NrrBtUdn2MDU11dxwww0mNDTUvP7662bfvn2msLDQ3HfffaZPnz7m8OHDNkRcc6gVjh21QtWoD/xHneAf6gP/USdUjtrAN2oD39j2+4ftv29s731jG+9bVcuU98wVY4x59913TVhYmFmxYoVd4dZ5NFdgjCktCNu3b28cDofp27dvlStht9ttbrjhBhMdHW02btxYQ1HWThkZGaZbt27mvvvuM6mpqebAgQPmqquuMqeeeqqZMmWKtbEvu/K65pprTHR0tF8FaH3jb7689u7dax566CHTqFGjgDllvLIc3XnnnSY/P9/MmTPHnHfeeWb16tV2h2s7X/kaOHCgufvuu01eXp7Jzc01M2bMMGFhYaZNmzamT58+JiEhwaxatcru8GtEVctdZmamMcaYW265xQQHB5ukpCRz7rnnmmbNmgXcZ8yf7WF6erqZPn26CQkJMR06dDB9+vQx8fHx9f7zRK1w7KgVqkZ94D/qBP9QH/iPOqFy1Aa+URv4xrbfP2z/fWN77xvbeN/8XabKNnf79etnrrnmGuN2u49qZKJqNFdgCgsLzSOPPGLGjh1rfvnlFzNo0CDTrVu3Sgujr776yrRr1y6gjqbwJTk52bRt29asXbvWeq6oqMhMmzbNDBo0yDz44IOmoKDAGFN6tMU777xjmjVrFrBzPFYnX7/++qv505/+ZNq1axdQxUJlOTrllFPMo48+aowx5Y7kCWRV5evhhx82hYWFxhhj1qxZY2bPnm0++eQTs3PnTrtCrnH+LHfFxcXm8OHDZubMmeayyy4zU6dOrfdHO/1RdbeHq1atMu+//7557733TGpqas0GW8OoFY4PtULVqA/8R53gH+oD/1En+EZt4Bu1QeXY9vuH7b9vbO99YxvvW3WWKa/nnnvObN26taZDrTdorsC43W4ze/Zs89FHHxljjDly5EiVhVFaWppJT0+vyTBrrS1btph27dqZzz//3BhTemE+77/33nuv6du3r/nxxx+t8du3bzc7duywJdbaoDr52rNnj5k7d67Zvn27bfHaoaoc9e7d2yxevNgYc/Tp0YGoqnz16dPHLFq0yM4QbedPjpYsWWKND9TPVXW2h4GWI2qF40OtUDXqA/9RJ/iH+sB/1Am+URv4Rm1QObb9/mH77xvbe9/YxvtWnWXK+xqOj8OY/38lNgQ0t9utoKAg6/GhQ4eUlJSknJwczZkzR506dVJJSYlWrFih/v37Kzw83MZoa5eioiINGzZMzZs312effaagoCDr4nTGGPXp00f9+vXTW2+9JWNMwF8cyp989e3bV2+//bbdodqmOp8pkC9/sNz5rzrbwwEDBigsLMzGaGsWtcKxo1aoGusp/7Hd8w958h/LX+WoDXyjNvCNbb9/WP/4xnbMN3LjG7mpeU67A0Dt4C2IvL22uLg4ffnll4qKitJFF12kDRs2aPLkybrrrruUl5dnZ6i1isfjUVhYmGbNmqUff/xRt956qyRZKy2Hw6ELL7xQBw4ckKSALZi8/M1XRkaGzZHap7qfqUBHvqrGclc91dke5ubm2hlqjaNWODbUClVjPeU/tnv+IU/+Y/mrGrWBb9QGFWPb7x/WP76xHfON3PhGbuxBcwWSfi+GvBt1Y4zi4+P11VdfqVGjRurdu7feeustzZw5U3FxcXaGWqs4nU653W717NlTb731lt5//31de+212r9/vzUmNTVVsbGxcrvdNkZaO5CvqpGj6iFfVSNH1cP20Ddyc2xYBqtGjvxHrvxDnvxHrqrG9s83clMxliv/kCffyI1v5MY3cmMPpgWDdSpvdna2PB6PGjVqVO71CRMmaO7cufrxxx/VvXt3e4KsJf54uq731Lrc3FwVFRVpzZo1Gj9+vNq0aaPGjRsrLi5Oc+bM0dKlS9WrVy8bI7cH+aoaOaoe8lU1cuS/P+aK7eHvyM2x83g8cjp/P36JZfBo5Mh/5Mo/5Ml/5Kpyf8wP27/fkRvfqL/9Q558Ize+kRvfyE3twJkrAa6kpERBQUHasWOHunXrpqVLl1qvGWP0wgsv6D//+Y/mz59f7wuiyng7ut5epDHGWmnt2LFDnTt31i+//KKRI0dqw4YNSkpKUsuWLdW0aVOtWLEi4FZa5Ktq5Kh6yFfVyJH/fOWK7SG5OR4HDx6U9PsRY1JpPlkGf0eO/Eeu/EOe/EeuKucrP2z/yE1lUlJSdOTIkaMOSGG5Ko88+UZufCM3vpGbWsbPC9+jjtu+fbt5+eWXzV133WW+/fZbk5GRYb22a9cuEx8fb2688Ubj8Xis5z0ej/nhhx/M1q1b7Qi51tiyZYuZMmWKueSSS8yjjz5qtm/fbr3mzd0NN9xgPB6PKSkpMcYYK49ut9uWmO1EvqpGjqqHfFWNHPnPn1wF6vaQ3By7LVu2mKioKHPTTTdZz3mXNZbBUuTIf+TKP+TJf+Sqcv7kJ1C3f+TGtzVr1hiHw2HeeOONo15jufodefKN3PhGbnwjN7UPZ64EgOTkZA0bNkxz587VF198ocmTJ+vNN9+U2+2Wy+XS3Llzdc011+jVV18t1/V0OBwaMWKEOnbsaGP09kpOTtaQIUN05MgReTweff3113r//fdljJHL5dKcOXP0pz/9Sa+99pocDod1QT+vQLswHfmqGjmqHvJVNXLkP39zFYjbQ3JzfDZu3KiIiAglJyfr5ptvllR6kd/i4mKrznrllVcCehkkR/4jV/4hT/4jV5XzJz///ve/A3L7R24qtnbtWg0dOlR//etfNWHChKNe/+yzz6i/RZ4qQ258Ize+kZtaysbGDmrAjh07TKdOnczUqVNNcXGxMcaY+++/33Ts2NEUFBQYY4zJzMy0M8RaKyUlxbRp08Y8+OCD1nM33HCDueOOO8qN83aCAx35qho5qh7yVTVy5D9y5Ru5OX5fffWV6dy5s3niiSdMr169zM0332y9tnv3bhsjqz3Ikf/IlX/Ik//IVeXIj2/k5mibNm0ywcHBZvr06caY0iPBv/vuO/PKK6+Yn376yRw4cMB6PpCRJ9/IjW/kxjdyU3sF293cwcnjdrs1Z84c9evXT5MnT7YuPjdlyhS99957+u2339S7d2/FxMTYHGnt43a7NX/+fI0cOVL33HOPdZGoiIgIrV+/XmeccYbatGmjW265RUOGDDnqIlKBhnxVjRxVD/mqGjnyH7nyjdycGL169dKAAQN04403KjQ0VP/5z3909913KysrS4MGDdKECRMUEhJid5i2Ikf+I1f+IU/+I1eVIz++kZvyPB6P/ve//8ntdmvcuHGSpNGjR+vQoUPasWOH4uLi1K5dOz3zzDPq3bu3zdHahzz5Rm58Ize+kZtazo6ODmrOf/7zH/Pcc8/9v/buL7TK+g/g+Occ9k9m2raWhas5m3EWmalzF0F/JFzQVVg66iYQCtpNJP1DZP1RyqQIuyiyopssKAjKLqKgICuYrs0/bRBMQanMlXO1TnM72z6/C9kpf/o5389zfv32nJ3zfl3pOc/gw/vwwHEfn+c577VTp07ppZdeql9++eUFx//zXqml7tixY/r9999n//7MM89oVVWVPvfcc9rV1aUdHR26dOnS8+5JX8roFUajaOgVRiM/Wtlo879Lp9N6ww03aF9fn6bTad29e7fW1dVpIpHQw4cPqypX/tDIj1Y+dPKjVW70sdHmQr/88os++OCDWllZqddff72uX79eDx48qBMTE/rhhx9qe3u7btiwQUdHR+MeNVZ0stHGRhsbbQoXy5USMrM4GRsb01Qqpd3d3dn3PvroIz1x4kRcoxWsmWZnz57VO++8Uz/55JPse/v27dPLL79cP/vss7jGKzj0CqNRNPQKo5EfrWy0yd/ExIROTk5qe3u77tu3T1VVOzo6dMGCBbps2bILbq9WimjkRysfOvnRKjf62GhjGxoa0s7OTm1tbdWBgYHz3nv55Zf1iiuu0B9//DGm6QoHnWy0sdHGRpvCxG3BiszPP/8svb29MjExIVdffbW0traKyLnbfsw8yCiZTEoymcze1mPLli3y9ttvS3d3d2xzF4J/tmtsbJTVq1dLIpGQqakpqayslL1790oymZTp6WlJJpNSW1srixYtktra2rhHjwW9wmgUDb3CaORHKxtt8vfPdkuWLJFVq1Zlb4eyevVqGRwclN27d8tXX30le/fulSNHjsiOHTukrKxMXnrppZinnx008qOVD538aJUbfWy0sV3sdyz19fWydetWOX78uFxzzTUi8vfvXJqbm6WmpkYqKipinnx20clGGxttbLSZQ+Le7uDfc/jwYV26dKm2tbXpZZddpq2trfrBBx9ccNyZM2e0vr5ev/nmG922bZtWVVXpgQMHYpi4cHja/fct05588klds2aN/vrrr7M5akGgVxiNoqFXGI38aGWjTf5C7Z5++mlNJBLa1NSk3333naqe+8716quv6tGjR+Mae1bRyI9WPnTyo1Vu9LHRxnaxNu+//372/YvdVv3hhx/WdevW6Z9//jmbo8aKTjba2Ghjo83cwnKlSAwODmpDQ4M+/vjjOjIyoj09PXr//ffrpk2bdHJy8rwTb3R0VFeuXKm33XabVlVVaU9PT4yTxy9KO1XV48eP62OPPaY1NTV66NChmKaOD73CaBQNvcJo5EcrG23yl6tdJpNRVdVMJqOdnZ26f/9+Vf37Hz1TU1OxzT2baORHKx86+dEqN/rYaGPL53vTo48+qrW1tdnn0ZQCOtloY6ONjTZzD8uVIjA+Pq6bN2/WjRs36vj4ePb1t956S+vq6vS333477/iRkRFtbGzU2tpaPXjw4GyPW1Citjtw4IB2dnbqihUrSrIdvcJoFA29wmjkRysbbfIXtV0popEfrXzo5Eer3Ohjo40tapvu7m7dtGmTplIp7evrm+Vp40MnG21stLHRZm7imStFYHp6WhoaGqSlpUUqKipEVSWRSMhNN90k8+fPl0wmc97xCxculAceeEDuvvtuSaVSMU1dGKK2a21tlbGxMdm6datceeWVMU0dH3qF0SgaeoXRyI9WNtrkL2q7mZ9JJpMxTBsPGvnRyodOfrTKjT422tiitmlra5PR0VF59tlnZfHixTFNPfvoZKONjTY22sxRs7vLwf/LsWPHsn+euUTs5MmT2tzcrCdOnMi+V+rPVrkYb7tSv33aDHqF0SgaeoXRyI9WNtrkz9uut7d31mcrFDTyo5UPnfxolRt9bLSx8b3Jh0422thoY6PN3FP8/+WgSJ08eVL2798vn376qUxPT0tTU5OIiExNTUkikRARkd9//13OnDmT/Zmuri5pb2+X06dPi6rGMnchyLfdunXrSrIdvcJoFA29wmjkRysbbfKXb7vbb7+9ZNrRyI9WPnTyo1Vu9LHRxsb3Jh862Whjo42NNkVgdnc5+DccOnRIGxsb9dprr9WFCxdqKpXSd999V0+fPq2qf282f/jhB62vr9fh4WHdtm2bzps3r+Q3m7SLhl5hNIqGXmE08qOVjTb5o10Yjfxo5UMnP1rlRh8bbWy08aGTjTY22thoUxxYrswxQ0NDmkqldMuWLXr06FH96aeftKOjQ1taWvSpp57SoaGh7LGnTp3SlStXakdHh1ZUVJT8iUe7aOgVRqNo6BVGIz9a2WiTP9qF0ciPVj508qNVbvSx0cZGGx862Whjo42NNsWD5coc09/fr0uWLLngRHriiSd0+fLlunPnTk2n06qqOjAwoIlEQufNm6d9fX0xTFtYaBcNvcJoFA29wmjkRysbbfJHuzAa+dHKh05+tMqNPjba2GjjQycbbWy0sdGmePDMlTkmk8nI5OSk/PXXXyIiMjY2JiIiO3bskLVr18prr70mg4ODIiJSU1MjnZ2d0tvbKzfeeGNcIxcM2kVDrzAaRUOvMBr50cpGm/zRLoxGfrTyoZMfrXKjj402Ntr40MlGGxttbLQpHglVnnwz17S1tcn8+fPliy++EBGR8fFxqaysFBGRNWvWSHNzs7z33nsiInL27FmpqqqKbdZCQ7to6BVGo2joFUYjP1rZaJM/2oXRyI9WPnTyo1Vu9LHRxkYbHzrZaGOjjY02xYErVwpcOp2W0dFR+eOPP7Kvvf7669Lf3y/33XefiIhUVlbK5OSkiIjccsstkk6ns8eW8olHu2joFUajaOgVRiM/Wtlokz/ahdHIj1Y+dPKjVW70sdHGRhsfOtloY6ONjTbFi+VKARsYGJD169fLrbfeKi0tLbJnzx4REWlpaZFdu3bJ559/Lhs2bJBMJiPJ5LmPcmhoSKqrq2VyclJK+aIk2kVDrzAaRUOvMBr50cpGm/zRLoxGfrTyoZMfrXKjj402Ntr40MlGGxttbLQpcrP5gBf49ff3a11dnT7yyCO6Z88e3bx5s5aXl2tvb6+qqqbTaf3444+1oaFBU6mU3nXXXbpx40atrq7WI0eOxDx9vGgXDb3CaBQNvcJo5EcrG23yR7swGvnRyodOfrTKjT422tho40MnG21stLHRpvjxzJUCNDw8LPfee6+kUinZtWtX9vW16cLthQAAA2RJREFUa9fK8uXL5ZVXXsm+Njo6Ktu3b5fh4WGpqqqShx56SK677ro4xi4ItIuGXmE0ioZeYTTyo5WNNvmjXRiN/GjlQyc/WuVGHxttbLTxoZONNjba2GhTGsriHgAXymQyMjIyIvfcc4+IiExPT0symZSmpiYZHh4WERFVFVWVSy65RF544YXzjitltIuGXmE0ioZeYTTyo5WNNvmjXRiN/GjlQyc/WuVGHxttbLTxoZONNjba2GhTGvikCtCiRYvknXfekZtvvllERKampkREZPHixdmTK5FISDKZPO9BSIlEYvaHLTC0i4ZeYTSKhl5hNPKjlY02+aNdGI38aOVDJz9a5UYfG21stPGhk402NtrYaFMaWK4UqGXLlonIuW1leXm5iJzbZg4NDWWPef755+XNN9+UyclJEeHkm0G7aOgVRqNo6BVGIz9a2WiTP9qF0ciPVj508qNVbvSx0cZGGx862Whjo42NNsWP24IVuGQyKaqaPbFmNptdXV2yfft26evrk7IyPsaLoV009AqjUTT0CqORH61stMkf7cJo5EcrHzr50So3+thoY6OND51stLHRxkab4sWVK3OAqoqISFlZmVx11VXy4osvys6dO6Wnp0dWrFgR83SFjXbR0CuMRtHQK4xGfrSy0SZ/tAujkR+tfOjkR6vc6GOjjY02PnSy0cZGGxttihMrsTlgZptZXl4ub7zxhixYsEC+/vprWbVqVcyTFT7aRUOvMBpFQ68wGvnRykab/NEujEZ+tPKhkx+tcqOPjTY22vjQyUYbG21stClOXLkyh9xxxx0iIvLtt99Ka2trzNPMLbSLhl5hNIqGXmE08qOVjTb5o10Yjfxo5UMnP1rlRh8bbWy08aGTjTY22thoU1wSOnNNEuaEdDot1dXVcY8xJ9EuGnqF0SgaeoXRyI9WNtrkj3ZhNPKjlQ+d/GiVG31stLHRxodONtrYaGOjTfFguQIAAAAAAAAAABABtwUDAAAAAAAAAACIgOUKAAAAAAAAAABABCxXAAAAAAAAAAAAImC5AgAAAAAAAAAAEAHLFQAAAAAAAAAAgAhYrgAAAAAAAAAAAETAcgUAAAAAAAAAACAClisAAAAAAAAAAAARsFwBAAAAAAAAAACIgOUKAAAAAAAAAABABP8BdMkiV+FtXVEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Skipping the first n days of volatility forecast\n",
    "n_days_to_skip = 10\n",
    "x = vol_tracker.get_dates()[n_days_to_skip:]\n",
    "fig = plt.figure(figsize=(20, 10))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(x, vol_tracker.get_annual_volatilities()[n_days_to_skip:],\n",
    "        label='Historical Annual Volatility (GARCH(1,1) ω=%.5f, α=%.5f, β=%.5f)' \n",
    "            % (vol_estimator.omega, vol_estimator.alpha, vol_estimator.beta),\n",
    "        linewidth=2, color='k')\n",
    "\n",
    "# Forecasting volatility of Apple stock 200 days into the future\n",
    "future_volatilities = vol_tracker.get_annual_volatility_forecast_for_next_n_days(200)\n",
    "ax.plot(future_volatilities.index, future_volatilities, label='Forecast Annual Volatility', linewidth=1, color='k')\n",
    "ax.hlines(vol_tracker.get_annual_long_term_volatility(), xmin=future_volatilities.index[0], xmax=future_volatilities.index[-1],\n",
    "         label=\"Long-term Annual Volatility\", linestyle='--')\n",
    "ax.legend()\n",
    "ax.grid(True)\n",
    "x_axis = x.append(future_volatilities.index)\n",
    "ax.set_xticks(x_axis[::36])\n",
    "ax.set_xticklabels(x_axis[::36].strftime('%Y-%m-%d'), rotation=45)\n",
    "ax.yaxis.set_major_formatter(mtick.PercentFormatter(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nonprofit-movie",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing the volatility term structure of Apple stock for 5 years into the future\n",
    "A very important notion in pricing options is the _volatility term structure_. It defines the relationship between\n",
    "the maturity of options and their volatilities. In other words it defines what the average volatility for a given maturity is forecast to be. Given the mean reverting nature of volatility, volatility for the longer terms trends towards the mean volatility of a given asset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "complex-contract",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import floor, ceil\n",
    "\n",
    "terms = [x / 100 for x in range(5, 505, 5)]\n",
    "term_vols = [vol_tracker.get_annual_term_volatility_forecast(term) * 100 for term in terms]\n",
    "series = pd.Series(term_vols, index=terms)\n",
    "\n",
    "ax = series.plot(figsize=(20,10), grid=True, kind='bar', title='Term structure of ' + TICKER + ' volatility')\n",
    "ax.set_ylim(bottom=floor(series.min()), top=ceil(series.max()))\n",
    "ax.yaxis.set_major_formatter(mtick.PercentFormatter())\n",
    "ax.set_ylabel('Annual Volatility')\n",
    "_ = ax.set_xlabel('Terms in years')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lined-times",
   "metadata": {},
   "source": [
    "## Pricing using Black-Scholes-Merton Pricer\n",
    "The Black-Scholes-Merton model can be used to price European options, including on stock that pays dividends. With enough customizations it can also be used to price American call options (even those paying dividends). This is based on the fact that it is never optimal to exercise an American call option prematurely except on days immediately preceeding ex-dividend days for the stock. The `pricing.options.BlackScholesMertonPricer` class from this repository implements this customization to price American call options.\n",
    "\n",
    "Let's put it to use to price an AAPL call option with a strike of $180. Apple pays dividends. It's essential to take into account dividends that get payed during the lifetime of an option to get an accurate price.\n",
    "\n",
    "Market makers tend to calculate the life time of options using trading days rather than calendar days. The `pricing.options.BlackScholesMertonPricer` class supports both ways of pricing options. It's determined by the `holidays` parameter of its constructor, passing an array of `datetime64[D]` values implies calculating the life of\n",
    "the option using the number trading days to its expiry and dividing by 252. Not passing a value for this parameter\n",
    "will imply calculating the life of the option using the number of calendar days to its expiry and dividing by a value between 365 and 366. It **does** make an impact of about 3\\%-5\\% on the price of the option depending on its maturity, for longer-dated options the impact is smaller. In the below notebook I price based on the trading\n",
    "calendar of the New-York Stock Exchange. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "other-palmer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-01-17, price: 44.41, σ: 0.2165, Δ: 0.990, Γ: 0.001, ν: 2.656\n"
     ]
    }
   ],
   "source": [
    "strike = 180.\n",
    "\n",
    "# yfinance returns the most recent ex-dividend date in the last row\n",
    "#ticker = yfin.Ticker(TICKER)\n",
    "last_divs = ticker.dividends.iloc[-1:]\n",
    "\n",
    "# An approximate rule for Apple's ex-dividend dates -- ex-dividend date is on the first Friday\n",
    "# of the last month of a season if that Friday is the 5th day of the month or later, otherwise\n",
    "# it falls on the second Friday of that month.\n",
    "idx = (pd.date_range(last_divs.index[0].date(), freq='WOM-1FRI', periods=30)[::3])\n",
    "idx = idx.map(lambda dt: dt if dt.day >= 5 else dt+BDay(5))\n",
    "divs = pd.Series([last_divs.iloc[0]] * len(idx), index=idx, name=TICKER + ' Dividends')\n",
    "\n",
    "# Taking the trading calendar into account when pricing\n",
    "import pandas_market_calendars as mcal\n",
    "holidays = mcal.get_calendar('NYSE').holidays().holidays\n",
    "\n",
    "cur_price = asset_prices.iloc[-1]\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, vol_tracker, strike, curve, cur_price, ticker=TICKER,\n",
    "                                          dividends=divs, opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "clean-dictionary",
   "metadata": {},
   "source": [
    "Sometimes you might want to price using _an implied volatility_ for a given expiry date. You get the implied volatilty from the option prices of market makers. The `pricing.options.BlackScholesMertonPricer` class supports this. Just enter the implied volatility value instead of passing it a volatility_tracker object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "stunning-airfare",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-01-17, price: 46.81, σ: 0.4342, Δ: 0.891, Γ: 0.004, ν: 18.654\n"
     ]
    }
   ],
   "source": [
    "# Pricing with an implied volatility of 43.42% (implied volatility for this contract as of 15th Sep 2023)\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, .4342, strike, curve, cur_price, ticker=TICKER,\n",
    "                                          dividends=divs, opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "inside-skirt",
   "metadata": {},
   "source": [
    "As you can see, a different volatility value resulted in a different price.\n",
    "\n",
    "Let's now price an AAPL call option with a longer maturity. This is a little more complex as there are more ex-dividend dates during the option's lifetime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "norman-error",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 52.98, σ: 0.2165, Δ: 0.890, Γ: 0.004, ν: 44.056\n"
     ]
    }
   ],
   "source": [
    "maturity_date = curve.date + relativedelta(years=1, month=12, day=1, weekday=FR(3))\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, vol_tracker, strike, curve, cur_price, ticker=TICKER,\n",
    "                                          dividends=divs, opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "expressed-amino",
   "metadata": {},
   "source": [
    "If you wonder where the volatility forecast came from, it came from the GARCH(1, 1) `vol_tracker` object I passed to the BlackScholesMertonPricer. You can easily see this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bridal-grave",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21654014947256187"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol_tracker.get_annual_term_volatility_forecast(curve.to_years(maturity_date))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "optical-democracy",
   "metadata": {},
   "source": [
    "## Pricing using Binomial Tree Pricer\n",
    "The Binomial Tree model can be used to price any European or American option, including on stock that pays dividends.\n",
    "\n",
    "Let's put it to use to price an AAPL call and put option with a strike of $180 and compare resulting prices for call options. The constructor of the `BinomialTreePricer` class takes exactly the same parameters as its\n",
    "`BlackScholesMertonPricer` counterpart. I will use it using the trading calendar of the NYSE to calculate\n",
    "the lifetime of options priced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "current-export",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 53.02, σ: 0.2165, Δ: 0.890, Γ: 0.004, ν: 41.432\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers: 0.040067\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve, cur_price, ticker=TICKER,\n",
    "                                             dividends=divs, opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(bin_tree_pricer)\n",
    "\n",
    "print('Price difference between Black-Scholes-Merton and Binomial Treee pricers: %.6f'\n",
    "      % abs(pricer.get_price() - bin_tree_pricer.get_price()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rubber-torture",
   "metadata": {},
   "source": [
    "Let's now price an AAPL put option with the same maturity. You cannot price put options with a `BlackScholesMertonPricer`, with a `BinomialTreePricer` you can."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fitting-hands",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 3.10, σ: 0.2165, Δ: -0.114, Γ: 0.004, ν: 42.618\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer_put = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve, cur_price, is_call=False,\n",
    "                                                 ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                                 holidays=holidays)\n",
    "print(bin_tree_pricer_put)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "executed-front",
   "metadata": {},
   "source": [
    "#### Put-Call Parity\n",
    "An important theoretical property of the price of an American option is the so-called put-call parity, which is expressed as:\n",
    "$$S_0 - D - K <= C - P <= S_0 - K\\cdot e^{-r\\cdot T}$$\n",
    "where:\n",
    "* C is the price of an American call option\n",
    "* P is the price of the corresponding American put option\n",
    "* S<sub>0</sub> is the present price of the underlying stock\n",
    "* D is the present value of the dividents whose ex-dividend dates happen before the maturity date of the option\n",
    "* K is the strike price\n",
    "* T is the liefteime of the option expressed in years\n",
    "* r is the riskless rate for maturity T\n",
    "\n",
    "Let's put it to the test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "apparent-appeal",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 41.69 <= 49.92 <= 51.23\n"
     ]
    }
   ],
   "source": [
    "from math import exp\n",
    "price_difference = bin_tree_pricer.get_price() - bin_tree_pricer_put.get_price()\n",
    "left_hand_side_expr = bin_tree_pricer.s0 - bin_tree_pricer.get_npv_dividends() - bin_tree_pricer.strike\n",
    "right_hand_side_expr = bin_tree_pricer.s0 - bin_tree_pricer.strike * exp(-bin_tree_pricer.r * bin_tree_pricer.T)\n",
    "\n",
    "assert left_hand_side_expr <= price_difference <= right_hand_side_expr\n",
    "print(f'Put-Call parity: {left_hand_side_expr:.2f} <= {price_difference:.2f} <= {right_hand_side_expr:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "roman-leave",
   "metadata": {},
   "source": [
    "If you wish to price with a given implied volatility, just pass it to the pricer as the second parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "owned-dispatch",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 59.34, σ: 0.3297, Δ: 0.817, Γ: 0.003, ν: 63.014\n",
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 9.54, σ: 0.3297, Δ: -0.189, Γ: 0.004, ν: 63.635\n"
     ]
    }
   ],
   "source": [
    "impl_vol = .3297\n",
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, curve, cur_price, ticker=TICKER,\n",
    "                                             dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                             holidays=holidays)\n",
    "print(bin_tree_pricer)\n",
    "bin_tree_pricer_put = options.BinomialTreePricer(maturity_date, impl_vol, strike, curve, cur_price, is_call=False,\n",
    "                                                 ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                                 holidays=holidays)\n",
    "print(bin_tree_pricer_put)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "growing-summer",
   "metadata": {},
   "source": [
    "## Pricing with your own discount curve\n",
    "You might want to prefer to price using your own discount curve. The `YieldCurve` class of the `pricing.curves` package makes it fairly easy to do."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "italian-bermuda",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reusing 'relativedelta' offsets defined in Cell 3, which are for 0, 1 month, 3 months, 6 months, 1 year, 2 years,\n",
    "# 3 years, 5 years, 7 years, 10 years, 20 years, 30 years.\n",
    "\n",
    "# Defining a flat curve with a discount rate of 3% and yearly compounding frequency.\n",
    "custom_curve = curves.YieldCurve(today, offsets, [.03]*len(offsets), compounding_freq=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "helpful-butler",
   "metadata": {},
   "source": [
    "Now pricing with out own flat curve and a given implied volatility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "blind-cotton",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 57.63, σ: 0.3297, Δ: 0.806, Γ: 0.004, ν: 65.293\n",
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 10.18, σ: 0.3297, Δ: -0.197, Γ: 0.004, ν: 65.665\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, custom_curve, cur_price,\n",
    "                                             ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                             holidays=holidays)\n",
    "print(bin_tree_pricer)\n",
    "bin_tree_pricer_put = options.BinomialTreePricer(maturity_date, impl_vol, strike, custom_curve, cur_price,\n",
    "                                                 is_call=False, ticker=TICKER, dividends=divs,\n",
    "                                                 opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(bin_tree_pricer_put)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "958378d4-b16f-4bad-a81e-e624660587ae",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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