SABR_volatility.ipynb

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   "source": [
    "# Calibrating volatility smiles with SABR\n",
    "The SABR model, built in 2002, stands as a key stochastic volatility framework in finance for modeling derivatives. SABR stands for \"stochastic alpha, beta, rho\" which are the key inputs to the model.\n",
    "\n",
    "SABR is good at capturing the market-observed anomalies such as skew and smile.\n",
    "\n",
    "It operates on the premise that asset prices follow a geometric Brownian motion while volatility follows an Ornstein-Uhlenbeck process, parameterized by alpha (initial volatility level), beta (variance elasticity), rho (price-volatility correlation), and nu (volatility's volatility).\n",
    "\n",
    "One of its standout features is the closed-form approximation for implied volatility—known as the Hagan formula—which allows for fast and accurate computations of implied volatility across strike prices."
   ],
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   "source": [
    "# Importing libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from openbb_terminal.sdk import openbb\n",
    "from pysabr import Hagan2002LognormalSABR\n",
    "from pysabr import hagan_2002_lognormal_sabr as sabr\n",
    "from pysabr.black import lognormal_call"
   ],
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     "data": {
      "text/plain": "          contractSymbol optionType  expiration  strike  lastPrice     bid  \\\n0     SPY231106C00340000       call  2023-11-06   340.0      95.13   95.04   \n1     SPY231106C00350000       call  2023-11-06   350.0      80.28   85.04   \n2     SPY231106C00360000       call  2023-11-06   360.0      53.31   75.05   \n3     SPY231106C00370000       call  2023-11-06   370.0      59.15   65.05   \n4     SPY231106C00375000       call  2023-11-06   375.0      59.58   60.06   \n...                  ...        ...         ...     ...        ...     ...   \n5804  SPY260116P00580000        put  2026-01-16   580.0     166.41  142.50   \n5805  SPY260116P00600000        put  2026-01-16   600.0     164.70  162.50   \n5806  SPY260116P00640000        put  2026-01-16   640.0     210.00  219.50   \n5807  SPY260116P00660000        put  2026-01-16   660.0     250.00  222.50   \n5808  SPY260116P00670000        put  2026-01-16   670.0     239.45  232.50   \n\n         ask  openInterest  volume  impliedVolatility  \n0      95.26           2.0    24.0           1.384769  \n1      85.26           2.0     1.0           1.244144  \n2      75.27           1.0     0.0           1.109379  \n3      65.27           1.0     3.0           0.972168  \n4      60.27           4.0     4.0           0.905763  \n...      ...           ...     ...                ...  \n5804  147.50           0.0     0.0           0.123910  \n5805  167.50           1.0     3.0           0.134851  \n5806  224.50           0.0     1.0           0.273689  \n5807  227.50           2.0     2.0           0.164559  \n5808  237.50           0.0     2.0           0.169137  \n\n[5809 rows x 10 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>contractSymbol</th>\n      <th>optionType</th>\n      <th>expiration</th>\n      <th>strike</th>\n      <th>lastPrice</th>\n      <th>bid</th>\n      <th>ask</th>\n      <th>openInterest</th>\n      <th>volume</th>\n      <th>impliedVolatility</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>SPY231106C00340000</td>\n      <td>call</td>\n      <td>2023-11-06</td>\n      <td>340.0</td>\n      <td>95.13</td>\n      <td>95.04</td>\n      <td>95.26</td>\n      <td>2.0</td>\n      <td>24.0</td>\n      <td>1.384769</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>SPY231106C00350000</td>\n      <td>call</td>\n      <td>2023-11-06</td>\n      <td>350.0</td>\n      <td>80.28</td>\n      <td>85.04</td>\n      <td>85.26</td>\n      <td>2.0</td>\n      <td>1.0</td>\n      <td>1.244144</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>SPY231106C00360000</td>\n      <td>call</td>\n      <td>2023-11-06</td>\n      <td>360.0</td>\n      <td>53.31</td>\n      <td>75.05</td>\n      <td>75.27</td>\n      <td>1.0</td>\n      <td>0.0</td>\n      <td>1.109379</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>SPY231106C00370000</td>\n      <td>call</td>\n      <td>2023-11-06</td>\n      <td>370.0</td>\n      <td>59.15</td>\n      <td>65.05</td>\n      <td>65.27</td>\n      <td>1.0</td>\n      <td>3.0</td>\n      <td>0.972168</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>SPY231106C00375000</td>\n      <td>call</td>\n      <td>2023-11-06</td>\n      <td>375.0</td>\n      <td>59.58</td>\n      <td>60.06</td>\n      <td>60.27</td>\n      <td>4.0</td>\n      <td>4.0</td>\n      <td>0.905763</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>5804</th>\n      <td>SPY260116P00580000</td>\n      <td>put</td>\n      <td>2026-01-16</td>\n      <td>580.0</td>\n      <td>166.41</td>\n      <td>142.50</td>\n      <td>147.50</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.123910</td>\n    </tr>\n    <tr>\n      <th>5805</th>\n      <td>SPY260116P00600000</td>\n      <td>put</td>\n      <td>2026-01-16</td>\n      <td>600.0</td>\n      <td>164.70</td>\n      <td>162.50</td>\n      <td>167.50</td>\n      <td>1.0</td>\n      <td>3.0</td>\n      <td>0.134851</td>\n    </tr>\n    <tr>\n      <th>5806</th>\n      <td>SPY260116P00640000</td>\n      <td>put</td>\n      <td>2026-01-16</td>\n      <td>640.0</td>\n      <td>210.00</td>\n      <td>219.50</td>\n      <td>224.50</td>\n      <td>0.0</td>\n      <td>1.0</td>\n      <td>0.273689</td>\n    </tr>\n    <tr>\n      <th>5807</th>\n      <td>SPY260116P00660000</td>\n      <td>put</td>\n      <td>2026-01-16</td>\n      <td>660.0</td>\n      <td>250.00</td>\n      <td>222.50</td>\n      <td>227.50</td>\n      <td>2.0</td>\n      <td>2.0</td>\n      <td>0.164559</td>\n    </tr>\n    <tr>\n      <th>5808</th>\n      <td>SPY260116P00670000</td>\n      <td>put</td>\n      <td>2026-01-16</td>\n      <td>670.0</td>\n      <td>239.45</td>\n      <td>232.50</td>\n      <td>237.50</td>\n      <td>0.0</td>\n      <td>2.0</td>\n      <td>0.169137</td>\n    </tr>\n  </tbody>\n</table>\n<p>5809 rows × 10 columns</p>\n</div>"
     },
     "execution_count": 4,
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     "output_type": "execute_result"
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   ],
   "source": [
    "symbol = \"SPY\"\n",
    "expiration = \"2026-01-16\"\n",
    "spy = openbb.stocks.options.chains(symbol, source=\"YahooFinance\")\n",
    "spy"
   ],
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   "id": "df288ad96f477bf"
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "calls = spy[spy.optionType == \"call\"]\n",
    "jan_2026_c = calls[calls.expiration == expiration].set_index(\"strike\")\n",
    "jan_2026_c[\"mid\"] = (jan_2026_c.ask + jan_2026_c.ask) / 2\n",
    "\n",
    "puts = spy[spy.optionType == \"put\"]\n",
    "jan_2026_p = puts[puts.expiration == expiration].set_index(\"strike\")\n",
    "jan_2026_p[\"mid\"] = (jan_2026_p.ask + jan_2026_p.ask) / 2\n",
    "\n",
    "strikes = jan_2026_c.index\n",
    "vols = jan_2026_c.impliedVolatility * 100"
   ],
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    "ExecuteTime": {
     "end_time": "2023-11-04T15:48:04.987323Z",
     "start_time": "2023-11-04T15:48:04.941518Z"
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   "id": "8bd09eb86dfceef"
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  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "# Fit the SABR model\n",
    "f = (\n",
    "    (jan_2026_c.mid - jan_2026_p.mid)\n",
    "    .dropna()\n",
    "    .abs()\n",
    "    .sort_values()\n",
    "    .index[0]\n",
    ")\n",
    "t = (pd.Timestamp(expiration) - pd.Timestamp.now()).days / 365\n",
    "beta = 0.5"
   ],
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   },
   "id": "64bd7938e59410e0"
  },
  {
   "cell_type": "markdown",
   "source": [
    "Put-call parity defines the relationship between put options, call options, and the forward price of the underlying. The t parameter is the fraction of time until expiration.\n",
    "\n",
    "The beta parameter governs the shape of the forward rate, which influences the shape of the implied volatility smile. A beta of 1 implies a lognormal distribution, which is consistent with the Black-Scholes model. Moving beta away from 1 allows for different shapes of volatility smiles. In practice, setting beta to 0.5 is usually a safe bet.\n",
    "\n",
    "Once we set the parameters, we instantiate the model and call fit to get alpha, rho, and volvol."
   ],
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  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [],
   "source": [
    "\n",
    "sabr_lognormal = Hagan2002LognormalSABR(\n",
    "    f=f,\n",
    "    t=t,\n",
    "    beta=beta\n",
    ")\n",
    "\n",
    "alpha, rho, volvol = sabr_lognormal.fit(strikes, vols)"
   ],
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   "cell_type": "markdown",
   "source": [
    "## Generate a fitted volatility smile\n",
    "\n",
    "Now that we have alpha, rho, and volvol, we can generate the calibrated volatility smile."
   ],
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   "id": "3ceef1850c5f5967"
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  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "calibrated_vols = [\n",
    "    sabr.lognormal_vol(strike, f, t, alpha, beta, rho, volvol) * 100\n",
    "    for strike in strikes\n",
    "]\n",
    "plt.plot(\n",
    "    strikes, \n",
    "    calibrated_vols\n",
    ")\n",
    "\n",
    "plt.xlabel(\"Strike\")\n",
    "plt.ylabel(\"Volatility\")\n",
    "plt.title(\"Volatility Smile\")\n",
    "plt.plot(strikes, vols)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-04T15:49:44.503920Z",
     "start_time": "2023-11-04T15:49:44.301567Z"
    }
   },
   "id": "d2da07fa37b3b65c"
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: xlabel='strike'>"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can assess the model error as well.\n",
    "black_values = []\n",
    "for strike, calibrated_vol in zip(strikes.tolist(), calibrated_vols):\n",
    "    black_value = lognormal_call(\n",
    "        strike, \n",
    "        f, \n",
    "        t, \n",
    "        calibrated_vol / 100, \n",
    "        0.05, \n",
    "        cp=\"call\"\n",
    "    )\n",
    "    black_values.append(black_value)\n",
    "\n",
    "\n",
    "option_values = pd.DataFrame(\n",
    "    {\n",
    "        \"black\": black_values,\n",
    "        \"market\": jan_2026_c.mid\n",
    "    },\n",
    "    index=strikes\n",
    ")\n",
    "\n",
    "\n",
    "(option_values.black - option_values.market).plot.bar()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-04T15:50:25.125302Z",
     "start_time": "2023-11-04T15:50:24.235646Z"
    }
   },
   "id": "6b9385f2fe35d39d"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "3be87bd5ab1bddb4"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}