vol_plot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy import sqrt,mean,log,diff\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n",
    "import yfinance as yf # https://github.com/ranaroussi/yfinance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook calculates volatility curves $\\sigma (K, T)$ of an option whose value satisfies $V_t(S, K, T) = BS(S_t, \\sigma, K, T)$. We start from the Black-Scholes assumption of Brownian motion $dS_t=\\mu S_t dt + \\sigma S_t dW_t$ with the volatility $\\sigma$ as the diffusion term and constant interest rates. We opt for a self-financing strategy. Solving the resulting PDE for the option's value $V_t(S, K, T)$ with boundary conditions for a call/push option, we obtain the solution returned by bsm_price.\n",
    "\n",
    "From there, we solve for the volatility $\\sigma(K, T)$ which, when substituted into the Black-Scholes expression, yields the previously obtained solution for the price. We use a simple bisection method to minimise the discrepancy of an option_price from data and the bsm_price calculated using an adjusted volatility. Option chain data is gained from Yahoo Finance using the yfinance library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bsm_price(option_type, sigma, s, k, r, T, q):\n",
    "    # calculate the BS price of European call and put options\n",
    "    sigma = float(sigma)\n",
    "    d1 = (np.log(s / k) + (r - q + sigma ** 2 * 0.5) * T) / (sigma * np.sqrt(T))\n",
    "    d2 = d1 - sigma * np.sqrt(T)\n",
    "    if option_type == 'c':\n",
    "        price = np.exp(-r*T) * (s * np.exp((r - q)*T) * stats.norm.cdf(d1) - k *  stats.norm.cdf(d2))\n",
    "        return price\n",
    "    elif option_type == 'p':\n",
    "        price = np.exp(-r*T) * (k * stats.norm.cdf(-d2) - s * np.exp((r - q)*T) *  stats.norm.cdf(-d1))\n",
    "        return price\n",
    "    else:\n",
    "        print('No such option type %s') %option_type\n",
    "        \n",
    "def implied_vol(option_type, option_price, s, k, r, T, q):\n",
    "    # implementation based on https://www.quantconnect.com/tutorials/introduction-to-options/historical-volatility-and-implied-volatility\n",
    "    if np.isnan(option_price): return np.nan\n",
    "    \n",
    "    # apply bisection method to get the implied volatility by solving the BSM function\n",
    "    precision = 1e-6 #1e-5\n",
    "    upper_vol = 500.0\n",
    "    max_vol = 500.0\n",
    "    min_vol = 0.0001\n",
    "    lower_vol = 0.0001\n",
    "    iteration = 0\n",
    "\n",
    "    while 1:\n",
    "        iteration += 1\n",
    "        mid_vol = (upper_vol + lower_vol) / 2.0\n",
    "        price = bsm_price(option_type, mid_vol, s, k, r, T, q)\n",
    "            \n",
    "        if option_type == 'c':\n",
    "            lower_price = bsm_price(option_type, lower_vol, s, k, r, T, q)\n",
    "            if (lower_price - option_price) * (price - option_price) > 0:\n",
    "                lower_vol = mid_vol\n",
    "            else:\n",
    "                upper_vol = mid_vol\n",
    "            if abs(price - option_price) < precision: break \n",
    "            if mid_vol > max_vol - 5 :\n",
    "                mid_vol = 0.000001\n",
    "                break\n",
    "\n",
    "        elif option_type == 'p':\n",
    "            upper_price = bsm_price(option_type, upper_vol, s, k, r, T, q)\n",
    "\n",
    "            if (upper_price - option_price) * (price - option_price) > 0:\n",
    "                upper_vol = mid_vol\n",
    "            else:\n",
    "                lower_vol = mid_vol\n",
    "            if abs(price - option_price) < precision: break \n",
    "            if iteration > 50: break\n",
    "\n",
    "    return mid_vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#implied_vol('c', 0.3, 3, 3, 0.032, 30.0/365, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IV_plot(opt, option_type, s, expiry_index): # s: underlying price\n",
    "    opt = opt.reset_index()\n",
    "    opt = opt[opt[\"expiry\"] == opt[\"expiry\"][expiry_index]]\n",
    "    data = opt.set_index(['expiry', 'strike'])\n",
    "        \n",
    "    r = 0.01 # risk free rate\n",
    "    d = 0.01 # continuous dividend yield\n",
    "    expiry = data.index.get_level_values('expiry')[0] # get the expiry\n",
    "    current_date = datetime.now() # get the current date\n",
    "    time_to_expire = float((expiry - current_date).days)/365 # compute time to expiration\n",
    "    premium = (data['ask'] + data['bid'])/2 # option premium\n",
    "    strike = list(data.index.get_level_values('strike')) # get the strike price\n",
    "    IV = []\n",
    "    for i in range(len(data)):\n",
    "        IV.append(implied_vol(option_type, premium.values[i], s, strike[i], r, time_to_expire, d))\n",
    "\n",
    "    plt.figure(figsize=(16, 7))\n",
    "    a = plt.scatter(strike, IV, c='r', label=\"IV by solving BSM\")\n",
    "    b = plt.scatter(strike, data['impliedVolatility'], c='b', label=\"IV from Yahoo Finance\")\n",
    "    plt.grid()\n",
    "    plt.xlabel('strike')\n",
    "    if option_type == 'c':\n",
    "        plt.ylabel('Implied Volatility for call option')\n",
    "        plt.legend((a, b), (\"IV(call) by solving BSM\", \"IV(call) from Yahoo Finance\"))\n",
    "    elif option_type == 'p':\n",
    "        plt.ylabel('Implied Volatility for put options')\n",
    "        plt.legend((a, b), (\"IV(put) by solving BSM\", \"IV(put) from Yahoo Finance\"))\n",
    "\n",
    "    return strike, IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock = yf.Ticker(\"aapl\") # e.g. aapl, spy\n",
    "s = (stock.history().tail(1)['Close'].iloc[0]) # current underlying price\n",
    "\n",
    "DF_calls, DF_puts = stock.option_chain(stock.options[0])\n",
    "DF_calls['expiry'], DF_puts['expiry'] = datetime.strptime(stock.options[0], '%Y-%m-%d'), datetime.strptime(stock.options[0], '%Y-%m-%d')\n",
    "for expiryDate in stock.options[1:]:\n",
    "    # add current expiry date to dataframe\n",
    "    calls, puts = stock.option_chain(expiryDate)\n",
    "\n",
    "    # add expiryDate column, append to DF_calls, DF_puts\n",
    "    calls['expiry'], puts['expiry'] = datetime.strptime(expiryDate, '%Y-%m-%d'), datetime.strptime(expiryDate, '%Y-%m-%d')\n",
    "    DF_calls, DF_puts = DF_calls.append(calls), DF_puts.append(puts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21d0a01bac0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tW6ahQ4fq1ltvVVdXl1atWqVly5b1xvfee+9p+vTpeuaZZ3TSSSf1JveLFy/W+eefrzVr1igSieiyyy4L3L63O++8s3fo8m233bbP/j/84Q967LHHdP/99/f29A4bNkz33nuvnnrqKXV0dOiKK66Qu0uSXnnlFV1yySV6/vnndeCBB+qnP/2pJCkSieiSSy7RM888o9/97nc67LDD9NBDD+mVV17RE088oaefflpdXV169NFHU/53zBWJLgAAAICkliyREkb+SoquL1mSv3vEe3V37dqllStX6uyzz5YUTbYOOeSQPseeccYZGj58uEaPHq2mpiY98cQTWd/v0EMPDUyQ4z7xiU9o1KhRkqTHHntM8+fPlySdfPLJ2rRpk7Zs2SJJmjNnjoYMGaJJkyZp9+7dmj17tiRp0qRJ6k7xaNFLLrlERxxxRG9P87Jly3p7bd944w298sorkqShQ4f29lY3NDT0Xu/xxx/XZz/7WUnR4diPPfZY4Pa9JQ5dvvDCC/fZf+aZZ6qqqkrHHntsby+yu+urX/2q6uvrdcopp+jNN9/s3Tdu3DhNmTKlT5xbt27Vm2++qbPOOktSNFGurq7WQw89pIceekjHHXecpk6dqpdeeqn3/eYTz9EFAAAAkFSqka8ZjojNyLx58zRr1izNmDFD9fX1OvTQQyVJw4cP144dO/oca2b7rA8ePFg9PT292/Y+Z287duzQ8OHD08a133779f4c77lMFsuHPvQhSVJVVZWGDBnSu72qqirl/N6qqipVVUX7HDs7O/Xwww/r8ccfV3V1tRobG3vfQ+L1Bg0alPJ6e/9e0m1PJ/6epD3vva2tTW+//ba6uro0ZMgQ1dXV9caZePygQYP05z//OenvLH69q6++WhdddFFOsWWKHl0AAAAASdXUZLc9F0cffbQOPvhgXXXVVb3DliVpwoQJWrt2bZ9jV65cqR07dmjTpk3q7OzU8ccfr9raWr3wwgvauXOntmzZokceeaT3+JEjR2rr1q296+6uP/7xj6qrq8sqxpNOOkltsfHanZ2dGj16tPbff/8c3u2+tmzZooMOOkjV1dV66aWX9Pvf/z7tOR//+Md75za3tbXpxBNPDNyerzgPPfRQDRkyRB0dHVq3bl3g8fvvv7/Gjh2rn/3sZ5KknTt3avv27Tr11FN16623atu2bZKkN998U2+99Vbe4oyjRxcAAABAUi0t0Tm5icOXq6uj2/Np3rx5uvrqq3uHuUrSMcccoy1btmjr1q0aOXKkJOmEE07Qpz71Ka1fv15f+9rXdPjhh0uSzjnnHNXX12v8+PE67rjjeq/R3NysOXPm6LDDDlNHR4e6uro0ffp0DR6cXRp07bXX6sILL1R9fb2qq6t1++235+FdR82ePVu33HKL6uvr9eEPf1jTp09Pe86yZcv0+c9/XjfeeKMOOeSQ3nm2qbbnQyQS0emnn65p06ZpypQpOuaYY9Ke86Mf/UgXXXSRrrnmGg0ZMkR33XWXZs2apRdffFEf+9jHJEUfoXTHHXf09uTni6XqUi5H06ZN81WrVhU7jJQ6OzvV2NhY7DBQRmgzyBZtBrmg3SBbtJny9uKLL2rChAkZH9/WFp2Tu359tCe3pUWKRLK7Z2Kymo1vfetbGjlypBYuXKhrr71WI0aM0JVXXpn1deIuv/xyzZ07VzNnzsz5GiiM1atX9/mjhSSZWZe7T8vkfIYuDzRh1ocHAABAxYlEpO5uqacn+pptktsfF198cZ/5n/01ceJEktwBgqHLA0m8Pnx87Em8PrxU2E8sAAAAIAPDhg3rrXZ87bXX9vt6ixYt6vc1UB7o0R1IClEfHgAAACWvkqYvovLko32S6A4khagPDwAAgJI2bNgwbdq0iWQXJcndtWnTJu3evbtf12Ho8kBSUxMdrpxsOwAAAAaEsWPHasOGDXr77bcLds8dO3Zo2LBhBbsfytuwYcP03nvv9esaoSW6ZnarpNMkveXuE5Ps/5Kk+MTQwZImSDrE3TebWbekrZJ2S9qVaWUtpFGo+vAAAAAoWUOGDNG4ceMKes/Ozs59KugCQdI9pzedMIcuL5c0O9VOd7/R3ae4+xRJV0v6jbtvTjikKbafJDdfIhGptVWqrZXMoq+trRSiAgAAAFBRQuvRdfdHzawuw8PnSVoRVixIEImQ2AIAAACoaBbmJPRYont/sqHLCcdUS9og6X/Fe3TN7HVJ70hySd9399aA85slNUvSmDFjGtrb2/MWf75t27ZNI0aMKHYYKCO0GWSLNoNc0G6QLdoMskWbQbaStZmmpqauTEf8lkIxqtMl/XavYct/5e4bzexQSb8ys5fc/dFkJ8eS4FZJmjZtmjc2NoYecK46OztVyvGh9NBmkC3aDHJBu0G2aDPIFm0G2epvmymFxwudp72GLbv7xtjrW5LulXRCEeICAAAAAJShoia6ZnaApBmSViZs28/MRsZ/ljRL0nPFiRAAAAAAUG7CfLzQCkmNkkab2QZJSyUNkSR3vyV22FmSHnL3xIckjZF0r5nF4/uxu/9HWHECAAAAACpLmFWX52VwzHJFH0OUuO01SZPDiQoAAAAAUOlKYY4uAAAAAAB5Q6ILAAAAAKgoJLoAAAAAgIpCogsAAAAAqCgkugAAAACAikKiCwAAAACoKCS6AAAAAICKQqILAAAAAKgoJLoAAAAAgIpCogsAAAAAqCgkugAAAACAikKiCwAAAACoKCS6AAAAAICKQqILAAAAAKgoJLoAAAAAgIpCogsAAAAAqCgkugAAAACAikKiCwAAAACoKCS6AAAAAICKQqILAAAAAKgoJLoAAAAAgIpCogsAAAAAqCgkugAAAACAikKiCwAAAACoKCS6AAAAAICKQqJbAG1tUl2d1NUVfW1rK3ZEAAAAAFC5Bhc7gErX1iY1N0vbt0fX162LrktSJFK8uAAAAACgUtGjG7IlS/YkuXHbt0e3AwAAAADyj0Q3ZOvXZ7cdAAAAANA/JLohq6nJbjsAAAAAoH9IdEPW0iJVV/fdVl0d3Q4AAAAAyD8S3ZBFIlJrq1RbG12vrY2uU4gKAAAAAMJB1eUCiESiS2en1N1d7GgAAAAAoLLRowsAAAAAqCgkugAAAACAikKiCwAAAACoKCS6AAAAAICKElqia2a3mtlbZvZciv2NZrbFzJ6OLdck7JttZi+b2VozuyqsGAeitjaprk6qqoq+trUVOyIAAAAAyK8wqy4vl/RdST8MOOY/3f20xA1mNkjS9yR9QtIGSU+a2X3u/kJYgQ4UbW1Sc7O0fXt0fd266LrE444AAAAAVI7QenTd/VFJm3M49QRJa939NXd/X1K7pDPyGtwAtWTJniQ3bvv26HYAAAAAqBTm7uFd3KxO0v3uPjHJvkZJP1W013ajpCvd/Xkz+4yk2e6+MHbcfEkfdffFKe7RLKlZksaMGdPQ3t4ewjvJj23btmnEiBFFu39XV+p9DQ2FiwOZK3abQfmhzSAXtBtkizaDbNFmkK1kbaapqanL3adlcn6YQ5fTeUpSrbtvM7NPSvqZpPGSLMmxKbNxd2+V1CpJ06ZN88bGxhBCzY/Ozk4VM74FC6LDlfdWWyt1dxc6mpi2tmiX8vr1Uk2N1NLCOOoExW4zKD+0GeSCdoNs0WaQLdoMstXfNlO0qsvu/q67b4v9/KCkIWY2WtEe3iMTDh2raI8v+qmlRaqu7rutujq6vSjik4bXrZPc90wapkIWAAAAgH4oWqJrZn9hZhb7+YRYLJskPSlpvJmNM7Ohks6TdF+x4qwkkYjU2hrtwTWLvra2FrEDlUnDAAAAAEIQ2tBlM1shqVHSaDPbIGmppCGS5O63SPqMpIvNbJekP0s6z6MThneZ2WJJv5Q0SNKt7v58WHEONJFICY0MXr8+u+0AAAAAkIHQEl13n5dm/3cVffxQsn0PSnowjLhQQmpqkk8arqkpfCwAAAAAKkbRhi4DpTdpGAAAAEAlINFF8ZTcpGEAAAAAlaCYjxcCSmzSMAAAAIBKQI8uAAAAAKCikOgCAAAAACoKiS4AAAAAoKKQ6AIAAAAAKgqJLgAAAACgopDoAgAAAAAqCokuAAAAAKCikOgCAAAAACoKiS4AAAAAoKKQ6AIAAAAAKgqJLgAAAACgopDoAgAAAAAqCokuAAAAAKCikOgCAAAAACoKiS4AAAAAoKJkleia2UFmVh9WMAAAAAAA9FfaRNfMOs1sfzMbJekZSbeZ2T+HHxoAAAAAANnLpEf3AHd/V9KnJd3m7g2STgk3LAAAAAAAcpNJojvYzA6TdI6k+0OOBwAAAACAfskk0b1O0i8lrXX3J83sKEmvhBsWAAAAAAC5GZzuAHe/S9JdCeuvSfqbMIMCAAAAACBXaRNdMztE0iJJdYnHu/vnwwsLAAAAAIDcpE10Ja2U9J+SHpa0O9xwAAAAAADon0wS3Wp3/0rokQAAAAAAkAeZFKO638w+GXokAAAAAADkQSaJ7uWKJrs7zGxrbHk37MAAAAAAAMhFJlWXRxYiEAAAAAAA8iGTOboys7mSToqtdrr7/eGFBAAAAABA7tIOXTazGxQdvvxCbLk8tg0oO21tUl2dVFUVfW1rK3ZEAAAAAPItkx7dT0qa4u49kmRmt0taLemqMAMD8q2tTWpulrZvj66vWxddl6RIpHhxAQAAAMivTIpRSdKBCT8fEEYgQNiWLNmT5MZt3x7dDgAAAKByZNKj+w1Jq82sQ5IpOlf36lCjAkKwfn122wEAAACUp0yqLq8ws05Jxyua6H7F3f8YdmBAvtXURIcrJ9sOAAAAoHKkHLpsZsfEXqdKOkzSBklvSDo8tg0oKy0tUnV1323V1dHtAAAAACpH0Bzdv4u9/lOS5aZ0FzazW83sLTN7LsX+iJmtiS2/M7PJCfu6zexZM3vazFZl/G5QdgpZBTkSkVpbpdpaySz62tpKISoAAACg0qQcuuzusXq0muPuOxL3mdmwDK69XNJ3Jf0wxf7XJc1w93fMbI6kVkkfTdjf5O5/yuA+KFPFqIIciZDYAgAAAJUuk6rLv8twWx/u/qikzQH7f+fu78RWfy9pbAaxoIJQBRkAAABAGMzdk+8w+wtJR0i6Q9JnFS1EJUn7S7rF3Y9Je3GzOkn3u/vENMddKekYd18YW39d0juSXNL33b014NxmSc2SNGbMmIb29vZ0YRXNtm3bNGLEiGKHUTK6ulLva2goXByljDaDbNFmkAvaDbJFm0G2aDMlbvNm6c03pfffl4YOlY44Qho1qqghJWszTU1NXe4+LZPzg6ounyppgaI9rf+csH2rpK9mF2ZqZtYk6X9LOjFh81+5+0YzO1TSr8zspVgP8T5iSXCrJE2bNs0bGxvzFVredXZ2qpTjK7QFC5JXQa6tlbq7Cx1NaaLNIFu0GeSCdoNs0WaQLdpMCdt7PqEUrdha5GI2/W0zKYcuu/vt7t4kaYG7NyUsc939npzvmMDM6iX9m6Qz3H1Twr03xl7fknSvpBPycT+UFqogAwAAAEVWofMJM5mj22lmy8zsKTPrMrN/MbOD+3tjM6uRdI+k+e7+Xwnb9zOzkfGfJc2SlLRyM8pbOVVBLmR1aAAAAKBg1q/PbnuZCBq6HNcu6VFJfxNbj0i6U9IpQSeZ2QpJjZJGm9kGSUslDZEkd79F0jWSDpZ0s5lJ0q7YeOsxku6NbRss6cfu/h9ZvSuUjXKoglyM6tAAAABAQdTUJJ9PWFNT+FjyKJNEd5S7/33C+j+Y2ZnpTnL3eWn2L5S0MMn21yRN3vcMoDiCRnOQ6AIAAKCstbQkn6Nb5vMJMxm63GFm55lZVWw5R9IDYQcGlIoKHc0BAAAAlNd8wixk0qN7kaS/U/QxQ1I0OX7PzP5Okrv7/mEFB5SCCh3NAQAAAESVw3zCLKXt0XX3ke5e5e6DY0tVbNtIklwMBOmqQ1OoCgAAACgtmfToyszmSjopttrp7veHFxJQWuJ/3FqyJDpcuaYmmuRGIhSqAgAAAEpR2h5dM7tB0uWSXogtl8e2AQNGJCJ1d0s9PdHXxOS3Ah87BgAAAJS1THp0Pylpirv3SJKZ3S5ptaSrwgwMKAcUqgIAAABKTyZVlyXpwISfDwgjEKAcpSpIRaEqAAvamhcAACAASURBVAAAoHgySXS/IWm1mS2P9eZ2Sbo+3LCA8pCuUBUAAACAwsuk6vIKSdMl3RNbPubu7WEHBpSDdI8doyIzAAAAUHgZDV129z+4+33uvtLd/xh2UEA5SVWoKl6Red06yX1PRWaSXQAAANAjEq5M5+gCyBIVmQEAAJAUPSKhI9EFQkJFZgAAACRFj0joMnmO7o8y2QagLyoyAwAAICl6REKXSY/uRxJXzGyQpIZwwgEqBxWZAQAAkBQ9IqFLmeia2dVmtlVSvZm9G1u2SnpL0sqCRQiUqXQVmQEAADBA0SMSusGpdrj7NyR9w8y+4e5XFzAmoGJEIiS2AAAA2Ev8C+KSJdHhyjU10SSXL455kzLRTfALMztp743u/mgI8QAAAABA5aNHJFSZJLpfSvh5mKQTJHVJOjmUiAAAAAAA6Ie0ia67n564bmZHSvpmaBEBAAAAANAPuTxHd4OkifkOBAAAAACAfEjbo2tm35HksdUqSVMkPRNmUAAAAAAA5CqTObqrEn7eJWmFu/82pHgAAAAAAOiXTObo3m5mQyUdo2jP7suhRwUAAAAAQI4yGbr8SUnfl/SqJJM0zswucvdfhB0cAAAAAADZyqQY1T9LanL3RnefIalJ0rfCDQtALtrapLo6qaoq+trWVqk3BQAAAFLLZI7uW+6+NmH9NUlvhRQPgBy1tUnNzdL27dH1deui61KIzyIvyk0BAACAYJn06D5vZg+a2QIzu0DSzyU9aWafNrNPhxwfgAwtWbIn34zbvj26vbJuCgAAkANGoQ0omSS6wyT9t6QZkholvS1plKTTJZ0WWmQAkkr1Gb1+ffLjU23Pi6LcFAAAIEvxUWjr1knue0ahkexWrEyqLl9YiECAgaatLdrxuX69VFMjtbSkH+0bNFK4pia6vreamvzGvc/FC35TAACALAWNQmO6VUXKpEcXQJ7l+kfFoM/olhapurrvvurq6PbQFOWmAAAAWWIU2oBDogsUQa5TW4M+oyMRqbVVqq2VzKKvra0h/5GyKDcFAADIUqrRZoxCq1iBia6ZVZnZOYUKBhgocv2jYrrP6EhE6u6WenqirwXJN4tyUwAAgCwwCm3ACUx03b1H0uICxQIMGLn+UbFfn9FUGgQAAAMVo9AGnEyGLv/KzK40syPNbFR8CT0yoILlmrDm/BlNpUEAADDQMQptQElbdVnS52OvlyRsc0lH5T8cYGCIf65mW3U5fm7Wn8tUGgQAAMAAksnjhcYVIhBgoMkpYc0VlQYBAAAwgKRNdM1siKSLJZ0U29Qp6fvu/kGIcQHIJ553CwAAgAEkkzm6/yqpQdLNsaUhti2Qmd1qZm+Z2XMp9puZLTOztWa2xsymJuybbWYvx/ZdldlbAZBSJpOCKVYFAAAwIFXi18BM5uge7+6TE9Z/bWbPZHDecknflfTDFPvnSBofWz6qaPL8UTMbJOl7kj4haYOkJ83sPnd/IYN7Akgm3aTgeLGq+DzeeLGqxHMBAABQcSr1a2AmPbq7zezo+IqZHSVpd7qT3P1RSZsDDjlD0g896veSDjSzwySdIGmtu7/m7u9Lao8dC6A/gioNBhWrAgAAQMWq1K+B5u7BB5jNlHSbpNckmaRaSRe6e0fai5vVSbrf3Scm2Xe/pBvc/bHY+iOSviKpTtJsd18Y2z5f0kfdPenzfM2sWVKzJI0ZM6ahvb09XVhFs23bNo0YMaLYYaCMFKzNdHWl3tfQEP79kTd8ziAXtBtkizaDbNFmSlepfg1M1maampq63H1aJuenHLpsZme7+12KJrjjJX1Y0UT3JXffmXvIe26RZJsHbE/K3VsltUrStGnTvLGxMQ+hhaOzs1OlHB9KT8HazIIFyYtV1dZGe39RNvicQS5oN8gWbQbZos2UrlL9GtjfNhM0dPnq2OtP3X2nu69x92fylORK0fm3Ryasj5W0MWA7gLBkUqwKAAAAFadSvwYGJbqbzKxD0jgzu2/vJQ/3vk/S+bHqy9MlbXH3P0h6UtJ4MxtnZkMlnRc7FkBYIhGptTX6pzuz6Gtra99iVZVWig8AAABpvwaWq6Cqy5+SNFXSjyT9U7YXNrMVkholjTazDZKWShoiSe5+i6QHJX1S0lpJ2yVdGNu3y8wWS/qlpEGSbnX357O9P4AsRSLJP9EqtRQfAAAAJKX+GljOUia6sYrHvzezj7v729le2N3npdnvki5Jse9BRRNhAMUWVIqv0j4RAQAAUBHSPl4olyQXQAVZvz677QAAAECRZfIcXQADWU1NdtsBAACAIkub6JrZqEIEAqBEVWopPgAAgCKi1me4MunR/X9mdpeZfdLMkj3jFkAlq9RSfAAAAEUSr/W5bp3kvqfWJ8lu/mSS6P6lpFZJ8yWtNbPrzewvww0LQEmJRKJPDO/pib6S5AIAAOQsqNYn8iOTYlTu7r+KVVFeKOkCSU+Y2W/M7GOhRwgAAAAAFYRan+HLZI7uwWZ2uZmtknSlpEsljZZ0haQfhxwfAAAAAFQUan2GL5Ohy49L2l/Sme7+KXe/x913ufsqSbeEGx4AAAAAVBZqfYYvk0T3/7r737v7hvgGMztbktz9H0OLDEBZoGIgAABAdqj1Gb5MEt2rkmy7Ot+BACg/aSsGhpEFk1kDAIAKQK3PcKVMdM1sjpl9R9IRZrYsYVkuaVfBIgRQsgIrBvanbn6qZJZa/AAAAMhAUI/uRkmrJO2Q1JWw3Cfp1PBDA1DqAisG5lo3PyiZpRY/AAAAMjA41Q53f0bSM2bW5u704ALYR01NNA9Ntj3nuvlBySy1+AEAAJCBoKHLP4n9uNrM1uy9FCg+ACUssGJgrnXzg5JZavEDAAAgA0FDly+PvZ4m6fQkC4AyEkYNp8CKgenq5qcKKCiZpRY/AAAAMpAy0XX3P8Re1yVbChcigP4Ks4ZTyoqBQVlwUEBByWy6WvxUZAYAACnwNWFgSTlH18y2SvJkuyS5u+8fWlQA8ipo2muopewjkeQ3CAqou3vPMfHhyvEkN+ia8eQ5ft148hw/BwAADFh8TRh4gnp0R7r7/kmWkSS5QHkpuRpO6QLK5cFyVGQGAAAp8DVh4AkqRrV/7HVUsqVwIQLor5Kr4RRGQCWXzQMAgFLB14SBJ6gY1Y9jr12KPk838Vm6q0KOC0AeZVLDqaDzVsIoKlVy2TwAACgVfE0YeIKGLp8Wex3n7kfFXuPLUYULEUB/ZVLDKaxiVTkFlAsqMgMAgBT4mjDwBPXoSpLM7JFMtgEobUHTXosybyWXebjprpfv5FmiRCMAABUgrK8JKF1BVZeHSaqWNNrMDlK02rIk7S/p8ALEBqBAKmbeSqqKzLmiRCMAABUj318TUNqCenQvUnQ+7jHqOz93paTvhR8agEJh3koKlGgEAAAoS0FzdP/F3cdJunKvObqT3f27BYwRQMiYt5JCxXR1AwAADCxp5+i6+3fMbKKZnWNm58eXQgQHoDAyKVY1IKep0tUNAABQllLO0Y0zs6WSGiUdK+lBSXMkPSbph6FGBqCgUs1bGdDTVFta+r55ia5uAACAMpC2R1fSZyTNlPRHd79Q0mRJHwo1KgAlo2KmqQZ1S6faR4lGAACAspS2R1fSn929x8x2mdn+kt6SxHN0gQGiIqapBnVLS8Fd1pRoBAAAKDuZJLqrzOxAST9QtOryNklPhBoVgJJRUxPN/ZJtLxvpuqVT7SPBBQAAKEuZFKP6P+7+P+5+i6RPSLogNoQZwABQERWZg7ql+9NlPWCrdAEAAJS2lD26ZjY1aJ+7PxVOSABKSbxTc8mSaO5XUxNNcsuqszNdt3QuXdYDukoXAABAaQsauvxPAftc0sl5jgVAiSr7aarpqifnUlk5aDh0Wf+yAABZa2sr878IA5UnZaLr7k2FDAQAQpNJt3S2X1AqokoXAKDfGOEDlKS0c3TNbIiZXWZmd8eWxWY2pBDBARiYcnkSUFqRiNTdLfX0RF8Tv3wE7Usl1dDmsqrSBQDot4p5Dh9QWTKpuvyvkoZIujm2Pj+2bWFYQQEYuPrzJKCCSjccGgAwMDDCByhJaXt0JR3v7he4+69jy4WSjg87MAADU9Afxkvqj+aRiNTaKtXWSmbR19bWPRk3FZkBYGBghA9QkjJJdHeb2dHxFTM7StLuTC5uZrPN7GUzW2tmVyXZ/yUzezq2PGdmu81sVGxft5k9G9u3KtM3BKB05JLrhfUkoFCkGvIc75Zet05y39P1TLILAJWnIp7DB1SeTBLdL0nqMLNOM/uNpF9LuiLdSWY2SNL3JM2RdKykeWZ2bOIx7n6ju09x9ymSrpb0G3ffnHBIU2z/tAzfD4ASkWuuF/SH8bL5o3lJdT0DAEKVboQPgKJImeia2QNmFpH0e0njJV0WWz7s7h0ZXPsESWvd/TV3f19Su6QzAo6fJ2lFxpEDKGm55npBfxgvmz+al1zXMwAgVLkUNQQQKnP35DvMzpB0nqSZkjoUTUIfjCWt6S9s9hlJs919YWx9vqSPuvviJMdWS9og6X/Fe3TN7HVJ7yj6zN7vu3trivs0S2qWpDFjxjS0t7dnEl5RbNu2TSNGjCh2GCgj5dxmurpS72tokDZvlt58U3r/fWnoUOmII6RRo6L7w9hXUM8+Gw1ib0OHSpMmhXrrcm4zKB7aDbJFm0G2aDPIVrI209TU1JXpaN+g5+iulLTSzIZLmivpAkm3mNmDkla4+6/SXNuSXTbFsadL+u1ew5b/yt03mtmhkn5lZi+5+6NJ4myV1CpJ06ZN88bGxjRhFU9nZ6dKOT6UnnJuMwsWRIcr7622NnXB4v6M9Nq7WnM+rpmzN99MHUzI/z3Luc2geGg3yBZtBtmizSBb/W0zaefouvuf3f1Odz9L0ixJx0n6jwyuvUHSkQnrYyVtTHHsedpr2LK7b4y9viXpXkWHQgMoE0HDjMOYwlpS02KpyAwAAFBUaRNdMxtjZpea2W8l/UzSQ5IaMrj2k5LGm9k4MxuqaDJ7X5LrHyBphqSVCdv2M7OR8Z8VTbCfy+CeAEpEUK4XxhTWkpsWS0VmAACAokk5dNnMFilaIOrDku6R9GV3/22mF3b3XWa2WNIvJQ2SdKu7P29mX4jtvyV26FmSHnL39xJOHyPpXjOLx/hjd8+kFxlACYlEkg8brqlJPqy5P9WTw7hmKIK6nileAgAAkBdBPbofl3SDpCPd/dJsktw4d3/Q3f/S3Y9295bYtlsSkly5+3J3P2+v815z98mx5SPxcwFUhjCqJ4dVkTnvo4xLrusZAACg8qRMdN39Qnd/yN17ChkQgMoXxiMHw7hmKKOMy+ZhwAAAAOUr7RxdAAhDGI8czPc1Qylw1Z+u56Du5fi+ri4KXAEAgAGPRBcAUghllHGuFZmDupcT90kUuAIAAANeUDGqUUEn7vXMWwCoOKEVuEpVpWvvhwHHE1YpffcyBa4AAAB6BfXodklaFXt9W9J/SXol9nNX+KEBQGGk6kQNq8BVSkHJbFD3MgWuAAxEPJMcQICgYlTj3P0oRR8PdLq7j3b3gyWdpujjhgCgbOQyIjiMAleBghLWoCJWFLgCMNDwTHIAaWQyR/d4d38wvuLuv5A0I7yQACC/gr4PpRsRHFTgKu+dCUEJa1D3csG7ngGgyEKpFgigkmSS6P7JzP6vmdWZWa2ZLZG0KezAACBfch0RHCSUzoSghDWoezlxn1SArmcAKDKmbABII5NEd56kQyTdG1sOiW0DgLKQ64jgIKF0JqQbKx3UvRzf19CQ/NlKzGUDUEmYsgEgjbSJrrtvdvfLJf21u0919y9ScRlAOcl1RHCQ0DoTwnjAMHPZAFQapmwASCNtomtmHzezFyS9EFufbGY3hx4ZAORJriOCg5RVZwJz2QBUmoJXCwRQbjIZuvwtSacqNi/X3Z+RdFKYQQFAPvVnRHAq6ToTSmqkcLru55IKFgAyFMYImBzxMQqUnsGZHOTub5hZ4qbd4YQDAOGI12zK5/WkPQWt4sOgI5E9I4XjnajxkcKJ5xVUTU00iGTbSy5YACgvfIwCpSmTHt03zOzjktzMhprZlZJeDDkuACh5qToTSm6kcFD3c7pg6aYAgEAl95kPQFJmie4XJF0i6QhJGyRNia0DAJIouadeBI3dDgqWIlYAkFbJfeYDkJRZ1eU/uXvE3ce4+6Hu/jl35zm6AJBCSRaqStX9HBQs3RQAkFZJfuYDSJ3omtmXY6/fMbNley+FCxEAyktZPfUiKFi6KQAgrbL6zAcGkKAe3fg83FWSupIsAIAk0lV5Lqlpr0HBpuumKKk3AgDFwZOOgNKUsuqyu/889np74cIBgMqQqspzSVbnTBVsS0vfYKU93RQl+UYAoDjyXdkfQP8FDV3+uZndl2opZJAAUCnKatprUDdFWb0RAPkSH8jR1cVADgClLeg5ujcVLAoAGCD6M+21rS35c3tDlaqbgvm7wIDDQA4A5SRlj667/ya+SHpc0juSNkt6PLYNAJClXKtzpnvST8F7WZi/Cww4DOQAUE7SPl7IzD4l6VVJyyR9V9JaM5sTdmAAUInSVedMlR8GfcFMTIKlAj3uNuiN8PxdoCIxkANAOUmb6Er6J0lN7t7o7jMkNUn6VrhhAUBlCpr2GpQfBn3BLEovC/N3gQGH58UCKCeZJLpvufvahPXXJL0VUjwAUPEiEam7W+rpib7G57YF5YdBXzCL1suS6o3Q7QNUpJYWqXrorj7bqofu4nmxAEpSJonu82b2oJktMLMLJP1c0pNm9mkz+3TI8QHAgBGUHwaNFC65Xhbm7wIVKaI2tfoi1apbklSrbrX6IkXEv2EApSeTRHeYpP+WNENSo6S3JY2SdLqk00KLDAAGmKD8MGikcLp5vwXH/F2gMi1ZosgHy9WtcWpQl7o1TpEPljMtAUBJSpvouvuFAcvnCxEkAAwE6RLWVCOFE5NgqW8SHFfQTlTm7wKVqcSmJTA4BECQTKoujzOzfzaze8zsvvhSiOAAYCAJyg8zObe7W2po6JsES0XqRGX+LlAQBU32SmieBINDAKSTydDln0nqlvQdRSswxxcAQJ6lyg/7I10nakl9UaaLBshYwZO9EponweAQAOlkkujucPdl7t7h7r+JL6FHBgDIi6BO1JL6okwXDZCVgid7mcyTKBAGhwBIJ5NE91/MbKmZfczMpsaX0CMDAORFUCdqwXt7mb8L7CPXf2fr13lW2/MiaJ5EAZXQKGoAJSqTRHeSpEWSbtCeYcs3hRkUACB/gjpRi9Lby/xdoFe6f2dBSXDNoDeTXjPV9kpSQqOoAZSoTBLdsyQd5e4z3L0ptpwcdmAAgPwI6kTtT29v3jF/FwNQ0L+zdElwy+6vqFrv9Tm3Wu+pZfdXChR98fSneB+AgSGTRPcZSQeGHQgAIDypOlFz7e2VQsg7mb+LASho+HG6PzZFan+rVi1Srbpl6lGtutWqRYrU/jbkqEtDGMX7AFSOTBLdMZJeMrNf8nghAKgsufb2hpJ3Mn8XA1DQ8OO0o/lbWhSpXqlujVOPBqlb4xSpXsn4XQBQZonuUkWHL18vHi8EABUnl97e0IpYMX8XFSrVv4mg4cc1o7YlvVbvdsbvAkBKaRPdxEcKZft4ITObbWYvm9laM7sqyf5GM9tiZk/HlmsyPRfIt1Ka/hePpaur+LFg4Ar6Dl3wIlbM30UZC/o3ETT8uEVfTZ4E66t7NjB+FwCSSpnomtlWM3s3ybLVzN5Nd2EzGyTpe5LmSDpW0jwzOzbJof/p7lNiy3VZngvkRSlN/0uMRWIqIoor1XfoghexYv4uyljgv4mA4ceRzd9NngRv/m5R3gcAlJOUia67j3T3/ZMsI919/wyufYKkte7+mru/L6ld0hkZxtWfc4GsldL0v1KKBUilP0WscsL8XZSxwOfdppkoH9GKvkmwVvCwWADIgLmH81BxM/uMpNnuvjC2Pl/SR919ccIxjZJ+KmmDpI2SrnT35zM5N+EazZKaJWnMmDEN7e3tobyffNi2bZtGjBhR7DCQRFdX6n0NDYWLQ+oby9ix27Rhw542U+hYUH4K+TmzebP05pvS++9LQ4dKRxwhjRolPftsdNvehg6VJk1KfV7OSukfcJni/0/herbrA72vIftsH6oPNKlh3+29Nm+OjlDo6dmzraoqmgz36x9N/9FmkC3aDLKVrM00NTV1ufu0jC7g7qEsks6W9G8J6/MlfWevY/aXNCL28yclvZLpucmWhoYGL2UdHR3FDgEp1A56w6NjHvsutYPeKGosN93UUdRYUH5K4XPmjjvcq6v7/luqro5uD9qXs9raff/xStHt8YBqa93Noq/9ulllKoV2UwlSNbU79Fmv1ra+7V7b/A59NveLFhltBtmizSBbydqMpFWeYT6aSdXlXG2QdGTC+lhFe217ufu77r4t9vODkoaY2ehMzgXyKajq5UCOBchFwUcZM38XJSDXglNpUWwKAHISZqL7pKTxZjbOzIZKOk9Sn+fvmtlfmJnFfj4hFs+mTM4F8qlfX0JCjEVSUWMBclXQpwQxfxclINeCUwCAcISW6Lr7LkmLJf1S0ouSfuLR+bdfMLMvxA77jKTnzOwZScsknRfrlU56blixAiX1JSQhlgZ18YUIFSW0pwTlmlnzWCLkSc4FpwAAoRgc5sVjw5Ef3GvbLQk/f1dS0hr5yc4FQhP/srFkSfQLcE1NNLEsxpeQxFik6BeiYsUC5FlLS3Q4Z2LP196jjOP74kM/pX40/5qaPc/q2nt7KDfEQFUz6E2t2z026XZpbLRN0a4AoGDCHLoMlJdSmgcVj6WhofixAHlUUvN3GdaMHKQaBEB9BQAoLSS6AICCKugo46DMmmHNyFJoBacAAHkX6tBlAAAyFdoo41RDRhnWjCwFDQKItLQo0tysyPYVe3ZWV0strYUNEgAgiR5dAECJKPgoY4Y1I5UUvfkUnAKA8kGiCwAoCQUfZcywZiQTMD45WlhqX73bS6nWAwAMcCS6AICSkSpPCHosUdC8ydK7IUrekiVq236G6vS6qrRbdXpdbdvPkJYsoeAUAJQREl0AQMkrq2HN9PaWtbZ1f6Vm/UDrVCdXldapTs36gdrW/RUFpwCgjJDoAgBKXtkMa6a3t+wtGfSP2q79+mzbrv20ZNA/Si0tilSvVLfGqUeD1K1xilSvjP4BBABQUkh0AQBloSyGNVPEqrQE/ZUjVcGp3UckvdT63UdQcAoAygiJLgCgrJXUsGaKWJWOoL9yBBWcqrWkl+vdTsEpACgLJLoAgLJWUsOa+9O9TBKcX0F/5QgqOBXwdwwAQPkg0QUAlL2SGdaca/cySXD+rV+vNs3rm8xqXnR7UMEpRicDQEUg0QUAVKyCF0/OtXu5P0lwzsFWtrZRi5Mns6MWBxecEqOTAaASkOgCACpWUYon59K9nGsSLFHpOYUluj55MqvrgwtOAQAqAokuAKCilUzx5KDu5VyTYKl/XdPxfV1d+esJLnTvcqrqyZtHJD18/eYR6QtOAQDKHokuAGBAKnjx5KDu5VyT4MSgkgWbaeVhKT/zgvvTu5zDo4ACqycH/NooOAUAA4C7V8zS0NDgpayjo6PYIaDM0GaQLdpMdu64w7221t0s+nrHHdHttbXu0cyp7xI/prq67/bq6j3n5j2YdDcMCjbDfR033ZTdm8zlF5fuvae6X9C+gPvl+haQGT5rkC3aDLKVrM1IWuUZ5ob06AIABqx8F0+W+jFyN1Uw6coA59o1HUZxrFy7wtM8CijlvoDKyul+bRScAoDKNrjYAQAAUGriSU8sl+od7hqJSPPnJz8ncaRwPC+L54CJ18w5oFQXCAp2yZI9Q5MTxcf1ptqXaxJcU5P6mkG/nHQJcop9baMWq3nTN3qLTsUrK2vUaEUU/GsDAFQ2enQBAEii0EWs+lXDKZeu6TCKY+XaFR50v5qa5L22NTWBlZUBAAMbiS4AAFkIo4hVaE8IChq/m7hPyk9xrEhEbRf8UnWD3ogmpYPeUNsFv0z/PKeWFrUNWdA3mR2yILr9k3ckfx7uJ+8IrKwMABjYSHQBAMhCUO4YlAMGJbOhzfuNB5xqMmp8X0ND5vOCA5Lgtjap+fYTtW732GhSunusmm8/MRpvwC+nTRE1217JrP1AbYpoyYMnJu+1ffDEtAWpAQADF4kuAABZyncRq1yfEBSXy5N5cn6TAUlwYMIe0Gu7ZIm0/f2+ZUO2vz847e+GxwQBAFIh0QUAIE+COkKDErb+zPvN9FG5yZLkeBLc1ZVdgtymiOrUrSr1qE7dalOk972keo9Bvba5/m7SVVYGAAxcVF0GACCPUlX6DSpI3NLStyCxtKdnMqjKs5Q+EQ7al6oIcq77gt5jUK9trr8bicrKAIDk6NEFAKAAgobZ5jrvVwrnUbm57su1UFeuvxsAAFIh0QUAoADSJWy5zPuV0j6ZJ+W+XBPkoH25Juy5/m4AAEiFRBcAgALJJWFLlwSG8ajcXPcFvcd0CTvJLAAgn5ijCwBAiQuahxrfHq9QHJ/Xmnh8qn1Bc19z3Rf0HtLFCQBAvpDoAgBQ5tIlwsn2JSaeUrSnONMEOd2+XOIEACCfSHQBABig4olnZ2d0uHCyfUHnAQBQqpijCwAAAACoKCS6AAAAAICKQqILAAAAAKgoJLoAAAAAgIpCogsAAAAAqCihJrpmNtvMXjaztWZ2VZL9ETNbE1t+Z2aTE/Z1m9mzZva0ma0KM04AAAAAQOUI7fFCZjZI0vckfULSBklPmtl97v5CwmGvS5rh7u+Y2RxJrZI+mrC/yd3/FFaMAAAAAIDKE2aP7gmS1rr7a+7+vqR2SWckHuDuv3P3d2Krv5c0NsR4AAAAAAADQJiJ7hGS3khY3xDblsr/lvSLhHWX9JCZdZlZcwjxAQAAAAAqkLl7OBc2O1vSqe6+MLY+X9IJ7n5pkmObJN0s6UR33xTbdri7bzSzQyX9/8qm8QAAC+xJREFUStKl7v5oknObJTVL0pgxYxra29tDeT/5sG3bNo0YMaLYYaCM0GaQLdoMckG7QbZoM8gWbQbZStZmmpqautx9WibnhzZHV9Ee3CMT1sdK2rj3QWZWL+nfJM2JJ7mS5O4bY69vmdm9ig6F3ifRdfdWRef2atq0ad7Y2JjHt5BfnZ2dKuX4UHpoM8gWbQa5oN0gW7QZZIs2g2z1t82EOXT5SUnjzWycmQ2VdJ6k+xIPMLMaSfdImu/u/5WwfT8zGxn/WdIsSc+FGCsAAAAAoEKE1qPr7rvMbLGkX0oaJOlWd3/ezL4Q23+LpGskHSzpZjOTpF2xrugxku6NbRss6cfu/h9hxfr/27v3WEnr+o7j78/uuuouItrVVW4ubfCy3hC3BNq0BbURtXH7R01otpGutRsIomJ6gWyjsQmpFRJDo5UQpdj0VEPRttsWK0g8XpKyalUQvG6QXVZQLk2t263C4rd/zIMMZ2fOnjnLnJn9nfcr2cwzv+d5Zn8n+9k585n5zYwkSZIkqR3jXLpMVV0PXD9n7Mq+7TcDbx5w3h3AS+eOS5IkSZJ0KONcuixJkiRJ0pKz6EqSJEmSmmLRlSRJkiQ1xaIrSZIkSWqKRVeSJEmS1BSLriRJkiSpKRZdSZIkSVJTLLqSJEmSpKZYdCVJkiRJTbHoSpIkSZKaYtGVJEmSJDXFoitJkiRJaopFV5IkSZLUFIuuJEmSJKkpFl1JkiRJUlMsupIkSZKkplh0JUmSJElNsehKkiRJkppi0ZUkSZIkNcWiK0mSJElqikVXkiRJktQUi64kSZIkqSkWXUmSJElSUyy6kiRJkqSmWHQlSZIkSU2x6EqSJEmSmmLRlSRJkiQ1xaIrSZIkSWqKRVeSJEmS1BSLriRJkiSpKRZdSZIkSVJTLLqSJEmSpKZYdCVJkiRJTbHoSpIkSZKaYtGVJEmSJDXFoitJkiRJaopFV5IkSZLUlLEW3SRnJ/l2kl1JLh6wP0n+qtt/a5JTF3quJEmSpAFmZmDDBlixonc5MzPpGUlLbmxFN8lK4APAa4CNwO8m2TjnsNcAJ3d/tgEfHOFcSZIkSf1mZpjZ+mk27J5lRR1gw+5ZZrZ+2rKrZWecr+ieBuyqqjuq6kHgY8DmOcdsBv62em4Gjkny7AWeK0mSJKnPzNt2su2h97ObDRQr2M0Gtj30fmbetnPSU5OW1DiL7nHAXX3X93ZjCzlmIedKkiRJ6rP9gXewn7WPGdvPWrY/8I4JzUiajFVjvO0MGKsFHrOQc3s3kGyjt+yZ9evXMzs7O8IUl9a+ffumen6aPmZGozIzWgxzo1GZmel14eUAdw7cNzs7eHwpmBmN6nAzM86iuxc4oe/68cDdCzxm9QLOBaCqrgKuAti0aVOdeeaZhzXpcZqdnWWa56fpY2Y0KjOjxTA3GpWZmV6//zv72P3AUQeNP+cX9nHn/QePLxUzo1EdbmbGuXT5S8DJSU5Ksho4B9gx55gdwBu7T18+HfhRVd2zwHMlSZIk9bn0iqNYs/rAY8bWrD7ApVdMruRKkzC2V3Sr6kCStwCfAlYCV1fV7UnO6/ZfCVwPvBbYBewHts537rjmKkmSJLVgyxaAVWzfDnv2wIknwqWXrurGpeVjnEuXqarr6ZXZ/rEr+7YLuGCh50qSJEma35YtWGy17I1z6bIkSZIkSUvOoitJkiRJaopFV5IkSZLUFIuuJEmSJKkpFl1JkiRJUlMsupIkSZKkplh0JUmSJElNsehKkiRJkppi0ZUkSZIkNcWiK0mSJElqikVXkiRJktQUi64kSZIkqSmpqknP4XGT5D5g96TnMY91wP2TnoSOKGZGozIzWgxzo1GZGY3KzGhUgzLznKp6xkJObqroTrskX66qTZOeh44cZkajMjNaDHOjUZkZjcrMaFSHmxmXLkuSJEmSmmLRlSRJkiQ1xaK7tK6a9AR0xDEzGpWZ0WKYG43KzGhUZkajOqzM+B5dSZIkSVJTfEVXkiRJktQUi64kSZIkqSkW3TFKckyS65J8K8k3k5yR5OlJbkzy3e7yaZOep6ZHkouS3J7ktiQfTfIkM6N+Sa5Ocm+S2/rGhmYkySVJdiX5dpJXT2bWmqQhmbms+910a5J/THJM3z4zs8wNykzfvj9KUknW9Y2ZmWVuWGaSXNjl4vYk7+0bNzMa9vvplCQ3J/laki8nOa1v30i5seiO1xXAv1fV84GXAt8ELgZuqqqTgZu66xJJjgPeCmyqqhcBK4FzMDN6rGuAs+eMDcxIko30MvTC7py/TrJy6aaqKXENB2fmRuBFVfUS4DvAJWBm9HPXcHBmSHIC8JvAnr4xMyMYkJkkZwGbgZdU1QuBy7txM6NHXMPB9zXvBd5dVacA7+yuLyo3Ft0xSXI08OvAhwGq6sGq+m96/+E/0h32EeC3JzNDTalVwJOTrALWAHdjZtSnqj4H/Nec4WEZ2Qx8rKp+WlXfA3YBp6FlZVBmquqGqjrQXb0ZOL7bNjMadj8D8D7gT4D+TzI1MxqWmfOB91TVT7tj7u3GzYyAobkp4Ohu+6n0HgvDInJj0R2fXwTuA/4myVeTfCjJWmB9Vd0D0F0+c5KT1PSoqu/Te7ZzD3AP8KOqugEzo0MblpHjgLv6jtvbjUn93gR8sts2MxooyeuB71fVLXN2mRkN81zg15LsTPLZJL/cjZsZzeftwGVJ7qL3uPiSbnzk3Fh0x2cVcCrwwap6GfC/uORU8+jeV7kZOAk4Flib5PcmOysd4TJgzO+U088l2Q4cAGYeGRpwmJlZ5pKsAbbTW0Z40O4BY2ZG0Hss/DTgdOCPgWuTBDOj+Z0PXFRVJwAX0a2OZRG5seiOz15gb1Xt7K5fR6/4/jDJswG6y3uHnK/l51XA96rqvqp6CPgE8CuYGR3asIzsBU7oO+54Hl0CpGUuybnAbwFbquqRBwtmRoP8Er0nYW9Jcie9XHwlybMwMxpuL/CJ6vki8DNgHWZG8zuX3mNggH/g0eXJI+fGojsmVfUD4K4kz+uGXgl8A9hB7x+Q7vKfJzA9Tac9wOlJ1nTPeL6S3geYmRkdyrCM7ADOSfLEJCcBJwNfnMD8NGWSnA38KfD6qtrft8vM6CBV9fWqemZVbaiqDfQecJ7aPdYxMxrmn4BXACR5LrAauB8zo/ndDfxGt/0K4Lvd9si5WTW2KQrgQmAmyWrgDmArvScXrk3yB/SKzRsmOD9NkarameQ64Cv0lhJ+FbgKOAozo06SjwJnAuuS7AXeBbyHARmpqtuTXEvvSbYDwAVV9fBEJq6JGZKZS4AnAjf2nlfj5qo6z8wIBmemqj486FgzIxh6P3M1cHX31TEPAud2q0fMjIChuflD4Irug1l/AmyDxd3X5NHVSpIkSZIkHflcuixJkiRJaopFV5IkSZLUFIuuJEmSJKkpFl1JkiRJUlMsupIkSZKkplh0JUmaUknenmTNPPs/lGRjt71v6WYmSdJ08+uFJEmaUknuBDZV1f0D9q3s/w7BJPuq6qilnJ8kSdPKV3QlSZoCSdYm+bcktyS5Lcm7gGOBzyT5THfMviR/nmQncEaS2SSb5tzOuiT/keR1SZ6R5ONJvtT9+dUJ/GiSJC25VZOegCRJAuBs4O6qeh1AkqcCW4Gz+l7RXQvcVlXv7I55zA0kWQ/sAP6sqm5M8vfA+6rqC0lOBD4FvGBJfhpJkibIoitJ0nT4OnB5kr8E/rWqPj+3yAIPAx8fcv4TgJuAC6rqs93Yq4CNfbdzdJKnVNWPH9+pS5I0XSy6kiRNgar6TpKXA68F/iLJDQMO+0n/+3LnOAD8J/Bq4JGiuwI4o6r+73GfsCRJU8z36EqSNAWSHAvsr6q/Ay4HTgV+DDxlgTdRwJuA5ye5uBu7AXhL399xyuM3Y0mSppev6EqSNB1eDFyW5GfAQ8D5wBnAJ5PcU1VnHeoGqurhJOcA/5Lkf4C3Ah9Iciu93/mfA84b208gSdKU8OuFJEmSJElNcemyJEmSJKkpFl1JkiRJUlMsupIkSZKkplh0JUmSJElNsehKkiRJkppi0ZUkSZIkNcWiK0mSJElqyv8Dgp+fciXgQUMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "k_call, IV_call = IV_plot(DF_calls, 'c', s, 8)\n",
    "k_put,  IV_put  = IV_plot(DF_puts,  'p', s, 8)\n",
    "\n",
    "plt.figure(figsize=(16, 7))\n",
    "e = plt.scatter(k_call, IV_call, c='red',   label=\"IV(call options)\")\n",
    "f = plt.scatter(k_put,  IV_put,  c='black', label=\"IV(put options)\")\n",
    "plt.xlabel('strike')\n",
    "plt.ylabel('Implied Volatility')\n",
    "plt.legend((e,f), (\"IV (call options)\", \"IV (put options)\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "do_quandl = False\n",
    "if do_quandl:\n",
    "    import quandl\n",
    "\n",
    "    quandl.ApiConfig.api_key = 'NxTUTAQswbKs5ybBbwfK'\n",
    "    goog_table = quandl.get('WIKI/GOOG')\n",
    "    # use the daily data of Google(NASDAQ: GOOG) from 01/2016 to 08/2016\n",
    "    close = goog_table['2016-01':'2016-08']['Adj. Close']\n",
    "    r = diff(log(close))\n",
    "    r_mean = mean(r)\n",
    "    diff_square = [(r[i]-r_mean)**2 for i in range(0,len(r))]\n",
    "    std = sqrt(sum(diff_square)*(1.0/(len(r)-1)))\n",
    "    vol = std*sqrt(252)\n",
    "\n",
    "    vol"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}