euro-equity-options-pricing-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "communist-conviction",
   "metadata": {},
   "source": [
    "# Pricing equity options denominated in Euro\n",
    "In this notebook I price American equity options denominated in Euro using volatility tracking, riskless zero rate 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), [Eurostat](https://ec.europa.eu/eurostat/data/database), 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 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": "pharmaceutical-turtle",
   "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, eurostat, yfinance, and pandas-market-calendars\n",
    "# !pip install pandas-datareader -U\n",
    "# !pip install sdmx1 -U\n",
    "# !pip install yfinance -U\n",
    "# !pip install pandas-market-calendars -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "atlantic-seattle",
   "metadata": {},
   "source": [
    "## Constructing a riskless zero rate curve for Euro\n",
    "Since I already covered it in a separate notebook, I will simply import it (along with all other imports that this notebook needs). The resultant YieldCurve object is assigned to the `curve` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "particular-terrorist",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run euro-riskless-rate-curve-construction-example.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceb965a7-e738-41a1-bcf2-e0ef5209d883",
   "metadata": {},
   "source": [
    "### Constructing a riskless zero rate curve for USD\n",
    "We'll also need a riskless rate curve for the USD to be able to calculate forward exchange rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d303c522-1d98-4c2f-8634-fc2bc62db282",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Saving the riskless rate curve for the EURO\n",
    "curve_euro = curve\n",
    "\n",
    "# Loading the risless rate curve for USD\n",
    "%run riskless-yield-construction-example.ipynb\n",
    "curve_usd = curve\n",
    "\n",
    "# Riskless curve for the EURO will remain the main curve for the rest of this notebook\n",
    "curve = curve_euro"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ruled-brother",
   "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 Shell plc\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": 4,
   "id": "marked-marriage",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4027.79193 after 37 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000046235915, α=0.20309, β=0.48323\n"
     ]
    }
   ],
   "source": [
    "# Shell plc as traded on Euronext Amsterdam\n",
    "TICKER = 'SHELL.AS'\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() - DateOffset(years=+2))\n",
    "ticker = yfin.Ticker(TICKER)\n",
    "data = ticker.history(start=start, actions=False, auto_adjust=False)\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": "essential-taylor",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "social-construction",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4027.77510 after 94 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000046134839, α=0.19891, β=0.48341\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": "answering-subdivision",
   "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": "overhead-links",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for Shell plc\n",
    "Now that we have obtained optimal values for the GARCH(1, 1) parameters ω, α, and β, we can proceed to forecast the volatility of Shell stock. I created class `volatility.parameter_estimators.GARCHVolatilityTracker` to assist with this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "homeless-contributor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of SHELL.AS for term 0.2110 years: 0.19438\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 March options, i.e. maturity on the 3rd Friday of next March\n",
    "from dateutil.relativedelta import FR\n",
    "maturity_date = curve.date + relativedelta(years=0 if curve.date.month < 3 else 1, month=3, 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": "dirty-verse",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing historical and future volatility of Shell stock for 200 business days into the future"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "freelance-bottom",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "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:] * 100,\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 Shell 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 * 100, label='Forecast Annual Volatility', linewidth=1, color='k')\n",
    "ax.hlines(vol_tracker.get_annual_long_term_volatility() * 100, 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())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "forty-potential",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing the volatility term structure of Shell 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": 8,
   "id": "coupled-output",
   "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": "parallel-station",
   "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 a Shell call option with a strike of €28. Shell pays dividends. It's essential to take into account dividends paid during the lifetime of an option to ensure accurate pricing. An interesting nuance about Shell is that it switched to declaring its dividend in USD, making it more challenging to price options where the underlying asset is Shell's equity priced in Euros, as is the case in this notebook. It would actually be easier to price its USD option, where the underlying asset is Shell's share price traded on the NYSE (ticker `SHEL`) and also priced in USD. To correctly convert Shell stock future dividends into Euros, we need to calculate forward exchange rate for the `EURUSD` currency pair. The standard formula for this is:\n",
    "$S_{t}=S_{0}\\cdot e^{(r_{f}-r_{d})\\cdot t}$\n",
    "where\n",
    "* $S_{t}$ is the forward `EURUSD` exchange rate for maturity `t`\n",
    "* $S_{0}$ is the current `EURUSD` exchange rate\n",
    "* $r_{d}$ is the riskless Euro interest rate for  maturity `t`\n",
    "* $r_{f}$ is the riskless USD interest rate for maturity `t`\n",
    "\n",
    "Market makers tend to calculate the lifetime of options using trading days rather than calendar days. The `pricing.options.BlackScholesMertonPricer` class supports both methods 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 remaining part of this notebook, I price options based on the trading calendar of the Eurex exchange."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "atlantic-hayes",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-03-21, price: 3.40, σ: 0.1943, Δ: 0.963, Γ: 0.040, ν: 0.836\n"
     ]
    }
   ],
   "source": [
    "strike = 28.\n",
    "\n",
    "# Yahoo-dividends returns the most recent ex-dividend date in the last row\n",
    "last_divs = ticker.dividends.iloc[-1:]\n",
    "\n",
    "# An approximate rule for Shell's ex-dividend dates -- ex-dividend date is on the second Thursday\n",
    "# of the last month of a season.\n",
    "idx = (pd.date_range(last_divs.index[0].date(), freq='WOM-2THU', periods=30)[::3])\n",
    "divs = pd.Series([last_divs.iloc[0]] * len(idx), index=idx, name=TICKER + ' Dividends')\n",
    "\n",
    "# Shell aims to grow the dividend per share by around 4 percent every year\n",
    "divs.loc['2025':] *= 1.04\n",
    "divs.loc['2026':] *= 1.04\n",
    "divs.loc['2027':] *= 1.04\n",
    "\n",
    "# Shell recently switched to declaring dividends in USD, as a result the above estimates of future dividends are \n",
    "# also in USD. Since the underlying share is priced in EUR, we need to convert these USD dividend amounts into EUR.\n",
    "# I will use a simplistic approach of using the current EURUSD spot rate. A better approach would to use\n",
    "# the riskless rate USD curve and calculate forward exchange rates using riskneutral valuation.\n",
    "eurusd = yfin.Ticker('EURUSD=X').history(start=today-BDay(12), end=today, actions=False, auto_adjust=False)\n",
    "eurusd_rate = eurusd['Adj Close']\n",
    "\n",
    "# Calculate risk-neutral forward EURUSD rates\n",
    "from math import exp\n",
    "fwd_fx_rate = divs.loc[today:].index.to_series().map(pd.Timestamp.date).map(lambda dt: eurusd_rate.iloc[-1] * exp(\n",
    "    (curve_usd.get_yield_for_maturity_date(dt) - curve.get_yield_for_maturity_date(dt)) * curve.to_years(dt)))\n",
    "\n",
    "# Converting dividends from USD into EUR\n",
    "divs /= fwd_fx_rate\n",
    "divs.dropna(inplace=True)\n",
    "\n",
    "# Taking the trading calendar into account when pricing\n",
    "import pandas_market_calendars as mcal\n",
    "holidays = mcal.get_calendar('EUREX').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": "purple-andrews",
   "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": "personalized-revolution",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-03-21, price: 3.69, σ: 0.3200, Δ: 0.785, Γ: 0.064, ν: 4.147\n"
     ]
    }
   ],
   "source": [
    "# Pricing with an implied volatility of 32%\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, .32, strike, curve, cur_price,\n",
    "                                          ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "departmental-eagle",
   "metadata": {},
   "source": [
    "As you can see, a different volatility resulted in a significant change in the price.\n",
    "\n",
    "Let's now price a Shell 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": "terminal-contamination",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-12-19, price: 3.76, σ: 0.1931, Δ: 0.736, Γ: 0.060, ν: 9.190\n"
     ]
    }
   ],
   "source": [
    "# Let's get volatility forecast for next December options, i.e. maturity on the 3rd Friday of next December\n",
    "maturity_date = curve.date + relativedelta(years=0 if curve.date.month < 3 else 1, month=12, day=1, weekday=FR(3))\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, vol_tracker, strike, curve, cur_price,\n",
    "                                          ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                          holidays=holidays)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "authentic-preparation",
   "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": "hidden-phrase",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19309403473233874"
      ]
     },
     "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": "gentle-texas",
   "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 a Shell call and put options with a strike of €28 and compare resulting prices for call options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "compatible-defendant",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-12-19, price: 3.88, σ: 0.1931, Δ: 0.768, Γ: 0.073, ν: 9.074\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers: 0.119862\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve, cur_price,\n",
    "                                             ticker=TICKER, dividends=divs, opt_type=options.OptionType.AMERICAN,\n",
    "                                             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": "floral-oliver",
   "metadata": {},
   "source": [
    "Let's now price a Shell put option with the same maturity. You cannot price put options with a BlackScholesMerton pricer, with a BinomialTreePricer you can."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "excellent-stereo",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN put option with strike 28.0 and maturity 2025-12-19, price: 1.15, σ: 0.1931, Δ: -0.291, Γ: 0.062, ν: 10.609\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": "declared-surname",
   "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": "natural-disclaimer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 1.93 <= 2.73 <= 3.88\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\\\n",
    "    * 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": "atlantic-looking",
   "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": "interested-marriage",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-12-19, price: 4.73, σ: 0.2800, Δ: 0.699, Γ: 0.046, ν: 10.327\n",
      "SHELL.AS AMERICAN put option with strike 28.0 and maturity 2025-12-19, price: 2.08, σ: 0.2800, Δ: -0.326, Γ: 0.044, ν: 10.805\n"
     ]
    }
   ],
   "source": [
    "impl_vol = .28\n",
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, 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, 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": "drawn-stevens",
   "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": "markdown",
   "id": "protected-honor",
   "metadata": {},
   "source": [
    "The `parallel_shift` method of the `YieldCurve` class allows for pricing using a parallel shift to the yield curve. Let's price the same options but with a curve points shifted down by 200bps. As expected, this makes calls cheaper and puts more expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "australian-fourth",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-12-19, price: 4.49, σ: 0.2800, Δ: 0.691, Γ: 0.050, ν: 9.596\n",
      "SHELL.AS AMERICAN put option with strike 28.0 and maturity 2025-12-19, price: 2.31, σ: 0.2800, Δ: -0.350, Γ: 0.045, ν: 11.113\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, curve.parallel_shift(-200), 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, curve.parallel_shift(-200),\n",
    "                                                 cur_price, is_call=False, ticker=TICKER, dividends=divs,\n",
    "                                                 opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(bin_tree_pricer_put)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "universal-saver",
   "metadata": {},
   "source": [
    "Let's now price with a flat discount curve, which I'll construct by reusing the offsets from earlier in this notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "specified-honey",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHELL.AS AMERICAN call option with strike 28.0 and maturity 2025-12-19, price: 4.70, σ: 0.2800, Δ: 0.699, Γ: 0.046, ν: 10.371\n",
      "SHELL.AS AMERICAN put option with strike 28.0 and maturity 2025-12-19, price: 2.10, σ: 0.2800, Δ: -0.329, Γ: 0.044, ν: 10.844\n"
     ]
    }
   ],
   "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 2% and yearly compounding frequency.\n",
    "custom_curve = curves.YieldCurve(today, offsets, [.02]*len(offsets), compounding_freq=1)\n",
    "\n",
    "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": "f8d98cc5-e45e-4f4d-9c46-13475594b43a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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