equity-options-pricing-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "killing-bennett",
   "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": "measured-fundamental",
   "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": "advance-highlight",
   "metadata": {},
   "source": [
    "## Constructing a riskless rate curve for USD\n",
    "Since I already covered it in a separate notebook, I will simply import it. 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": "useful-friendship",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": "smaller-admission",
   "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": "arabic-portfolio",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[*********************100%%**********************]  1 of 1 completed\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 3608.30089 after 107 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000001801096, α=0.02324, β=0.96674\n"
     ]
    }
   ],
   "source": [
    "# A kludge for pandas-datareader not being able to cope with latest Yahoo-Finance changes\n",
    "import yfinance as yfin\n",
    "yfin.pdr_override()\n",
    "\n",
    "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",
    "data = web.get_data_yahoo(TICKER, start, date.today())\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": "dynamic-temple",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dietary-religion",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 3605.96160 after 35 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000002426785, α=0.03851, β=0.95369\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": "dominican-commons",
   "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": "unnecessary-collection",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for Apple\n",
    "Now that we have obtined optimal values for GARCH(1, 1) parameters ω, α, and β, we can proceed to forecast the volatility of AAPL stock. I crated class `volatility.parameter_estimators.GARCHVolatilityTracker` to assist in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "global-characteristic",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of AAPL for term 0.7753 years: 0.20731\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": "perceived-apollo",
   "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": "voluntary-aberdeen",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": "german-omega",
   "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": "laden-trail",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": "above-wells",
   "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 he 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": "configured-dominant",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-01-17, price: 9.98, σ: 0.2073, Δ: 0.470, Γ: 0.013, ν: 58.851\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[-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[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[-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": "sophisticated-machine",
   "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": 9,
   "id": "infinite-somerset",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-01-17, price: 13.93, σ: 0.2742, Δ: 0.498, Γ: 0.010, ν: 59.018\n"
     ]
    }
   ],
   "source": [
    "# Pricing with an implied volatility of 27.42% (implied volatility for this contract as of 15th Sep 2023)\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, .2742, strike, curve, cur_price, ticker=TICKER,\n",
    "                                          dividends=divs, opt_type=options.OptionType.AMERICAN, holidays=holidays)\n",
    "print(pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "moved-malaysia",
   "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": 10,
   "id": "pressed-fault",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 18.54, σ: 0.2099, Δ: 0.562, Γ: 0.009, ν: 85.699\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": "collective-wilson",
   "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": 11,
   "id": "emerging-windows",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20993583120246853"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol_tracker.get_annual_term_volatility_forecast(curve.to_years(maturity_date))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dated-mills",
   "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": 12,
   "id": "unusual-doubt",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 18.63, σ: 0.2099, Δ: 0.559, Γ: 0.009, ν: 88.319\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers: 0.085766\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": "acquired-premises",
   "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": 13,
   "id": "sealed-circular",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 19.79, σ: 0.2099, Δ: -0.520, Γ: 0.012, ν: 81.722\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": "maritime-avatar",
   "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": 14,
   "id": "refined-spouse",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: -13.16 <= -1.17 <= 2.47\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": "choice-plastic",
   "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": 15,
   "id": "junior-thanksgiving",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 28.99, σ: 0.3297, Δ: 0.589, Γ: 0.005, ν: 85.045\n",
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 29.87, σ: 0.3297, Δ: -0.451, Γ: 0.006, ν: 84.334\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": "fitting-prototype",
   "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": 16,
   "id": "diagnostic-sodium",
   "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": "collective-twelve",
   "metadata": {},
   "source": [
    "Now pricing with out own flat curve and a given implied volatility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "absent-twist",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL AMERICAN call option with strike 180.0 and maturity 2025-12-19, price: 26.87, σ: 0.3297, Δ: 0.561, Γ: 0.006, ν: 86.174\n",
      "AAPL AMERICAN put option with strike 180.0 and maturity 2025-12-19, price: 32.15, σ: 0.3297, Δ: -0.459, Γ: 0.006, ν: 85.989\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": "ambient-newton",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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