equity-index-options-pricing-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "mysterious-jurisdiction",
   "metadata": {},
   "source": [
    "# Pricing equity index options\n",
    "In this notebook I price equity index 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": "clear-cartridge",
   "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 and yfinance\n",
    "# !pip install pandas-datareader -U\n",
    "# !pip install yfinance -U\n",
    "# !pip install pandas-market-calendars -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "empty-emission",
   "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": "compatible-frank",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Uncomment the below line if you want to price with a yield curve based on US Treasury Yields\n",
    "%run riskless-yield-construction-example.ipynb\n",
    "\n",
    "# Uncomment the below line if you want to price with a yield curve based on AMERIBOR rates\n",
    "#%run riskless-rate-curve-construction-ameribor.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "integral-inflation",
   "metadata": {},
   "source": [
    "## Estimating and forecasting volatility of the index, 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 index 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 S&P 500 (^GSPC)\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 data from the past two years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "norwegian-portrait",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4276.87395 after 100 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000002239146, α=0.05575, β=0.91028\n"
     ]
    }
   ],
   "source": [
    "TICKER = '^GSPC'\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 = yfin.Ticker(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": "political-character",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "binding-damage",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4276.33084 after 86 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000002311138, α=0.06624, β=0.90360\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": "handled-combine",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for S&P 500\n",
    "Now that we have obtained optimal values for GARCH(1, 1) parameters ω, α, and β, we can proceed to forecast S&P 500 volatility. I created class `volatility.parameter_estimators.GARCHVolatilityTracker` to assist in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "structured-washer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of ^GSPC for term 0.3753 years: 0.12638\n"
     ]
    }
   ],
   "source": [
    "vol_tracker = volatility_trackers.GARCHVolatilityTracker(vol_estimator.omega, vol_estimator.alpha,\n",
    "                                                         vol_estimator.beta, asset_prices)\n",
    "\n",
    "# The 3rd Friday of next March, i.e. 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": "about-nutrition",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing volatility term structure of S&P 500 index for 200 business days into the future\n",
    "In contrast to the `equity-options-pricing-example.ipynb` notebook where I visualized historical, and future volatilities, in this notebook I'll visualize the _volatility term structure_ for S&P 500, i.e. forecast average volatility for a certain future term expressed in years. 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": 6,
   "id": "physical-welsh",
   "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 S&P 500 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": "opposite-shoulder",
   "metadata": {},
   "source": [
    "## Pricing using Black-Scholes-Merton Pricer\n",
    "The Black-Scholes-Merton model can be used to price European options, including equity indices. With enough customizations it can also be used to price American call options (even those paying dividends or having a known\n",
    "dividend yield). Exchange and over-the-counter traded equity index options tend to be European.\n",
    "\n",
    "Let's put it to use to price an S&P 500 call and put options with a strike of 3900. Some of the stocks comprising S&P 500 pay dividends. It's essential to take into account the expected dividend yield of S&P 500 to achieve accurate pricing. Where do you get S&P 500's dividend yield? I calculate it based on forward dividend yields of individual S&P 500 companies in [this notebook](https://github.com/ilchen/US_Economic_Data_Analysis/blob/main/Stock_Market.ipynb). By running that notebook (please clone the corresponding repository), you will be able to obtain the forward dividend yield for the last business day. The class I use to calculate it [is here](https://github.com/ilchen/US_Economic_Data_Analysis/blob/main/stock_market/metrics.py#L13-L217). Alternatively, at the start of every month Aswath Damodaran @AswathDamodaran calculates the so-called equity risk premium (ERP) for S&P 500 and publishes it for download as a spreadsheet from [his website at STERN](https://pages.stern.nyu.edu/~adamodar/). `Spreadsheet to compute current ERP for current month`. From the date on S&P 500 dividends in tab `Buyback & Dividend computation`, you can\n",
    "calculate the current dividend yield as well as it's estimate for the next months.\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. For pricing options on SP500, whose underlying futures are traded allmost on all non-weekend days, whether to use a custom trading calendar or not doesn't make a big difference on the pricing. Therefore in this notebook I use calendar days for calculating the lifetime of options. If you want to price with it, please make use of the holidays calendar created in the below cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "together-sheriff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Taking the trading calendar into account when pricing\n",
    "import pandas_market_calendars as mcal\n",
    "holidays = mcal.get_calendar('NYSE').holidays().holidays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "simple-permission",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1275.93, σ: 0.1264, Δ: 0.995, Γ: 0.000, ν: 5.805\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 0.05, σ: 0.1264, Δ: -0.000, Γ: 0.000, ν: 5.805\n"
     ]
    }
   ],
   "source": [
    "strike = 4500.\n",
    "\n",
    "# Expected S&P 500 dividend yield\n",
    "q = 0.01304359214448552 # Updated for 1st November 2024\n",
    "\n",
    "cur_price = asset_prices.iloc[-1]\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, vol_tracker, strike, curve, cur_price,\n",
    "                                          ticker=TICKER, q=q)\n",
    "print(pricer)\n",
    "\n",
    "put_pricer = options.BlackScholesMertonPricer(maturity_date, vol_tracker, strike, curve, cur_price, is_call=False,\n",
    "                                              ticker=TICKER, q=q)\n",
    "print(put_pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "operational-dream",
   "metadata": {},
   "source": [
    "Sometimes you might want to price using _an implied volatility_ for the expiry date, implied volatilities are volatilities implied by option prices of market makers. You can easily use implied volatilities with \n",
    "the `BlackScholesMertonPricer` class, just pass the volatility value as the second parameter instead of\n",
    "a volatility tracker (I also use a custom trading calendar in the below cell):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "alleged-vulnerability",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1281.43, σ: 0.2100, Δ: 0.975, Γ: 0.000, ν: 173.791\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 5.84, σ: 0.2100, Δ: -0.021, Γ: 0.000, ν: 173.791\n"
     ]
    }
   ],
   "source": [
    "impl_vol = .21\n",
    "\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, impl_vol, strike, curve, cur_price,\n",
    "                                          ticker=TICKER, q=q, holidays=holidays)\n",
    "print(pricer)\n",
    "\n",
    "put_pricer = options.BlackScholesMertonPricer(maturity_date, impl_vol, strike, curve, cur_price, is_call=False,\n",
    "                                              ticker=TICKER, q=q, holidays=holidays)\n",
    "print(put_pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "listed-wichita",
   "metadata": {},
   "source": [
    "#### Put-Call Parity\n",
    "An important theoretical property of the price of a European option is the so-called put-call parity, which is expressed as:\n",
    "$$c - p = S_0\\cdot e^{-q\\cdot T} - K\\cdot e^{-r\\cdot T}$$\n",
    "where:\n",
    "* c is the price of a European call option\n",
    "* p is the price of the corresponding European put option\n",
    "* S<sub>0</sub> is the present price of the underlying stock\n",
    "* q is the expected dividend yield of the index\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": 10,
   "id": "durable-telephone",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 1275.59 = 1275.59\n"
     ]
    }
   ],
   "source": [
    "from math import exp\n",
    "price_difference = pricer.get_price() - put_pricer.get_price()\n",
    "\n",
    "right_hand_side_expr = pricer.s0 * exp(-pricer.q * pricer.T) - pricer.strike * exp(-pricer.r * pricer.T)\n",
    "\n",
    "assert np.allclose(price_difference, right_hand_side_expr, .1)\n",
    "print(f'Put-Call parity: {price_difference:.2f} = {right_hand_side_expr:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dressed-collapse",
   "metadata": {},
   "source": [
    "## Pricing using Binomial Tree Pricer\n",
    "The Binomial Tree model can be used to price any European or American option, including on index some of whose constituent stocks pay dividends.\n",
    "\n",
    "Let's put it to use to price an S&P 500 call and put option with a strike of 3900 and compare resulting prices with those obtained from the BlackScholesMertonPricer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "senior-recovery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1281.64, σ: 0.2100, Δ: 0.975, Γ: 0.000, ν: 211.183\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for calls: 0.213118\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 5.76, σ: 0.2100, Δ: -0.020, Γ: 0.000, ν: 211.183\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for puts: 0.082322\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, curve, cur_price,\n",
    "                                             ticker=TICKER, q=q)\n",
    "print(bin_tree_pricer)\n",
    "\n",
    "print('Price difference between Black-Scholes-Merton and Binomial Treee pricers for calls: %.6f'\n",
    "      % abs(pricer.get_price() - bin_tree_pricer.get_price()))\n",
    "bin_tree_put_pricer = options.BinomialTreePricer(maturity_date, impl_vol, strike, curve, cur_price, is_call=False,\n",
    "                                                 ticker=TICKER, q=q)\n",
    "print(bin_tree_put_pricer)\n",
    "\n",
    "print('Price difference between Black-Scholes-Merton and Binomial Treee pricers for puts: %.6f'\n",
    "      % abs(put_pricer.get_price() - bin_tree_put_pricer.get_price()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pleasant-discrimination",
   "metadata": {},
   "source": [
    "Now pricing with our volatility forecast:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "executed-geology",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1275.92, σ: 0.1264, Δ: 0.995, Γ: 0.000, ν: 7.591\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 0.03, σ: 0.1264, Δ: -0.000, Γ: 0.000, ν: 7.591\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve, cur_price,\n",
    "                                             ticker=TICKER, q=q)\n",
    "print(bin_tree_pricer)\n",
    "\n",
    "bin_tree_put_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve, cur_price, is_call=False,\n",
    "                                                 ticker=TICKER, q=q)\n",
    "print(bin_tree_put_pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "combined-blond",
   "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": "adolescent-central",
   "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\n",
    "and puts more expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "handmade-hindu",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1243.16, σ: 0.1264, Δ: 0.995, Γ: 0.000, ν: 10.357\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 0.05, σ: 0.1264, Δ: -0.000, Γ: 0.000, ν: 10.357\n"
     ]
    }
   ],
   "source": [
    "bin_tree_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve.parallel_shift(-200),\n",
    "                                             cur_price, ticker=TICKER, q=q)\n",
    "print(bin_tree_pricer)\n",
    "\n",
    "bin_tree_put_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, curve.parallel_shift(-200),\n",
    "                                                 cur_price, is_call=False, ticker=TICKER, q=q)\n",
    "print(bin_tree_put_pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unauthorized-desktop",
   "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": 14,
   "id": "conditional-chancellor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^GSPC EUROPEAN call option with strike 4500.0 and maturity 2025-03-21, price: 1234.20, σ: 0.1264, Δ: 0.995, Γ: 0.000, ν: 11.255\n",
      "^GSPC EUROPEAN put option with strike 4500.0 and maturity 2025-03-21, price: 0.05, σ: 0.1264, Δ: -0.000, Γ: 0.000, ν: 11.255\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, vol_tracker, strike, custom_curve,\n",
    "                                             cur_price, ticker=TICKER, q=q)\n",
    "print(bin_tree_pricer)\n",
    "\n",
    "bin_tree_put_pricer = options.BinomialTreePricer(maturity_date, vol_tracker, strike, custom_curve,\n",
    "                                                 cur_price, is_call=False, ticker=TICKER, q=q)\n",
    "print(bin_tree_put_pricer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "medieval-trustee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}