euro-equity-index-options-pricing-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "executed-evening",
   "metadata": {},
   "source": [
    "# Pricing equity index options in Euro\n",
    "In this notebook I price equity index options 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": "thrown-constitutional",
   "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\n",
    "# !pip install pandas-datareader -U\n",
    "# !pip install eurostat -U\n",
    "# !pip install yfinance==0.2.41\n",
    "# !pip install pandas-market-calendars -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "challenging-extreme",
   "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 imports that this notebook needs). The resultant YieldCurve object is\n",
    "assigned to the `curve` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "balanced-palestinian",
   "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": [
    "%run euro-riskless-rate-curve-construction-example.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "angry-marine",
   "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 AEX (^AEX)\n",
    "The AEX index is a capitalization-weighted index composed of 25 large capitalization Dutch companies. 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": "designing-bunch",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4374.28221 after 104 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000006249992, α=0.11334, β=0.80065\n"
     ]
    }
   ],
   "source": [
    "TICKER = '^AEX'\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, end=today, 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": "alternate-background",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "attended-wallet",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4374.27714 after 79 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000006307345, α=0.11568, β=0.79858\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": "proof-benjamin",
   "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": "decimal-wheel",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for AEX\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": 6,
   "id": "invisible-retreat",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of ^AEX for term 0.8164 years: 0.13458\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 June options, i.e. maturity on the 3rd Friday of next June\n",
    "from dateutil.relativedelta import FR\n",
    "maturity_date = curve.date + relativedelta(years=0 if curve.date.month < 6 else 1, month=6, 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": "convertible-privilege",
   "metadata": {},
   "source": [
    "#### Optional: Visualizing volatility term structure of AEX 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 volatility term structure for AEX, i.e. forecast average volatility for a certain future term expressed in years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "spectacular-vinyl",
   "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 AEX 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": "timely-offer",
   "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 AEX call and put options with a strike of 700. Some of the stocks comprising AEX pay dividends. It's essential to take into account the expected dividend yield of AEX to achieve accurate pricing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "quarterly-affect",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 196.83, σ: 0.1346, Δ: 0.953, Γ: 0.000, ν: 32.502\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.65, σ: 0.1346, Δ: -0.016, Γ: 0.000, ν: 32.502\n"
     ]
    }
   ],
   "source": [
    "strike = 700.\n",
    "\n",
    "# Expected AEX dividend yield\n",
    "q = .039\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": "suspended-anniversary",
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aging-figure",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 206.31, σ: 0.2400, Δ: 0.870, Γ: 0.001, ν: 141.384\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 10.14, σ: 0.2400, Δ: -0.099, Γ: 0.001, ν: 141.384\n"
     ]
    }
   ],
   "source": [
    "impl_vol = .24\n",
    "\n",
    "pricer = options.BlackScholesMertonPricer(maturity_date, impl_vol, strike, curve, cur_price,\n",
    "                                          ticker=TICKER, q=q)\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)\n",
    "print(put_pricer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "korean-vatican",
   "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": 11,
   "id": "narrative-diversity",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 196.1757 = 196.1757\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:.4f} = {right_hand_side_expr:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sensitive-source",
   "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 AEX call and put option with a strike of 700 and compare resulting prices with those obtained from the BlackScholesMertonPricer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "molecular-arena",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 205.96, σ: 0.2400, Δ: 0.875, Γ: 0.001, ν: 113.360\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for calls: 0.357240\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 9.78, σ: 0.2400, Δ: -0.095, Γ: 0.001, ν: 113.360\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for puts: 0.358679\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": "ultimate-relation",
   "metadata": {},
   "source": [
    "Now pricing with our volatility forecast:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "included-median",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 196.80, σ: 0.1346, Δ: 0.955, Γ: 0.000, ν: 29.659\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.62, σ: 0.1346, Δ: -0.015, Γ: 0.000, ν: 29.659\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": "rubber-child",
   "metadata": {},
   "source": [
    "Let's see if the put-call parity holds when pricing with `BinomialTreePricer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "public-moment",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 196.1771 = 196.1757\n"
     ]
    }
   ],
   "source": [
    "price_difference = bin_tree_pricer.get_price() - bin_tree_put_pricer.get_price()\n",
    "\n",
    "right_hand_side_expr = bin_tree_pricer.s0 * exp(-bin_tree_pricer.q * bin_tree_pricer.T)\\\n",
    "    - bin_tree_pricer.strike * exp(-bin_tree_pricer.r * bin_tree_pricer.T)\n",
    "\n",
    "assert np.allclose(price_difference, right_hand_side_expr, .1)\n",
    "print(f'Put-Call parity: {price_difference:.4f} = {right_hand_side_expr:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "romance-techno",
   "metadata": {},
   "source": [
    "It does, but not pricing with a given closed formula as is the case for the `BlackScholesMertonPricer` gave rise to\n",
    "a small difference."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "affiliated-welcome",
   "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": "marine-bulletin",
   "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": 15,
   "id": "divided-webster",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 185.81, σ: 0.1346, Δ: 0.950, Γ: 0.000, ν: 39.178\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.89, σ: 0.1346, Δ: -0.020, Γ: 0.000, ν: 39.178\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": "martial-atlas",
   "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": 16,
   "id": "israeli-graham",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 192.04, σ: 0.1346, Δ: 0.953, Γ: 0.000, ν: 33.537\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.73, σ: 0.1346, Δ: -0.017, Γ: 0.000, ν: 33.537\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",
    "\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, 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, custom_curve, cur_price,\n",
    "                                                 is_call=False, ticker=TICKER, q=q)\n",
    "print(bin_tree_put_pricer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "selective-interference",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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