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

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "vulnerable-portfolio",
   "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": "foster-adult",
   "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 -U\n",
    "# !pip install pandas-market-calendars -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fuzzy-discipline",
   "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": "cellular-duplicate",
   "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": "opposite-establishment",
   "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": "figured-stuff",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.9/site-packages/pandas/core/arraylike.py:405: RuntimeWarning: invalid value encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4403.61622 after 51 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000000000012, α=0.00780, β=0.99007\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": "aggregate-duration",
   "metadata": {},
   "source": [
    "##### Optional: Estimating with a faster estimator &mdash; GARCHVarianceTargetingParameterEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eligible-testing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective function: 4400.10204 after 84 iterations\n",
      "Optimal values for GARCH(1, 1) parameters:\n",
      "\tω=0.000000157054, α=0.02044, β=0.97734\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": "relative-warning",
   "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": "unlike-credits",
   "metadata": {},
   "source": [
    "#### Forecasting volatility for AEX\n",
    "Now that we have obtined optimal values for GARCH(1, 1) parameters ω, α, and β, we can proceed to forecast S&P 500 volatility. I crated class `volatility.parameter_estimators.GARCHVolatilityTracker` to assist in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ambient-lawyer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility of ^AEX for term 0.9315 years: 0.08172\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": "violent-heater",
   "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": 6,
   "id": "written-characterization",
   "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": "beginning-adrian",
   "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": 7,
   "id": "legal-brain",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 231.59, σ: 0.0817, Δ: 0.964, Γ: 0.000, ν: 0.302\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.00, σ: 0.0817, Δ: -0.000, Γ: 0.000, ν: 0.302\n"
     ]
    }
   ],
   "source": [
    "strike = 700.\n",
    "\n",
    "# Expected AEX dividend yield\n",
    "q = .039\n",
    "\n",
    "cur_price = asset_prices[-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": "discrete-train",
   "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": 8,
   "id": "alpine-sudan",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 240.47, σ: 0.2400, Δ: 0.884, Γ: 0.001, ν: 135.056\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 8.88, σ: 0.2400, Δ: -0.081, Γ: 0.001, ν: 135.056\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": "solved-enhancement",
   "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": 9,
   "id": "decreased-istanbul",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 231.5885 = 231.5885\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": "numerous-turning",
   "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": 10,
   "id": "thick-newark",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 240.46, σ: 0.2400, Δ: 0.886, Γ: 0.001, ν: 121.547\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for calls: 0.002474\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 8.87, σ: 0.2400, Δ: -0.079, Γ: 0.001, ν: 121.547\n",
      "Price difference between Black-Scholes-Merton and Binomial Treee pricers for puts: 0.004273\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": "rural-disposal",
   "metadata": {},
   "source": [
    "Now pricing with our volatility forecast:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "personalized-loading",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 231.59, σ: 0.0817, Δ: 0.966, Γ: 0.000, ν: 0.183\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.00, σ: 0.0817, Δ: -0.000, Γ: 0.000, ν: 0.183\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": "nuclear-lebanon",
   "metadata": {},
   "source": [
    "Let's see if the put-call parity holds when pricing with `BinomialTreePricer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "skilled-twelve",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Put-Call parity: 231.5903 = 231.5885\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": "bearing-shanghai",
   "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": "social-classroom",
   "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": "tired-ireland",
   "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": 13,
   "id": "mathematical-glory",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 218.81, σ: 0.0817, Δ: 0.966, Γ: 0.000, ν: 0.433\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.00, σ: 0.0817, Δ: -0.000, Γ: 0.000, ν: 0.433\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": "appropriate-prime",
   "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": "opposed-excess",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "^AEX EUROPEAN call option with strike 700.0 and maturity 2025-06-20, price: 223.99, σ: 0.0817, Δ: 0.966, Γ: 0.000, ν: 0.308\n",
      "^AEX EUROPEAN put option with strike 700.0 and maturity 2025-06-20, price: 0.00, σ: 0.0817, Δ: -0.000, Γ: 0.000, ν: 0.308\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": "reverse-bookmark",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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