euro-riskless-rate-curve-construction-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "distinguished-citizenship",
   "metadata": {},
   "source": [
    "## Constructing a riskless rate curve for Euro\n",
    "The first thing we need to do to price any option on an equity priced in Euro is construct the so-called riskless sport rate (aka zero-rate) curve for Euro. This is because pricing of derivatives is done in _the risk-neutral world_ where all investors are assumed not to require a premium for additional risks, hence future cashflows are discounted using the riskless rate to obtain their NPV.\n",
    "\n",
    "I use [the Euro area yield curve constructed daily by the ECB](https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/html/index.en.html) as proxies for riskless rates. These rates are derived from AAA-rated government bonds of the Euro area. Ideally, using swap rates might be better as government bond yields tend to be 3-4 basis points lower given that government bonds tend to be heavily used in repo trades. See the [this note from the ECB](https://www.ecb.europa.eu/pub/pdf/scpsps/ecb.sps27.en.pdf) for an explanation.\n",
    "\n",
    "I use the following dataseries provided by the [Eurostat](https://ec.europa.eu/eurostat/web/main/data/database):\n",
    "* `irt_euryld_d` &mdash; Euro yield curves (daily frequency). This series returns a dataset from which multiple yields can be extracted for maturities ranging from 3 months to 30 years: Instantaneous forward yield curve, Par yield curve, and Spot rate yield curve. For pricing options I use the Spot rate yield curve. The returned rates are presented using Annual percentage rates/yields and represent the average over a given business day. [The ECB uses continuous compounding](https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/shared/pdf/technical_notes.pdf) when calculating them.\n",
    "\n",
    "And one dataset from [FRED](https://fred.stlouisfed.org):\n",
    "* `ECBDFR` &mdash; ECB Deposit Facility Rate for Euro Area (daily frequency). I use it as proxy for overnight rate.\n",
    "\n",
    "I construct the Euro riskfree curve using 40 curve points with the following terms (which is pretty good for accurate pricing):\n",
    "* Overnight rate from the `ECBDFR` ECB Deposit Facility Rate for Euro Area series (adjusted for the actual/actual day count convention)\n",
    "* 3-, 4-, 5-, 6-, 7-, 8-, 9-, 10-, 11-months spot rate from the `irt_euryld_d` Euro yield curve series\n",
    "* 1-, 2-, 3-, ..., 29-, 30-years spot rate from the `irt_euryld_d` Euro yield curve series\n",
    "\n",
    "In the `pricing.curves.YieldCurve` class I use cubic splines by default to interpolate when constructing the curve. See [this article](http://web.math.ku.dk/~rolf/HaganWest.pdf) for more details on interpolation methods if you want to know more. Cubic splines is pretty advanced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "clean-funds",
   "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 eurostat libraries\n",
    "#!pip install pandas-datareader -U\n",
    "#!pip install eurostat -U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "horizontal-banking",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.ticker as mtick\n",
    "import pandas_datareader.data as web\n",
    "import yfinance as yfin\n",
    "from pandas.tseries.offsets import MonthBegin, BDay\n",
    "\n",
    "import eurostat\n",
    "\n",
    "from datetime import date\n",
    "import re\n",
    "\n",
    "from dateutil.relativedelta import relativedelta\n",
    "\n",
    "from volatility import parameter_estimators, volatility_trackers\n",
    "from pricing import curves, options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "protective-chart",
   "metadata": {},
   "outputs": [],
   "source": [
    "today = date.today()\n",
    "\n",
    "# The ECB provides yields for maturities ranging from 3 months till 30 years\n",
    "month_maturities = range(3, 12)\n",
    "year_maturities = range(1, 31)\n",
    "maturities = ['M'+str(maturity) for maturity in month_maturities]\n",
    "maturities.extend(['Y'+str(maturity) for maturity in year_maturities])\n",
    "\n",
    "# Taking the last 3 business days, and converting to decimal fractions\n",
    "euro_curves = eurostat.get_data_df('irt_euryld_d', filter_pars={\n",
    "    'startPeriod': (today-BDay(3)).date(), 'freq': 'D',\n",
    "    'yld_curv': 'SPOT_RT',\n",
    "    'maturity': maturities,\n",
    "    'bonds': 'CGB_EA_AAA', 'geo': 'EA'})\n",
    "euro_curves = euro_curves.drop(euro_curves.columns[:2].append(euro_curves.columns[3:5]), axis=1)\n",
    "euro_curves = euro_curves.set_index(euro_curves.columns[0]).T / 100.\n",
    "euro_spot_rates = euro_curves.set_axis(pd.DatetimeIndex(euro_curves.index, 'B'))\n",
    "\n",
    "# Taking the last 3 business days, and converting to decimal fractions\n",
    "ecb_deposit_rate = web.get_data_fred('ECBDFR', start=today-BDay(100)) / 100.\n",
    "\n",
    "# Make daily frequency explicit\n",
    "ecb_deposit_rate = ecb_deposit_rate.asfreq('D')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "convinced-civilian",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Converting ECB Deposit rates from actual/360 to actual/actual and then to a continuous compounding frequency\n",
    "leap_year_cond = lambda idx: idx.year % 4 == 0 & ((idx.year % 100 != 0) | (idx.year % 400 == 0))\n",
    "ecb_deposit_rate[leap_year_cond(ecb_deposit_rate.index)] *= 366. / 360\n",
    "ecb_deposit_rate[np.invert(leap_year_cond(ecb_deposit_rate.index))] *= 365. / 360\n",
    "\n",
    "# From annual to continuous compounding\n",
    "ecb_deposit_rate = np.log(1 + ecb_deposit_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "tough-depression",
   "metadata": {},
   "outputs": [],
   "source": [
    "date_now = euro_spot_rates.index[-1].date()\n",
    "offsets = [relativedelta(months=+maturity) for maturity in month_maturities]\n",
    "offsets.extend([relativedelta(years=+maturity) for maturity in year_maturities])\n",
    "offsets = [relativedelta()] + offsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "accurate-writing",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the riskless yield curve for Euro\n",
    "# Ideally want to call ecb_deposit_rate.loc[euro_spot_rates.index[-1]].to_numpy(),\n",
    "# however the FRED sometimes lags behind a little...\n",
    "curve = curves.YieldCurve(today, offsets,\n",
    "        np.append(\n",
    "            ecb_deposit_rate.iloc[-1,0],\n",
    "            euro_spot_rates.iloc[-1].to_numpy()),\n",
    "        compounding_freq=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "progressive-integration",
   "metadata": {},
   "source": [
    "### Optional: Visualizing the riskless yield curve for Euro\n",
    "The rates presented use a continuous compounding frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "divided-commission",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "curve_points = curve.get_curve_points(120)\n",
    "ax = curve_points.plot(figsize=(20,10), grid=True,\n",
    "                       title='Euro Riskless Rate Curve over month ' + euro_spot_rates.index[-1].strftime('%Y-%m-%d'),\n",
    "                       xlim=(curve_points.index[0], curve_points.index[-1]),\n",
    "                       xticks=curve_points.index[::4], xlabel='', rot=45)\n",
    "ax.yaxis.set_major_formatter(mtick.PercentFormatter(1))\n",
    "_ = ax.set_xticklabels(list(map(lambda x: x.strftime('%Y-%m'), curve_points.index[::4])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "scenic-rating",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert curve.date == BDay(1).rollforward(today).date()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "traditional-closer",
   "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
}