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 [ECB](https://data.ecb.europa.eu/data/data-categories):\n",
    "* `YC.B.U2.EUR.4F.G_N_A.SV_C_YM.SR_<maturity_designator>`. [This series](https://data.ecb.europa.eu/data/datasets/YC?dataset%5B0%5D=Financial%20market%20data%20-%20yield%20curve%20%28YC%29&filterSequence=dataset&advFilterDataset%5B0%5D=Financial%20market%20data%20-%20yield%20curve%20%28YC%29) returns spot rates that the ECB derives from yields on AAA-rated government bonds of the Euro Area that it calculates on every TARGET business day. The returned rates are presented using Annual percentage rates 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. **NB**: In the past I obtained these data useing [Eurostat](https://ec.europa.eu/eurostat/web/main/data/database), however due to delays in Eurostat updating its database, I switched to retrieving these data directly from the ECB.\n",
    "* `FM.B.U2.EUR.4F.KR.DFR.LEV` &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 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 sdmx1 libraries\n",
    "#!pip install pandas-datareader -U\n",
    "#!pip install sdmx1 -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 yfinance as yfin\n",
    "from pandas.tseries.offsets import MonthBegin, BDay, DateOffset\n",
    "\n",
    "import sdmx\n",
    "\n",
    "from datetime import date\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 = [(f'SR_{maturity}M', str(maturity)+'M') for maturity in month_maturities]\n",
    "maturities.extend([(f'SR_{maturity}Y', str(maturity)+'Y') for maturity in year_maturities])\n",
    "maturities1, maturities2 = zip(*maturities)\n",
    "\n",
    "ecb = sdmx.Client('ECB')\n",
    "# Taking the last 5 business days, and converting to decimal fractions\n",
    "data_msg = ecb.data('YC', key='B.U2.EUR.4F.G_N_A.SV_C_YM.' + '+'.join(maturities1), params={'startPeriod': (today-BDay(5)).date()})\n",
    "euro_curves = sdmx.to_pandas(data_msg.data[0]).loc['B', 'U2', 'EUR', '4F', 'G_N_A', 'SV_C_YM'] / 100.\n",
    "euro_curves = euro_curves.unstack(level=-2)\n",
    "euro_spot_rates = euro_curves.set_axis(pd.DatetimeIndex(euro_curves.index))  #, 'B'))\n",
    "euro_spot_rates = euro_spot_rates.loc[:, maturities1]\n",
    "euro_spot_rates.columns = maturities2\n",
    "\n",
    "# Taking the last 5 business days, and converting to decimal fractions\n",
    "# Retrieving the most recent ECB Deposit Facility Rate, and converting to decimal fractions\n",
    "data_msg = ecb.data('FM', key='B.U2.EUR.4F.KR.DFR.LEV', params={'startPeriod': (today-DateOffset(years=2)).date()})\n",
    "ecb_deposit_rate = sdmx.to_pandas(data_msg.data[0]).loc['B', 'U2', 'EUR', '4F', 'KR', 'DFR', 'LEV'] / 100.\n",
    "ecb_deposit_rate = ecb_deposit_rate.set_axis(pd.DatetimeIndex(ecb_deposit_rate.index))\n",
    "ecb_deposit_rate = pd.concat([ecb_deposit_rate, pd.Series(index=euro_spot_rates.index.difference(ecb_deposit_rate.index))])\n",
    "ecb_deposit_rate = ecb_deposit_rate.ffill().loc[euro_spot_rates.index[0]:]"
   ]
  },
  {
   "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 = [DateOffset(months=+maturity) for maturity in month_maturities]\n",
    "offsets.extend([DateOffset(years=+maturity) for maturity in year_maturities])\n",
    "offsets = [DateOffset(0)] + offsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "accurate-writing",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the riskless yield curve for Euro\n",
    "curve = curves.YieldCurve(today, offsets,\n",
    "        np.append(\n",
    "            ecb_deposit_rate.loc[euro_spot_rates.index[-1]],\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": "123dc85c-eed7-4d94-9ffe-c4b6946cf02e",
   "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
}