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"""
Copyright (C) 2020 Marcin Rybacki
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
"""
import unittest
import QuantLib as ql
EPSILON = 1.e-9
# Hypothetical market data
EUR_ZERO_RATES = [(ql.Period(1, ql.Days), 0.0048),
(ql.Period(1, ql.Years), 0.0048),
(ql.Period(2, ql.Years), 0.00475),
(ql.Period(3, ql.Years), 0.005),
(ql.Period(5, ql.Years), 0.0055),
(ql.Period(10, ql.Years), 0.007)]
EUR_BEI_SWAP_RATES = [(ql.Period(1, ql.Years), 0.0301),
(ql.Period(2, ql.Years), 0.0299),
(ql.Period(3, ql.Years), 0.0305),
(ql.Period(5, ql.Years), 0.0315),
(ql.Period(10, ql.Years), 0.0355)]
# Source:
# https://ec.europa.eu/eurostat/web/products-datasets/-/teicp240.
EU_FIXING_DATA = [(ql.Date(1, ql.April, 2018), 103.11),
(ql.Date(1, ql.May, 2018), 103.64),
(ql.Date(1, ql.June, 2018), 103.76),
(ql.Date(1, ql.July, 2018), 103.41),
(ql.Date(1, ql.August, 2018), 103.58)]
CAL = ql.TARGET()
DAY_COUNTER = ql.ActualActual(ql.ActualActual.ISDA)
BDC = ql.ModifiedFollowing
VALUATION_DATE = CAL.adjust(ql.Date(10, ql.September, 2018))
OBSERVATION_LAG = ql.Period(3, ql.Months)
def create_inflation_swap_helper(
reference_date,
inflation_data,
inflation_index,
interpolation,
observation_lag=OBSERVATION_LAG,
calendar=CAL,
business_day_convention=BDC,
day_counter=DAY_COUNTER):
maturity = CAL.advance(reference_date, inflation_data[0])
quote = ql.makeQuoteHandle(inflation_data[1])
return ql.ZeroCouponInflationSwapHelper(
quote,
observation_lag,
maturity,
calendar,
business_day_convention,
day_counter,
inflation_index,
interpolation,
)
def build_nominal_term_structure(
reference_date,
nominal_data):
nominal_dc = ql.Actual365Fixed()
dates = [CAL.advance(reference_date, x[0]) for x in nominal_data]
rates = [x[1] for x in nominal_data]
return ql.ZeroCurve(dates, rates, nominal_dc)
def build_hicp_index(
fixing_data,
inflation_crv_handle):
index = ql.EUHICP(inflation_crv_handle)
for x in fixing_data:
# force override in case of multiple use
index.addFixing(x[0], x[1], True)
return index
SEASONAL = {ql.January: 1.0, ql.February: 1.01, ql.March: 1.011,
ql.April: 1.009, ql.May: 1.008, ql.June: 1.012,
ql.July: 1.0078, ql.August: 1.006,
ql.September: 1.0085, ql.October: 1.0096,
ql.November: 1.0067, ql.December: 1.0055}
def construct_seasonality(reference_date):
frequency = ql.Monthly
seasonality_base_date = ql.Date(1, ql.January, reference_date.year())
factors = list(SEASONAL.values())
return ql.MultiplicativePriceSeasonality(
seasonality_base_date, frequency, factors)
def build_inflation_term_structure(
reference_date,
zero_coupon_swaps_data,
inflation_index,
interpolation,
observation_lag=OBSERVATION_LAG,
include_seasonality=False):
helpers = [create_inflation_swap_helper(reference_date,
x,
inflation_index,
interpolation)
for x in zero_coupon_swaps_data]
cpi_term_structure = ql.PiecewiseZeroInflation(
reference_date,
inflation_index.lastFixingDate(),
inflation_index.frequency(),
DAY_COUNTER,
helpers)
if include_seasonality:
seasonality = construct_seasonality(reference_date)
cpi_term_structure.setSeasonality(seasonality)
return cpi_term_structure
def create_inflation_swap(
inflation_idx,
start_date,
end_date,
rate,
interpolation,
observation_lag=OBSERVATION_LAG,
nominal=1.e6,
payer=ql.Swap.Payer):
return ql.ZeroCouponInflationSwap(
payer,
nominal,
start_date,
end_date,
CAL,
BDC,
DAY_COUNTER,
rate,
inflation_idx,
observation_lag,
interpolation)
def interpolate_historic_index(
inflation_idx, fixing_date, observation_lag=OBSERVATION_LAG):
first_dt = ql.Date(1, fixing_date.month(), fixing_date.year())
second_dt = ql.Date.endOfMonth(fixing_date) + 1
slope_numerator = fixing_date - first_dt
slope_denominator = (
(second_dt + observation_lag) - (first_dt + observation_lag))
slope = float(slope_numerator) / float(slope_denominator)
return inflation_idx.fixing(first_dt) + slope * (
inflation_idx.fixing(second_dt) - inflation_idx.fixing(first_dt))
class InflationTest(unittest.TestCase):
def setUp(self):
ql.Settings.instance().evaluationDate = VALUATION_DATE
self.inflation_ts_handle = ql.RelinkableZeroInflationTermStructureHandle()
self.nominal_ts_handle = ql.RelinkableYieldTermStructureHandle()
self.nominal_ts_handle.linkTo(
build_nominal_term_structure(VALUATION_DATE, EUR_ZERO_RATES))
self.discount_engine = ql.DiscountingSwapEngine(self.nominal_ts_handle)
def test_par_swap_pricing_fom_indexation_without_seasonality(self):
"""Testing pricing of par inflation swap for First-Of-Month indexation"""
inflation_idx = build_hicp_index(
EU_FIXING_DATA, self.inflation_ts_handle)
inflation_ts = build_inflation_term_structure(
VALUATION_DATE,
EUR_BEI_SWAP_RATES,
inflation_idx,
ql.CPI.Flat)
self.inflation_ts_handle.linkTo(inflation_ts)
zciis = create_inflation_swap(
inflation_idx,
VALUATION_DATE,
CAL.advance(VALUATION_DATE, ql.Period(10, ql.Years)),
0.0355,
ql.CPI.Flat)
zciis.setPricingEngine(self.discount_engine)
npv = zciis.NPV()
# Check whether swap prices to par
fail_msg = """ Failed to price zero coupon inflation swap to par:
index: {inflation_idx}
end date: {end_date}
observation lag: {observation_lag}
npv: {npv}
expected npv: {expected_npv}
tolerance: {tolerance}
""".format(inflation_idx=inflation_idx.familyName(),
end_date=zciis.maturityDate(),
observation_lag=OBSERVATION_LAG,
npv=npv,
expected_npv=0.0,
tolerance=EPSILON)
self.assertTrue(
abs(npv) < EPSILON,
msg=fail_msg)
def test_inflation_leg_payment_fom_indexation_without_seasonality(self):
"""Testing inflation leg payment for First-Of-Month indexation"""
inflation_idx = build_hicp_index(
EU_FIXING_DATA, self.inflation_ts_handle)
inflation_ts = build_inflation_term_structure(
VALUATION_DATE,
EUR_BEI_SWAP_RATES,
inflation_idx,
ql.CPI.Flat)
self.inflation_ts_handle.linkTo(inflation_ts)
zciis = create_inflation_swap(
inflation_idx,
VALUATION_DATE,
CAL.advance(VALUATION_DATE, ql.Period(10, ql.Years)),
0.0355,
ql.CPI.Flat)
zciis.setPricingEngine(self.discount_engine)
inflation_cf = ql.as_indexed_cashflow(
zciis.inflationLeg()[0])
# Obtaining base index for the inflation swap
swap_base_dt = inflation_cf.baseDate()
swap_base_fixing = inflation_idx.fixing(swap_base_dt)
# Replicate fixing projection
fixing_dt = inflation_cf.fixingDate()
ts_base_dt = inflation_ts.baseDate()
ts_base_fixing = inflation_idx.fixing(ts_base_dt)
# Apply FOM indexation rule
effective_fixing_dt = ql.Date(
1, fixing_dt.month(), fixing_dt.year())
fraction = inflation_ts.dayCounter().yearFraction(
ts_base_dt, effective_fixing_dt)
t = inflation_ts.timeFromReference(effective_fixing_dt)
zero_rate = inflation_ts.zeroRate(t)
expected_fixing = ts_base_fixing * (
1.0 + zero_rate)**fraction
expected_inflation_leg_payment = (
expected_fixing / swap_base_fixing - 1.0) * inflation_cf.notional()
actual_inflation_leg_payment = inflation_cf.amount()
fail_msg = """ Failed to replicate inflation leg payment
for First-Of-Month indexation:
index: {inflation_idx}
end date: {end_date}
observation lag: {observation_lag}
inflation leg payment: {actual_payment}
replicated payment: {expected_payment}
tolerance: {tolerance}
""".format(inflation_idx=inflation_idx.familyName(),
end_date=zciis.maturityDate(),
observation_lag=OBSERVATION_LAG,
actual_payment=actual_inflation_leg_payment,
expected_payment=expected_inflation_leg_payment,
tolerance=EPSILON)
self.assertAlmostEqual(
first=actual_inflation_leg_payment,
second=expected_inflation_leg_payment,
delta=EPSILON,
msg=fail_msg)
def test_lagged_fixing_method(self):
"""Testing lagged fixing method"""
inflation_idx = build_hicp_index(
EU_FIXING_DATA, self.inflation_ts_handle)
inflation_ts = build_inflation_term_structure(
VALUATION_DATE,
EUR_BEI_SWAP_RATES,
inflation_idx,
ql.CPI.Flat)
self.inflation_ts_handle.linkTo(inflation_ts)
maturity_date = ql.Date(25, ql.October, 2027)
lag = ql.Period(3, ql.Months)
indexation = ql.CPI.Flat
actual_fixing = ql.CPI.laggedFixing(inflation_idx, maturity_date, lag, indexation)
expected_fixing = inflation_idx.fixing(ql.Date(1, ql.July, 2027))
fail_msg = """ Failed to replicate lagged fixing:
index: {inflation_idx}
actual fixing: {actual_fixing}
expected fixing: {expected_fixing}
tolerance: {tolerance}
""".format(inflation_idx=inflation_idx.familyName(),
actual_fixing=actual_fixing,
expected_fixing=expected_fixing,
tolerance=EPSILON)
self.assertAlmostEqual(
first=actual_fixing,
second=expected_fixing,
msg=fail_msg,
delta=EPSILON)
if __name__ == '__main__':
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
|
