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"""
Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
Copyright (C) 2007 StatPro Italia srl
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 QuantLib as ql
import unittest
import math
flag = None
def raiseFlag():
global flag
flag = 1
def binaryFunction(x, y):
return 2.0 * x + y
def extrapolatedForwardRate(
firstSmoothingPoint,
lastLiquidForwardRate,
ultimateForwardRate,
alpha):
def calculate(t):
deltaT = t - firstSmoothingPoint
beta = (1.0 - math.exp(-alpha * deltaT)) / (alpha * deltaT)
return ultimateForwardRate + (
lastLiquidForwardRate - ultimateForwardRate) * beta
return calculate
class TermStructureTest(unittest.TestCase):
def setUp(self):
self.calendar = ql.TARGET()
today = self.calendar.adjust(ql.Date.todaysDate())
ql.Settings.instance().evaluationDate = today
self.settlementDays = 2
self.dayCounter = ql.Actual360()
self.settlement = self.calendar.advance(today, self.settlementDays, ql.Days)
deposits = [
ql.DepositRateHelper(
ql.makeQuoteHandle(rate / 100),
ql.Period(n, units),
self.settlementDays,
self.calendar,
ql.ModifiedFollowing,
False,
self.dayCounter,
)
for (n, units, rate) in [
(1, ql.Months, 4.581),
(2, ql.Months, 4.573),
(3, ql.Months, 4.557),
(6, ql.Months, 4.496),
(9, ql.Months, 4.490),
]
]
swaps = [
ql.SwapRateHelper(
ql.makeQuoteHandle(rate / 100),
ql.Period(years, ql.Years),
self.calendar,
ql.Annual,
ql.Unadjusted,
ql.Thirty360(ql.Thirty360.BondBasis),
ql.Euribor6M(),
)
for (years, rate) in [(1, 4.54), (5, 4.99), (10, 5.47), (20, 5.89), (30, 5.96)]
]
self.instruments = deposits + swaps
self.termStructure = ql.PiecewiseFlatForward(
self.settlement, self.instruments, self.dayCounter)
def tearDown(self):
ql.Settings.instance().evaluationDate = ql.Date()
def testImpliedObs(self):
"Testing observability of implied term structure"
global flag
flag = None
h = ql.RelinkableYieldTermStructureHandle()
settlement = self.termStructure.referenceDate()
new_settlement = self.calendar.advance(settlement, 3, ql.Years)
implied = ql.ImpliedTermStructure(h, new_settlement)
obs = ql.Observer(raiseFlag)
obs.registerWith(implied)
h.linkTo(self.termStructure)
if not flag:
self.fail("Observer was not notified of term structure change")
def testFSpreadedObs(self):
"Testing observability of forward-spreaded term structure"
global flag
flag = None
me = ql.SimpleQuote(0.01)
mh = ql.QuoteHandle(me)
h = ql.RelinkableYieldTermStructureHandle()
spreaded = ql.ForwardSpreadedTermStructure(h, mh)
obs = ql.Observer(raiseFlag)
obs.registerWith(spreaded)
h.linkTo(self.termStructure)
if not flag:
self.fail("Observer was not notified of term structure change")
flag = None
me.setValue(0.005)
if not flag:
self.fail("Observer was not notified of spread change")
def testZSpreadedObs(self):
"Testing observability of zero-spreaded term structure"
global flag
flag = None
me = ql.SimpleQuote(0.01)
mh = ql.QuoteHandle(me)
h = ql.RelinkableYieldTermStructureHandle()
spreaded = ql.ZeroSpreadedTermStructure(h, mh)
obs = ql.Observer(raiseFlag)
obs.registerWith(spreaded)
h.linkTo(self.termStructure)
if not flag:
self.fail("Observer was not notified of term structure change")
flag = None
me.setValue(0.005)
if not flag:
self.fail("Observer was not notified of spread change")
def testCompositeZeroYieldStructure(self):
"""Testing composite zero yield structure"""
settlement = self.termStructure.referenceDate()
compounding = ql.Compounded
freq = ql.Semiannual
flatTs = ql.FlatForward(
settlement,
ql.makeQuoteHandle(0.0085),
self.dayCounter)
firstHandle = ql.YieldTermStructureHandle(flatTs)
secondHandle = ql.YieldTermStructureHandle(self.termStructure)
compositeTs = ql.CompositeZeroYieldStructure(
firstHandle, secondHandle, binaryFunction, compounding, freq)
maturity = settlement + ql.Period(20, ql.Years)
expectedZeroRate = binaryFunction(
firstHandle.zeroRate(
maturity, self.dayCounter, compounding, freq).rate(),
secondHandle.zeroRate(
maturity, self.dayCounter, compounding, freq).rate())
actualZeroRate = compositeTs.zeroRate(
maturity, self.dayCounter, compounding, freq).rate()
failMsg = """ Composite zero yield structure rate replication failed:
expected zero rate: {expected}
actual zero rate: {actual}
""".format(expected=expectedZeroRate,
actual=actualZeroRate)
self.assertAlmostEqual(
first=expectedZeroRate,
second=actualZeroRate,
delta=1.0e-12,
msg=failMsg)
def testUltimateForwardTermStructure(self):
"""Testing ultimate forward term structure"""
settlement = self.termStructure.referenceDate()
ufr = ql.makeQuoteHandle(0.06)
llfr = ql.makeQuoteHandle(0.05)
fsp = ql.Period(20, ql.Years)
alpha = 0.05
baseCrvHandle = ql.YieldTermStructureHandle(self.termStructure)
ufrCrv = ql.UltimateForwardTermStructure(
baseCrvHandle, llfr, ufr, fsp, alpha)
cutOff = ufrCrv.timeFromReference(settlement + fsp)
forwardCalculator = extrapolatedForwardRate(
cutOff, llfr.value(), ufr.value(), alpha)
times = [ufrCrv.timeFromReference(settlement + ql.Period(x, ql.Years))
for x in [21, 30, 40, 50, 60, 70, 80, 90, 100]]
for t in times:
actualForward = ufrCrv.forwardRate(
cutOff, t, ql.Continuous, ql.NoFrequency, True).rate()
expectedForward = forwardCalculator(t)
failMsg = """ UFR term structure forward replication failed for:
time to maturity: {timeToMaturity}
expected forward rate: {expected}
actual forward rate: {actual}
""".format(timeToMaturity=t,
expected=expectedForward,
actual=actualForward)
self.assertAlmostEqual(
first=expectedForward,
second=actualForward,
delta=1.0e-12,
msg=failMsg)
def testTermStructureInterpolationSchemes(self):
"""Testing different interpolation schemes and their consistency"""
args = [self.settlement, self.instruments, self.dayCounter]
mapping = [
[ql.PiecewiseParabolicCubicZero,
ql.ParabolicCubicZeroCurve, 'Parabolic Zero'],
[ql.PiecewiseMonotonicParabolicCubicZero,
ql.MonotonicParabolicCubicZeroCurve, 'Monotone Parabolic Zero'],
[ql.PiecewiseLogParabolicCubicDiscount,
ql.LogParabolicCubicDiscountCurve, 'Log Parabolic Discount'],
[ql.PiecewiseMonotonicLogParabolicCubicDiscount,
ql.MonotonicLogParabolicCubicDiscountCurve, 'Monotone Log Parabolic Discount'],
]
for bootstrap, interp, name in mapping:
bootstrap_crv = bootstrap(*args)
dates, nodes = zip(*bootstrap_crv.nodes())
equivalent_crv = interp(dates, nodes, self.dayCounter)
for d in dates:
expected = equivalent_crv.zeroRate(
d, self.dayCounter, ql.Continuous, ql.NoFrequency).rate()
actual = bootstrap_crv.zeroRate(
d, self.dayCounter, ql.Continuous, ql.NoFrequency).rate()
failMsg = """ Interpolation check failed for:
interpolation: {interpolation}
expected zero rate: {expected}
actual zero rate: {actual}
""".format(interpolation=name,
expected=expected,
actual=actual)
self.assertAlmostEqual(
first=expected,
second=actual,
delta=1.0e-12,
msg=failMsg)
def testInterpolatedPiecewiseZeroSpreadedTermStructure(self):
"""Testing different interpolation schemes for zero spreaded term structure"""
h = ql.RelinkableYieldTermStructureHandle()
h.linkTo(self.termStructure)
spreads = [(1, 0.005), (2, 0.008), (3, 0.0103), (4, 0.0145), (5, 0.025)]
dates, quotes = zip(*[(h.referenceDate() + ql.Period(t, ql.Years),
ql.QuoteHandle(ql.SimpleQuote(s)))
for t, s in spreads])
args = [h, quotes, dates]
constructors = [ql.SpreadedLinearZeroInterpolatedTermStructure,
ql.SpreadedBackwardFlatZeroInterpolatedTermStructure,
ql.SpreadedCubicZeroInterpolatedTermStructure,
ql.SpreadedKrugerZeroInterpolatedTermStructure,
ql.SpreadedSplineCubicZeroInterpolatedTermStructure]
for constructor in constructors:
spreadedTs = constructor(*args)
for d, r in zip(dates, quotes):
expected = r.value()
zeroFromSpreadTS = spreadedTs.zeroRate(
d, self.dayCounter, ql.Continuous, ql.NoFrequency).rate()
zeroFromBaseTs = h.zeroRate(
d, self.dayCounter, ql.Continuous, ql.NoFrequency).rate()
actual = zeroFromSpreadTS - zeroFromBaseTs
failMsg = """ Interpolated piecewise zero spreaded term structure
zero rate replication failed for:
maturity: {maturity}
expected zero rate: {expected}
actual zero rate: {actual}
""".format(maturity=d,
expected=expected,
actual=actual)
self.assertAlmostEqual(
first=expected,
second=actual,
delta=1.0e-12,
msg=failMsg)
def testQuantoTermStructure(self):
"""Testing quanto term structure"""
today = ql.Date.todaysDate()
dividend_ts = ql.YieldTermStructureHandle(
ql.FlatForward(
today,
ql.makeQuoteHandle(0.055),
self.dayCounter
)
)
r_domestic_ts = ql.YieldTermStructureHandle(
ql.FlatForward(
today,
ql.makeQuoteHandle(-0.01),
self.dayCounter
)
)
r_foreign_ts = ql.YieldTermStructureHandle(
ql.FlatForward(
today,
ql.makeQuoteHandle(0.02),
self.dayCounter
)
)
sigma_s = ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
today,
self.calendar,
ql.makeQuoteHandle(0.25),
self.dayCounter
)
)
sigma_fx = ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
today,
self.calendar,
ql.makeQuoteHandle(0.05),
self.dayCounter
)
)
rho = ql.makeQuoteHandle(0.3)
s_0 = ql.makeQuoteHandle(100.0)
exercise = ql.EuropeanExercise(self.calendar.advance(today, 6, ql.Months))
payoff = ql.PlainVanillaPayoff(ql.Option.Call, 95.0)
vanilla_option = ql.VanillaOption(payoff, exercise)
quanto_ts = ql.YieldTermStructureHandle(
ql.QuantoTermStructure(
dividend_ts,
r_domestic_ts,
r_foreign_ts,
sigma_s,
ql.nullDouble(),
sigma_fx,
ql.nullDouble(),
rho.value()
)
)
gbm_quanto = ql.BlackScholesMertonProcess(s_0, quanto_ts, r_domestic_ts, sigma_s)
vanilla_engine = ql.AnalyticEuropeanEngine(gbm_quanto)
vanilla_option.setPricingEngine(vanilla_engine)
quanto_option = ql.QuantoVanillaOption(payoff, exercise)
gbm_vanilla = ql.BlackScholesMertonProcess(s_0, dividend_ts, r_domestic_ts, sigma_s)
quanto_engine = ql.QuantoEuropeanEngine(gbm_vanilla, r_foreign_ts, sigma_fx, rho)
quanto_option.setPricingEngine(quanto_engine)
quanto_option_pv = quanto_option.NPV()
vanilla_option_pv = vanilla_option.NPV()
message = """Failed to reproduce QuantoOption / EuropeanQuantoEngine NPV:
{quanto_pv}
by using the QuantoTermStructure as the dividend together with
VanillaOption / AnalyticEuropeanEngine:
{vanilla_pv}
""".format(
quanto_pv=quanto_option_pv,
vanilla_pv=vanilla_option_pv
)
self.assertAlmostEqual(
quanto_option_pv,
vanilla_option_pv,
delta=1e-12,
msg=message
)
def testLazyObject(self):
evaluationDate = ql.Settings.instance().evaluationDate
nodes = self.termStructure.nodes()
self.termStructure.freeze()
ql.Settings.instance().evaluationDate = self.calendar.advance(evaluationDate, 100, ql.Days)
# Check that dates and rates are unchanged
for i in range(len(self.termStructure.nodes())):
self.assertEqual(nodes[i][0], self.termStructure.nodes()[i][0])
self.assertEqual(nodes[i][1], self.termStructure.nodes()[i][1])
self.termStructure.recalculate()
# Check that dates have changed (except the reference, which is fixed)
for i in range(1, len(self.termStructure.nodes())):
self.assertNotEqual(nodes[i][0], self.termStructure.nodes()[i][0])
ql.Settings.instance().evaluationDate = evaluationDate
self.termStructure.unfreeze()
if __name__ == "__main__":
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
|
