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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Dimitri Reiswich
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
<http://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.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/instruments/compoundoption.hpp>
#include <ql/pricingengines/exotic/analyticcompoundoptionengine.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/utilities/dataformatters.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(CompoundOptionTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoffM, payoffD, exerciseM, \
exerciseD, s, q, r, today, \
v, expected, calculated, error, tolerance) \
BOOST_FAIL(\
"\nmother option type: " << payoffM->optionType() << \
"\ndaughter option type: " << payoffD->optionType() << \
"\nspot value: " << s << \
"\nstrike mother: " << payoffM->strike() << \
"\nstrike daughter: " << payoffD->strike() << \
"\ndividend yield: " << io::rate(q) << \
"\nrisk-free rate: " << io::rate(r) << \
"\nreference date: " << today << \
"\nmaturity mother: " << exerciseM->lastDate() << \
"\nmaturity daughter: " << exerciseD->lastDate() << \
"\nvolatility: " << io::volatility(v) << \
"\n expected " << greekName << ": " << expected << \
"\ncalculated " << greekName << ": " << calculated << \
"\nerror: " << error << \
"\ntolerance: " << tolerance);
struct CompoundOptionData {
Option::Type typeMother;
Option::Type typeDaughter;
Real strikeMother;
Real strikeDaughter;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time tMother; // time to maturity
Time tDaughter;// time to maturity
Volatility v; // volatility
Real npv; // expected result
Real tol; // tolerance
Real delta;
Real gamma;
Real vega;
Real theta;
};
BOOST_AUTO_TEST_CASE(testPutCallParity){
BOOST_TEST_MESSAGE("Testing compound-option put-call parity...");
// Test Put Call Parity for compound options.
// Formula taken from: "Foreign Exchange Risk", Wystup, Risk 2002
// Page 81, Equation 9.5
CompoundOptionData values[] = {
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol
{ Option::Put, Option::Call, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35},
{ Option::Call, Option::Call, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35},
{ Option::Call, Option::Put, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35},
{ Option::Call, Option::Call, 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11},
{ Option::Call, Option::Put , 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11},
{ Option::Call, Option::Call, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22},
{ Option::Call, Option::Put, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22},
{ Option::Call, Option::Call, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08},
{ Option::Call, Option::Put, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08},
{ Option::Call, Option::Call, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17},
{ Option::Call, Option::Put, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17},
};
Calendar calendar = TARGET();
DayCounter dc = Actual360();
Date todaysDate = Settings::instance().evaluationDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS(
new FlatForward(0, NullCalendar(), Handle<Quote>(rRate), dc));
ext::shared_ptr<YieldTermStructure> qTS(
new FlatForward(0, NullCalendar(), Handle<Quote>(qRate), dc));
ext::shared_ptr<BlackVolTermStructure> volTS(
new BlackConstantVol(todaysDate, NullCalendar(),
Handle<Quote>(vol), dc));
for (auto& value : values) {
ext::shared_ptr<StrikedTypePayoff> payoffMotherCall(
new PlainVanillaPayoff(Option::Call, value.strikeMother));
ext::shared_ptr<StrikedTypePayoff> payoffMotherPut(
new PlainVanillaPayoff(Option::Put, value.strikeMother));
ext::shared_ptr<StrikedTypePayoff> payoffDaughter(
new PlainVanillaPayoff(value.typeDaughter, value.strikeDaughter));
Date matDateMom = todaysDate + timeToDays(value.tMother);
Date matDateDaughter = todaysDate + timeToDays(value.tDaughter);
ext::shared_ptr<Exercise> exerciseCompound(
new EuropeanExercise(matDateMom));
ext::shared_ptr<Exercise> exerciseDaughter(
new EuropeanExercise(matDateDaughter));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
CompoundOption compoundOptionCall(payoffMotherCall,exerciseCompound,
payoffDaughter, exerciseDaughter);
CompoundOption compoundOptionPut(payoffMotherPut,exerciseCompound,
payoffDaughter, exerciseDaughter);
VanillaOption vanillaOption(EuropeanOption(payoffDaughter,
exerciseDaughter));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
ext::shared_ptr<PricingEngine> engineCompound(
new AnalyticCompoundOptionEngine(stochProcess));
ext::shared_ptr<PricingEngine> engineEuropean(
new AnalyticEuropeanEngine(stochProcess));
compoundOptionCall.setPricingEngine(engineCompound);
compoundOptionPut.setPricingEngine(engineCompound);
vanillaOption.setPricingEngine(engineEuropean);
Real discFact=rTS->discount(matDateMom);
Real discStrike = value.strikeMother * discFact;
Real calculated =
compoundOptionCall.NPV() + discStrike - compoundOptionPut.NPV()
- vanillaOption.NPV();
Real expected=0.0;
Real error=std::abs(calculated-expected);
Real tolerance=1.0e-8;
if(error>tolerance){
REPORT_FAILURE("put call parity", payoffMotherCall, payoffDaughter, exerciseCompound,
exerciseDaughter, value.s, value.q, value.r, todaysDate, value.v,
value.delta, calculated, error, tolerance);
}
}
}
BOOST_AUTO_TEST_CASE(testValues){
BOOST_TEST_MESSAGE("Testing compound-option values and greeks...");
CompoundOptionData values[] = {
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol, value, tol, delta, gamma, vega, theta
// Tolerance is taken to be pretty high with 1.0e-3, since the price/theta is very sensitive with respect to
// the implementation of the bivariate normal - which differs in the various implementations.
// Option Value Taken from Haug 2007, Greeks from www.sitmo.com
{ Option::Put, Option::Call, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35, 21.1965, 1.0e-3, -0.1966,0.0007, -32.1241, -3.3837},
//*********************************************************
// Option Values and Greeks taken from www.sitmo.com
{ Option::Call, Option::Call, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35, 17.5945, 1.0e-3, 0.3219,0.0038, 106.5185, -65.1614},
{ Option::Call, Option::Put, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35, 18.7128, 1.0e-3, -0.2906,0.0036, 103.3856, -46.6982},
{ Option::Put, Option::Put, 50.0, 520.0 , 500.0, 0.03, 0.08, 0.25, 0.5, 0.35, 15.2601, 1.0e-3, 0.1760,0.0005, -35.2570, -10.1126},
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol, value, tol, delta, gamma, vega, theta
{ Option::Call, Option::Call, 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11, 0.0729, 1.0e-3, 0.6614,2.5762, 0.5812, -0.0297},
{ Option::Call, Option::Put , 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11, 0.0074, 1.0e-3, -0.1334,1.9681, 0.2933, -0.0155},
{ Option::Put ,Option::Call, 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11, 0.0021, 1.0e-3, -0.0426,0.7252, -0.0052, -0.0058},
{ Option::Put, Option::Put , 0.05, 1.14 , 1.20, 0.0, 0.01, 0.5, 2.0, 0.11, 0.0192, 1.0e-3, 0.1626,0.1171, -0.2931, -0.0028},
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol, value, tol, delta, gamma, vega, theta
{ Option::Call, Option::Call, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22, 0.4419, 1.0e-3, 0.1049,0.0195, 11.3368, -6.2871},
{ Option::Call, Option::Put, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22, 2.6112, 1.0e-3, -0.3618,0.0337, 28.4843, -13.4124},
{ Option::Put, Option::Call, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22, 4.1616, 1.0e-3, -0.3174,0.0024, -26.6403, -2.2720},
{ Option::Put, Option::Put, 10.0, 122.0 , 120.0, 0.06, 0.02, 0.1, 0.7, 0.22, 1.0914, 1.0e-3, 0.1748,0.0165, -9.4928, -4.8995},
//*********************************************************
//*********************************************************
// Option Values and Greeks taken from mathfinance VBA implementation
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol, value, tol, delta, gamma, vega, theta
{ Option::Call, Option::Call, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08, 0.0099, 1.0e-3, 0.0285,0.0688, 0.7764, -0.0027},
{ Option::Call, Option::Put, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08, 0.9826, 1.0e-3, -0.7224,0.2158, 2.7279, -0.3332},
{ Option::Put, Option::Call, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08, 0.3585, 1.0e-3, -0.0720,-0.0835, -1.5633, -0.0117},
{ Option::Put, Option::Put, 0.4, 8.2 , 8.0, 0.05, 0.00, 2.0, 3.0, 0.08, 0.0168, 1.0e-3, 0.0378, 0.0635, 0.3882, 0.0021},
// type Mother, typeDaughter, strike Mother, strike Daughter, spot, q, r, t Mother, t Daughter, vol, value, tol, delta, gamma, vega, theta
{ Option::Call, Option::Call, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17, 0.0680, 1.0e-3, 0.4937,2.1271, 0.4418, -0.0843},
{ Option::Call, Option::Put, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17, 0.0605, 1.0e-3, -0.4169,2.0836, 0.4330, -0.0697},
{ Option::Put, Option::Call, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17, 0.0081, 1.0e-3, -0.0417,0.0761, -0.0045, -0.0020},
{ Option::Put, Option::Put, 0.02, 1.6 , 1.6, 0.013, 0.022, 0.45, 0.5, 0.17, 0.0078, 1.0e-3, 0.0413,0.0326, -0.0133, -0.0016}
};
Calendar calendar = TARGET();
DayCounter dc = Actual360();
Date todaysDate = Settings::instance().evaluationDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS(
new FlatForward(0, NullCalendar(), Handle<Quote>(rRate), dc));
ext::shared_ptr<YieldTermStructure> qTS(
new FlatForward(0, NullCalendar(), Handle<Quote>(qRate), dc));
ext::shared_ptr<BlackVolTermStructure> volTS(
new BlackConstantVol(todaysDate, NullCalendar(),
Handle<Quote>(vol), dc));
for (auto& value : values) {
ext::shared_ptr<StrikedTypePayoff> payoffMother(
new PlainVanillaPayoff(value.typeMother, value.strikeMother));
ext::shared_ptr<StrikedTypePayoff> payoffDaughter(
new PlainVanillaPayoff(value.typeDaughter, value.strikeDaughter));
Date matDateMom = todaysDate + timeToDays(value.tMother);
Date matDateDaughter = todaysDate + timeToDays(value.tDaughter);
ext::shared_ptr<Exercise> exerciseMother(
new EuropeanExercise(matDateMom));
ext::shared_ptr<Exercise> exerciseDaughter(
new EuropeanExercise(matDateDaughter));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
CompoundOption compoundOption(payoffMother,exerciseMother,
payoffDaughter, exerciseDaughter);
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
ext::shared_ptr<PricingEngine> engineCompound(
new AnalyticCompoundOptionEngine(stochProcess));
compoundOption.setPricingEngine(engineCompound);
Real calculated = compoundOption.NPV();
Real error = std::fabs(calculated - value.npv); //-values[i].npv
Real tolerance = value.tol;
if (error>tolerance) {
REPORT_FAILURE("value", payoffMother, payoffDaughter, exerciseMother, exerciseDaughter,
value.s, value.q, value.r, todaysDate, value.v, value.npv, calculated,
error, tolerance);
}
calculated = compoundOption.delta();
error = std::fabs(calculated - value.delta);
tolerance = value.tol;
if (error>tolerance) {
REPORT_FAILURE("delta", payoffMother, payoffDaughter, exerciseMother, exerciseDaughter,
value.s, value.q, value.r, todaysDate, value.v, value.delta, calculated,
error, tolerance);
}
calculated = compoundOption.gamma();
error = std::fabs(calculated - value.gamma);
tolerance = value.tol;
if (error>tolerance) {
REPORT_FAILURE("gamma", payoffMother, payoffDaughter, exerciseMother, exerciseDaughter,
value.s, value.q, value.r, todaysDate, value.v, value.gamma, calculated,
error, tolerance);
}
calculated = compoundOption.vega();
error = std::fabs(calculated - value.vega);
tolerance = value.tol;
if (error>tolerance) {
REPORT_FAILURE("vega", payoffMother, payoffDaughter, exerciseMother, exerciseDaughter,
value.s, value.q, value.r, todaysDate, value.v, value.vega, calculated,
error, tolerance);
}
calculated = compoundOption.theta();
error = std::fabs(calculated - value.theta);
tolerance = value.tol;
if (error>tolerance) {
REPORT_FAILURE("theta", payoffMother, payoffDaughter, exerciseMother, exerciseDaughter,
value.s, value.q, value.r, todaysDate, value.v, value.theta, calculated,
error, tolerance);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
