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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Thema Consulting SA
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.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/shared_ptr.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/instruments/doublebarrieroption.hpp>
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/pricingengines/barrier/analyticdoublebarrierbinaryengine.hpp>
#include <ql/pricingengines/barrier/fdhestondoublebarrierengine.hpp>
#include <ql/experimental/barrieroption/binomialdoublebarrierengine.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(DoubleBinaryOptionTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, barrierType, barrier_lo, \
barrier_hi, s, q, r, today, v, expected, calculated, \
error, tolerance) \
BOOST_ERROR(payoff->optionType() << " option with " \
<< barrierType << " barrier type:\n" \
<< " barrier_lo: " << barrier_lo << "\n" \
<< " barrier_hi: " << barrier_hi << "\n" \
<< payoffTypeToString(payoff) << " payoff:\n" \
<< " spot value: " << s << "\n" \
<< " strike: " << payoff->strike() << "\n" \
<< " dividend yield: " << io::rate(q) << "\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " maturity: " << exercise->lastDate() << "\n" \
<< " volatility: " << io::volatility(v) << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance << "\n");
struct DoubleBinaryOptionData {
DoubleBarrier::Type barrierType;
Real barrier_lo;
Real barrier_hi;
Real cash; // cash payoff for cash-or-nothing
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time t; // time to maturity
Volatility v; // volatility
Real result; // expected result
Real tol; // tolerance
};
BOOST_AUTO_TEST_CASE(testHaugValues) {
BOOST_TEST_MESSAGE("Testing cash-or-nothing double barrier options against Haug's values...");
DoubleBinaryOptionData values[] = {
/* The data below are from
"Option pricing formulas 2nd Ed.", E.G. Haug, McGraw-Hill 2007 pag. 181
Note: book uses cost of carry b, instead of dividend rate q
*/
// barrierType, bar_lo, bar_hi, cash, spot, q, r, t, vol, value, tol
{ DoubleBarrier::KnockOut, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 9.8716, 1e-4 },
{ DoubleBarrier::KnockOut, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 8.9307, 1e-4 },
{ DoubleBarrier::KnockOut, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 6.3272, 1e-4 },
{ DoubleBarrier::KnockOut, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 1.9094, 1e-4 },
{ DoubleBarrier::KnockOut, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 9.7961, 1e-4 },
{ DoubleBarrier::KnockOut, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 7.2300, 1e-4 },
{ DoubleBarrier::KnockOut, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 3.7100, 1e-4 },
{ DoubleBarrier::KnockOut, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 0.4271, 1e-4 },
{ DoubleBarrier::KnockOut, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 8.9054, 1e-4 },
{ DoubleBarrier::KnockOut, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 3.6752, 1e-4 },
{ DoubleBarrier::KnockOut, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 0.7960, 1e-4 },
{ DoubleBarrier::KnockOut, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 0.0059, 1e-4 },
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 3.6323, 1e-4 },
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 0.0911, 1e-4 },
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 0.0002, 1e-4 },
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 0.0000, 1e-4 },
{ DoubleBarrier::KIKO, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0000, 1e-4 },
{ DoubleBarrier::KIKO, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 0.2402, 1e-4 },
{ DoubleBarrier::KIKO, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 1.4076, 1e-4 },
{ DoubleBarrier::KIKO, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 3.8160, 1e-4 },
{ DoubleBarrier::KIKO, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0075, 1e-4 },
{ DoubleBarrier::KIKO, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 0.9910, 1e-4 },
{ DoubleBarrier::KIKO, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 2.8098, 1e-4 },
{ DoubleBarrier::KIKO, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 4.6612, 1e-4 },
{ DoubleBarrier::KIKO, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.2656, 1e-4 },
{ DoubleBarrier::KIKO, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 2.7954, 1e-4 },
{ DoubleBarrier::KIKO, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 4.4024, 1e-4 },
{ DoubleBarrier::KIKO, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 4.9266, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 2.6285, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 4.7523, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 4.9096, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 4.9675, 1e-4 },
// following values calculated with haug's VBA code
{ DoubleBarrier::KnockIn, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0042, 1e-4 },
{ DoubleBarrier::KnockIn, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 0.9450, 1e-4 },
{ DoubleBarrier::KnockIn, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 3.5486, 1e-4 },
{ DoubleBarrier::KnockIn, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 7.9663, 1e-4 },
{ DoubleBarrier::KnockIn, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0797, 1e-4 },
{ DoubleBarrier::KnockIn, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 2.6458, 1e-4 },
{ DoubleBarrier::KnockIn, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 6.1658, 1e-4 },
{ DoubleBarrier::KnockIn, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 9.4486, 1e-4 },
{ DoubleBarrier::KnockIn, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.9704, 1e-4 },
{ DoubleBarrier::KnockIn, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 6.2006, 1e-4 },
{ DoubleBarrier::KnockIn, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 9.0798, 1e-4 },
{ DoubleBarrier::KnockIn, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 9.8699, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 6.2434, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 9.7847, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 9.8756, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 9.8758, 1e-4 },
{ DoubleBarrier::KOKI, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0041, 1e-4 },
{ DoubleBarrier::KOKI, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 0.7080, 1e-4 },
{ DoubleBarrier::KOKI, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 2.1581, 1e-4 },
{ DoubleBarrier::KOKI, 80.00, 120.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 4.2061, 1e-4 },
{ DoubleBarrier::KOKI, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.0723, 1e-4 },
{ DoubleBarrier::KOKI, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 1.6663, 1e-4 },
{ DoubleBarrier::KOKI, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 3.3930, 1e-4 },
{ DoubleBarrier::KOKI, 85.00, 115.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 4.8679, 1e-4 },
{ DoubleBarrier::KOKI, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 0.7080, 1e-4 },
{ DoubleBarrier::KOKI, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 3.4424, 1e-4 },
{ DoubleBarrier::KOKI, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 4.7496, 1e-4 },
{ DoubleBarrier::KOKI, 90.00, 110.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 5.0475, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.10, 3.6524, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.20, 5.1256, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.30, 5.0763, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 100.00, 0.02, 0.05, 0.25, 0.50, 5.0275, 1e-4 },
// degenerate cases
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 80.00, 0.02, 0.05, 0.25, 0.10, 0.0000, 1e-4 },
{ DoubleBarrier::KnockOut, 95.00, 105.00, 10.00, 110.00, 0.02, 0.05, 0.25, 0.10, 0.0000, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 80.00, 0.02, 0.05, 0.25, 0.10, 10.0000, 1e-4 },
{ DoubleBarrier::KnockIn, 95.00, 105.00, 10.00, 110.00, 0.02, 0.05, 0.25, 0.10, 10.0000, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 80.00, 0.02, 0.05, 0.25, 0.10, 10.0000, 1e-4 },
{ DoubleBarrier::KIKO, 95.00, 105.00, 10.00, 110.00, 0.02, 0.05, 0.25, 0.10, 0.0000, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 80.00, 0.02, 0.05, 0.25, 0.10, 0.0000, 1e-4 },
{ DoubleBarrier::KOKI, 95.00, 105.00, 10.00, 110.00, 0.02, 0.05, 0.25, 0.10, 10.0000, 1e-4 },
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(100.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.04));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.01));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.25));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (auto& value : values) {
ext::shared_ptr<StrikedTypePayoff> payoff(
new CashOrNothingPayoff(Option::Call, 0, value.cash));
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise;
if (value.barrierType == DoubleBarrier::KIKO || value.barrierType == DoubleBarrier::KOKI)
exercise = ext::make_shared<AmericanExercise>(today, exDate);
else
exercise = ext::make_shared<EuropeanExercise>(exDate);
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new
BlackScholesMertonProcess(Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
// checking with analytic engine
ext::shared_ptr<PricingEngine> engine(
new AnalyticDoubleBarrierBinaryEngine(stochProcess));
DoubleBarrierOption opt(value.barrierType, value.barrier_lo, value.barrier_hi, 0, payoff,
exercise);
opt.setPricingEngine(engine);
Real calculated = opt.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE("value", payoff, exercise, value.barrierType, value.barrier_lo,
value.barrier_hi, value.s, value.q, value.r, today, value.v,
value.result, calculated, error, value.tol);
}
Size steps = 500;
// checking with binomial engine
engine = ext::shared_ptr<PricingEngine>(
new BinomialDoubleBarrierEngine<CoxRossRubinstein,
DiscretizedDoubleBarrierOption>(stochProcess,
steps));
opt.setPricingEngine(engine);
calculated = opt.NPV();
expected = value.result;
error = std::fabs(calculated-expected);
double tol = 0.22;
if (error>tol) {
REPORT_FAILURE("Binomial value", payoff, exercise, value.barrierType, value.barrier_lo,
value.barrier_hi, value.s, value.q, value.r, today, value.v,
value.result, calculated, error, tol);
}
}
}
BOOST_AUTO_TEST_CASE(testPdeDoubleBarrierWithAnalytical) {
BOOST_TEST_MESSAGE("Testing cash-or-nothing double barrier options "
"against PDE Heston version...");
const DayCounter dc = Actual360();
const Date todaysDate(30, Jan, 2023);
const Date maturityDate = todaysDate + Period(1, Years);
Settings::instance().evaluationDate() = todaysDate;
const Handle<Quote> spot(ext::make_shared<SimpleQuote>(100));
const Rate r = 0.075;
const Rate q = 0.03;
const Volatility vol = 0.4;
const Real kappa = 1.0;
const Real theta = vol*vol;
const Real rho = 0.0;
const Real sigma = 1e-4;
const Real v0 = theta;
const Handle<YieldTermStructure> rTS(flatRate(r, dc));
const Handle<YieldTermStructure> qTS(flatRate(q, dc));
const ext::shared_ptr<HestonModel> hestonModel =
ext::make_shared<HestonModel>(
ext::make_shared<HestonProcess>(
rTS, qTS, spot, v0, kappa, theta, sigma, rho));
const ext::shared_ptr<BlackScholesMertonProcess> bsProcess =
ext::make_shared<BlackScholesMertonProcess>(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(flatVol(todaysDate, vol, dc)));
const ext::shared_ptr<PricingEngine> analyticEngine =
ext::make_shared<AnalyticDoubleBarrierBinaryEngine>(bsProcess);
const ext::shared_ptr<PricingEngine> fdEngine =
ext::make_shared<FdHestonDoubleBarrierEngine>(
hestonModel, 201, 101, 3, 0,
FdmSchemeDesc::Hundsdorfer());
const ext::shared_ptr<Exercise> europeanExercise(
ext::make_shared<EuropeanExercise>(maturityDate));
const Real tol = 5e-3;
for (Size i=5; i < 18; i+=2) {
const Real dist = 10.0+5.0*i;
const Real barrier_lo = std::max(spot->value() - dist, 1e-2);
const Real barrier_hi = spot->value() + dist;
DoubleBarrierOption doubleBarrier(
DoubleBarrier::KnockOut, barrier_lo, barrier_hi, 0.0,
ext::make_shared<CashOrNothingPayoff>(
Option::Call, 0.0, 1.0),
europeanExercise);
doubleBarrier.setPricingEngine(analyticEngine);
const Real bsNPV = doubleBarrier.NPV();
doubleBarrier.setPricingEngine(fdEngine);
const Real slvNPV = doubleBarrier.NPV();
const Real diff = slvNPV - bsNPV;
if (std::fabs(diff) > tol) {
BOOST_ERROR(
"Failed to reproduce price difference for a Double-No-Touch "
<< "option between Black-Scholes and "
<< "Heston Stochastic Local Volatility model"
<< "\n Barrier Low : " << barrier_lo
<< "\n Barrier High : " << barrier_hi
<< "\n Black-Scholes Price: " << bsNPV
<< "\n Heston SLV Price : " << slvNPV
<< "\n diff : " << diff
<< "\n tolerance : " << tol);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
