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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 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
<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/time/calendars/nullcalendar.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/math/interpolations/bicubicsplineinterpolation.hpp>
#include <ql/instruments/barrieroption.hpp>
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/pricingengines/barrier/analyticbinarybarrierengine.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancecurve.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancesurface.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(BinaryOptionTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, barrierType, barrier, s, q,\
r, today, v, expected, calculated, error, tolerance) \
BOOST_FAIL(payoff->optionType() << " option with " \
<< barrierTypeToString(barrierType) << " barrier type:\n" \
<< " barrier: " << barrier << "\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 BinaryOptionData {
Barrier::Type barrierType;
Real barrier;
Real cash; // cash payoff for cash-or-nothing
Option::Type type;
Real strike;
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(testCashOrNothingHaugValues) {
BOOST_TEST_MESSAGE("Testing cash-or-nothing barrier options against Haug's values...");
BinaryOptionData values[] = {
/* The data below are from
"Option pricing formulas 2nd Ed.", E.G. Haug, McGraw-Hill 2007 pag. 180 - cases 13,14,17,18,21,22,25,26
Note:
q is the dividend rate, while the book gives b, the cost of carry (q=r-b)
*/
// barrierType, barrier, cash, type, strike, spot, q, r, t, vol, value, tol
{ Barrier::DownIn, 100.00, 15.00, Option::Call, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 4.9289, 1e-4 },
{ Barrier::DownIn, 100.00, 15.00, Option::Call, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 6.2150, 1e-4 },
// following value is wrong in book.
{ Barrier::UpIn, 100.00, 15.00, Option::Call, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 5.8926, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Call, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 7.4519, 1e-4 },
// 17,18
{ Barrier::DownIn, 100.00, 15.00, Option::Put, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 4.4314, 1e-4 },
{ Barrier::DownIn, 100.00, 15.00, Option::Put, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 3.1454, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Put, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 5.3297, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Put, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 3.7704, 1e-4 },
// 21,22
{ Barrier::DownOut, 100.00, 15.00, Option::Call, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 4.8758, 1e-4 },
{ Barrier::DownOut, 100.00, 15.00, Option::Call, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 4.9081, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Call, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Call, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 0.0407, 1e-4 },
// 25,26
{ Barrier::DownOut, 100.00, 15.00, Option::Put, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 0.0323, 1e-4 },
{ Barrier::DownOut, 100.00, 15.00, Option::Put, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Put, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 3.0461, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Put, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 3.0054, 1e-4 },
// other values calculated with book vba
{ Barrier::UpIn, 100.00, 15.00, Option::Call, 102.00, 95.00,-0.14, 0.10, 0.5, 0.20, 8.6806, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Call, 102.00, 95.00, 0.03, 0.10, 0.5, 0.20, 5.3112, 1e-4 },
// degenerate conditions (barrier touched)
{ Barrier::DownIn, 100.00, 15.00, Option::Call, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 7.4926, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Call, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 11.1231, 1e-4 },
// 17,18
{ Barrier::DownIn, 100.00, 15.00, Option::Put, 102.00, 98.00, 0.00, 0.10, 0.5, 0.20, 7.1344, 1e-4 },
{ Barrier::UpIn, 100.00, 15.00, Option::Put, 102.00, 101.00, 0.00, 0.10, 0.5, 0.20, 5.9299, 1e-4 },
// 21,22
{ Barrier::DownOut, 100.00, 15.00, Option::Call, 98.00, 99.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Call, 98.00, 101.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
// 25,26
{ Barrier::DownOut, 100.00, 15.00, Option::Put, 98.00, 99.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 15.00, Option::Put, 98.00, 101.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 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(value.type, value.strike, value.cash));
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> amExercise(new AmericanExercise(today,
exDate,
true));
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)));
ext::shared_ptr<PricingEngine> engine(
new AnalyticBinaryBarrierEngine(stochProcess));
BarrierOption opt(value.barrierType, value.barrier, 0, payoff, amExercise);
opt.setPricingEngine(engine);
Real calculated = opt.NPV();
Real error = std::fabs(calculated - value.result);
if (error > value.tol) {
REPORT_FAILURE("value", payoff, amExercise, value.barrierType, value.barrier, value.s,
value.q, value.r, today, value.v, value.result, calculated, error,
value.tol);
}
}
}
BOOST_AUTO_TEST_CASE(testAssetOrNothingHaugValues) {
BOOST_TEST_MESSAGE("Testing asset-or-nothing barrier options against Haug's values...");
BinaryOptionData values[] = {
/* The data below are from
"Option pricing formulas 2nd Ed.", E.G. Haug, McGraw-Hill 2007 pag. 180 - cases 15,16,19,20,23,24,27,28
Note:
q is the dividend rate, while the book gives b, the cost of carry (q=r-b)
*/
// barrierType, barrier, cash, type, strike, spot, q, r, t, vol, value, tol
{ Barrier::DownIn, 100.00, 0.00, Option::Call, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 37.2782, 1e-4 },
{ Barrier::DownIn, 100.00, 0.00, Option::Call, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 45.8530, 1e-4 },
{ Barrier::UpIn, 100.00, 0.00, Option::Call, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 44.5294, 1e-4 },
{ Barrier::UpIn, 100.00, 0.00, Option::Call, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 54.9262, 1e-4 },
// 19,20
{ Barrier::DownIn, 100.00, 0.00, Option::Put, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 27.5644, 1e-4 },
{ Barrier::DownIn, 100.00, 0.00, Option::Put, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 18.9896, 1e-4 },
// following value is wrong in book.
{ Barrier::UpIn, 100.00, 0.00, Option::Put, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 33.1723, 1e-4 },
{ Barrier::UpIn, 100.00, 0.00, Option::Put, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 22.7755, 1e-4 },
// 23,24
{ Barrier::DownOut, 100.00, 0.00, Option::Call, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 39.9391, 1e-4 },
{ Barrier::DownOut, 100.00, 0.00, Option::Call, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 40.1574, 1e-4 },
{ Barrier::UpOut, 100.00, 0.00, Option::Call, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 0.00, Option::Call, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 0.2676, 1e-4 },
// 27,28
{ Barrier::DownOut, 100.00, 0.00, Option::Put, 102.00, 105.00, 0.00, 0.10, 0.5, 0.20, 0.2183, 1e-4 },
{ Barrier::DownOut, 100.00, 0.00, Option::Put, 98.00, 105.00, 0.00, 0.10, 0.5, 0.20, 0.0000, 1e-4 },
{ Barrier::UpOut, 100.00, 0.00, Option::Put, 102.00, 95.00, 0.00, 0.10, 0.5, 0.20, 17.2983, 1e-4 },
{ Barrier::UpOut, 100.00, 0.00, Option::Put, 98.00, 95.00, 0.00, 0.10, 0.5, 0.20, 17.0306, 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 AssetOrNothingPayoff(value.type, value.strike));
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> amExercise(new AmericanExercise(today, exDate, true));
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)));
ext::shared_ptr<PricingEngine> engine(
new AnalyticBinaryBarrierEngine(stochProcess));
BarrierOption opt(value.barrierType, value.barrier, 0, payoff, amExercise);
opt.setPricingEngine(engine);
Real calculated = opt.NPV();
Real error = std::fabs(calculated - value.result);
if (error > value.tol) {
REPORT_FAILURE("value", payoff, amExercise, value.barrierType, value.barrier, value.s,
value.q, value.r, today, value.v, value.result, calculated, error,
value.tol);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
