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binaryoption.cpp
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binaryoption.cpp
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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
<[email protected]>. 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 "binaryoption.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;
#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");
namespace {
std::string barrierTypeToString(Barrier::Type type) {
switch(type){
case Barrier::DownIn:
return std::string("Down-and-in");
case Barrier::UpIn:
return std::string("Up-and-in");
case Barrier::DownOut:
return std::string("Down-and-out");
case Barrier::UpOut:
return std::string("Up-and-out");
default:
QL_FAIL("unknown exercise type");
}
}
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
};
}
void BinaryOptionTest::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 (Size i=0; i<LENGTH(values); i++) {
ext::shared_ptr<StrikedTypePayoff> payoff(new CashOrNothingPayoff(
values[i].type, values[i].strike, values[i].cash));
Date exDate = today + Integer(values[i].t*360+0.5);
ext::shared_ptr<Exercise> amExercise(new AmericanExercise(today,
exDate,
true));
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].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(values[i].barrierType,
values[i].barrier,
0,
payoff,
amExercise);
opt.setPricingEngine(engine);
Real calculated = opt.NPV();
Real error = std::fabs(calculated-values[i].result);
if (error > values[i].tol) {
REPORT_FAILURE("value", payoff, amExercise, values[i].barrierType,
values[i].barrier, values[i].s,
values[i].q, values[i].r, today, values[i].v,
values[i].result, calculated, error, values[i].tol);
}
}
}
void BinaryOptionTest::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 (Size i=0; i<LENGTH(values); i++) {
ext::shared_ptr<StrikedTypePayoff> payoff(new AssetOrNothingPayoff(
values[i].type, values[i].strike));
Date exDate = today + Integer(values[i].t*360+0.5);
ext::shared_ptr<Exercise> amExercise(new AmericanExercise(today,
exDate,
true));
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].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(values[i].barrierType,
values[i].barrier,
0,
payoff,
amExercise);
opt.setPricingEngine(engine);
Real calculated = opt.NPV();
Real error = std::fabs(calculated-values[i].result);
if (error > values[i].tol) {
REPORT_FAILURE("value", payoff, amExercise, values[i].barrierType,
values[i].barrier, values[i].s,
values[i].q, values[i].r, today, values[i].v,
values[i].result, calculated, error, values[i].tol);
}
}
}
test_suite* BinaryOptionTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Binary");
suite->add(QUANTLIB_TEST_CASE(&BinaryOptionTest::testCashOrNothingHaugValues));
suite->add(QUANTLIB_TEST_CASE(&BinaryOptionTest::testAssetOrNothingHaugValues));
return suite;
}