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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004, 2007 StatPro Italia srl
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 "forwardoption.hpp"
#include "utilities.hpp"
#include <ql/time/daycounters/actual360.hpp>
#include <ql/instruments/forwardvanillaoption.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/forward/forwardengine.hpp>
#include <ql/pricingengines/forward/forwardperformanceengine.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <map>
using namespace QuantLib;
using namespace boost::unit_test_framework;
#define REPORT_FAILURE(greekName, payoff, exercise, s, q, r, today, \
v, moneyness, reset, expected, calculated, \
error, tolerance) \
BOOST_FAIL("Forward " << exerciseTypeToString(exercise) << " " \
<< payoff->optionType() << " option with " \
<< payoffTypeToString(payoff) << " payoff:\n" \
<< " spot value: " << s << "\n" \
<< " strike: " << payoff->strike() <<"\n" \
<< " moneyness: " << moneyness << "\n" \
<< " dividend yield: " << io::rate(q) << "\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " reset date: " << reset << "\n" \
<< " maturity: " << exercise->lastDate() << "\n" \
<< " volatility: " << io::volatility(v) << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance);
QL_BEGIN_TEST_LOCALS(ForwardOptionTest)
struct ForwardOptionData {
Option::Type type;
Real moneyness;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time start; // time to reset
Time t; // time to maturity
Volatility v; // volatility
Real result; // expected result
Real tol; // tolerance
};
QL_END_TEST_LOCALS(ForwardOptionTest)
void ForwardOptionTest::testValues() {
BOOST_MESSAGE("Testing forward option values...");
/* The data below are from
"Option pricing formulas", E.G. Haug, McGraw-Hill 1998
*/
ForwardOptionData values[] = {
// type, moneyness, spot, div, rate,start, t, vol, result, tol
// "Option pricing formulas", pag. 37
{ Option::Call, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 4.4064, 1.0e-4 },
// "Option pricing formulas", VBA code
{ Option::Put, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 8.2971, 1.0e-4 }
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
boost::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
boost::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(today, qRate, dc));
boost::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(today, rRate, dc));
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(today, vol, dc));
boost::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
boost::shared_ptr<PricingEngine> engine(
new ForwardVanillaEngine<AnalyticEuropeanEngine>(stochProcess));
for (Size i=0; i<LENGTH(values); i++) {
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(values[i].type, 0.0));
Date exDate = today + Integer(values[i].t*360+0.5);
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
Date reset = today + Integer(values[i].start*360+0.5);
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].v);
ForwardVanillaOption option(values[i].moneyness, reset,
payoff, exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real error = std::fabs(calculated-values[i].result);
Real tolerance = 1e-4;
if (error>tolerance) {
REPORT_FAILURE("value", payoff, exercise, values[i].s,
values[i].q, values[i].r, today,
values[i].v, values[i].moneyness, reset,
values[i].result, calculated,
error, tolerance);
}
}
}
void ForwardOptionTest::testPerformanceValues() {
BOOST_MESSAGE("Testing forward performance option values...");
/* The data below are the performance equivalent of the
forward options tested above and taken from
"Option pricing formulas", E.G. Haug, McGraw-Hill 1998
*/
ForwardOptionData values[] = {
// type, moneyness, spot, div, rate,start, maturity, vol, result, tol
{ Option::Call, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 4.4064/60*std::exp(-0.04*0.25), 1.0e-4 },
{ Option::Put, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 8.2971/60*std::exp(-0.04*0.25), 1.0e-4 }
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
boost::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
boost::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(today, qRate, dc));
boost::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(today, rRate, dc));
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(today, vol, dc));
boost::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
boost::shared_ptr<PricingEngine> engine(
new ForwardPerformanceVanillaEngine<AnalyticEuropeanEngine>(
stochProcess));
for (Size i=0; i<LENGTH(values); i++) {
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(values[i].type, 0.0));
Date exDate = today + Integer(values[i].t*360+0.5);
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
Date reset = today + Integer(values[i].start*360+0.5);
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].v);
ForwardVanillaOption option(values[i].moneyness, reset,
payoff, exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real error = std::fabs(calculated-values[i].result);
Real tolerance = 1e-4;
if (error>tolerance) {
REPORT_FAILURE("value", payoff, exercise, values[i].s,
values[i].q, values[i].r, today,
values[i].v, values[i].moneyness, reset,
values[i].result, calculated,
error, tolerance);
}
}
}
QL_BEGIN_TEST_LOCALS(ForwardOptionTest)
template <template <class> class Engine>
void testForwardGreeks() {
std::map<std::string,Real> calculated, expected, tolerance;
tolerance["delta"] = 1.0e-5;
tolerance["gamma"] = 1.0e-5;
tolerance["theta"] = 1.0e-5;
tolerance["rho"] = 1.0e-5;
tolerance["divRho"] = 1.0e-5;
tolerance["vega"] = 1.0e-5;
Option::Type types[] = { Option::Call, Option::Put };
Real moneyness[] = { 0.9, 1.0, 1.1 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.04, 0.05, 0.06 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Integer lengths[] = { 1, 2 };
Integer startMonths[] = { 6, 9 };
Volatility vols[] = { 0.11, 0.50, 1.20 };
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
boost::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
boost::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
boost::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
boost::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
boost::shared_ptr<PricingEngine> engine(
new Engine<AnalyticEuropeanEngine>(stochProcess));
for (Size i=0; i<LENGTH(types); i++) {
for (Size j=0; j<LENGTH(moneyness); j++) {
for (Size k=0; k<LENGTH(lengths); k++) {
for (Size h=0; h<LENGTH(startMonths); h++) {
Date exDate = today + lengths[k]*Years;
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
Date reset = today + startMonths[h]*Months;
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(types[i], 0.0));
ForwardVanillaOption option(moneyness[j], reset,
payoff, exercise);
option.setPricingEngine(engine);
for (Size l=0; l<LENGTH(underlyings); l++) {
for (Size m=0; m<LENGTH(qRates); m++) {
for (Size n=0; n<LENGTH(rRates); n++) {
for (Size p=0; p<LENGTH(vols); p++) {
Real u = underlyings[l];
Rate q = qRates[m],
r = rRates[n];
Volatility v = vols[p];
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real value = option.NPV();
calculated["delta"] = option.delta();
calculated["gamma"] = option.gamma();
calculated["theta"] = option.theta();
calculated["rho"] = option.rho();
calculated["divRho"] = option.dividendRho();
calculated["vega"] = option.vega();
if (value > spot->value()*1.0e-5) {
// perturb spot and get delta and gamma
Real du = u*1.0e-4;
spot->setValue(u+du);
Real value_p = option.NPV(),
delta_p = option.delta();
spot->setValue(u-du);
Real value_m = option.NPV(),
delta_m = option.delta();
spot->setValue(u);
expected["delta"] = (value_p - value_m)/(2*du);
expected["gamma"] = (delta_p - delta_m)/(2*du);
// perturb rates and get rho and dividend rho
Spread dr = r*1.0e-4;
rRate->setValue(r+dr);
value_p = option.NPV();
rRate->setValue(r-dr);
value_m = option.NPV();
rRate->setValue(r);
expected["rho"] = (value_p - value_m)/(2*dr);
Spread dq = q*1.0e-4;
qRate->setValue(q+dq);
value_p = option.NPV();
qRate->setValue(q-dq);
value_m = option.NPV();
qRate->setValue(q);
expected["divRho"] = (value_p - value_m)/(2*dq);
// perturb volatility and get vega
Volatility dv = v*1.0e-4;
vol->setValue(v+dv);
value_p = option.NPV();
vol->setValue(v-dv);
value_m = option.NPV();
vol->setValue(v);
expected["vega"] = (value_p - value_m)/(2*dv);
// perturb date and get theta
Time dT = dc.yearFraction(today-1, today+1);
Settings::instance().evaluationDate() = today-1;
value_m = option.NPV();
Settings::instance().evaluationDate() = today+1;
value_p = option.NPV();
Settings::instance().evaluationDate() = today;
expected["theta"] = (value_p - value_m)/dT;
// compare
std::map<std::string,Real>::iterator it;
for (it = calculated.begin();
it != calculated.end(); ++it) {
std::string greek = it->first;
Real expct = expected [greek],
calcl = calculated[greek],
tol = tolerance [greek];
Real error = relativeError(expct,calcl,u);
if (error>tol) {
REPORT_FAILURE(greek, payoff, exercise,
u, q, r, today, v,
moneyness[j], reset,
expct, calcl, error, tol);
}
}
}
}
}
}
}
}
}
}
}
}
QL_END_TEST_LOCALS(ForwardOptionTest)
void ForwardOptionTest::testGreeks() {
BOOST_MESSAGE("Testing forward option greeks...");
SavedSettings backup;
testForwardGreeks<ForwardVanillaEngine>();
}
void ForwardOptionTest::testPerformanceGreeks() {
BOOST_MESSAGE("Testing forward performance option greeks...");
SavedSettings backup;
testForwardGreeks<ForwardPerformanceVanillaEngine>();
}
test_suite* ForwardOptionTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Forward option tests");
suite->add(BOOST_TEST_CASE(&ForwardOptionTest::testValues));
suite->add(BOOST_TEST_CASE(&ForwardOptionTest::testGreeks));
suite->add(BOOST_TEST_CASE(&ForwardOptionTest::testPerformanceValues));
suite->add(BOOST_TEST_CASE(&ForwardOptionTest::testPerformanceGreeks));
return suite;
}
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