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dividendoption.cpp
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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004, 2005, 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.
*/
// TODO: Figure out why tests for options with both continuous and discrete
// dividends fail.
#include "preconditions.hpp"
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/instruments/vanillaoption.hpp>
#include <ql/pricingengines/vanilla/analyticdividendeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <map>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(DividendOptionTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, s, q, r, today, \
v, expected, calculated, error, tolerance) \
BOOST_ERROR(exerciseTypeToString(exercise) << " " \
<< payoff->optionType() << " option with " \
<< 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);
// tests
BOOST_AUTO_TEST_CASE(testEuropeanValues) {
BOOST_TEST_MESSAGE(
"Testing dividend European option values with no dividends...");
Real tolerance = 1.0e-5;
Option::Type types[] = { Option::Call, Option::Put };
Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.00, 0.10, 0.30 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Integer lengths[] = { 1, 2 };
Volatility vols[] = { 0.05, 0.20, 0.70 };
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
for (auto& type : types) {
for (Real strike : strikes) {
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
std::vector<Date> dividendDates;
std::vector<Real> dividends;
for (Date d = today + 3 * Months; d < exercise->lastDate(); d += 6 * Months) {
dividendDates.push_back(d);
dividends.push_back(0.0);
}
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
ext::shared_ptr<PricingEngine> ref_engine(new AnalyticEuropeanEngine(stochProcess));
VanillaOption ref_option(payoff, exercise);
ref_option.setPricingEngine(ref_engine);
auto engine1 =
ext::make_shared<AnalyticDividendEuropeanEngine>(stochProcess, DividendVector(dividendDates, dividends));
VanillaOption option1(payoff, exercise);
option1.setPricingEngine(engine1);
auto engine2 =
ext::make_shared<AnalyticDividendEuropeanEngine>(stochProcess, DividendVector({ exDate + 6*Months }, { 1.0 }));
VanillaOption option2(payoff, exercise);
option2.setPricingEngine(engine2);
for (Real u : underlyings) {
for (Real m : qRates) {
for (Real n : rRates) {
for (Real v : vols) {
Rate q = m, r = n;
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real expected = ref_option.NPV();
Real calculated1 = option1.NPV();
Real calculated2 = option2.NPV();
Real error1 = std::fabs(calculated1 - expected);
Real error2 = std::fabs(calculated2 - expected);
if (error1 > tolerance) {
REPORT_FAILURE("value start limit", payoff, exercise, u, q, r,
today, v, expected, calculated1, error1,
tolerance);
}
if (error2 > tolerance) {
REPORT_FAILURE("value start limit", payoff, exercise, u, q, r,
today, v, expected, calculated2, error2,
tolerance);
}
}
}
}
}
}
}
}
}
// Reference pg. 253 - Hull - Options, Futures, and Other Derivatives 5th ed
// Exercise 12.8
BOOST_AUTO_TEST_CASE(testEuropeanKnownValue) {
BOOST_TEST_MESSAGE("Testing dividend European option against known value...");
Real tolerance = 1.0e-2;
Real expected = 3.67;
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
Date exDate = today + 180 * Days;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
std::vector<Date> dividendDates = {today + 2 * 30 * Days, today + 5 * 30 * Days};
std::vector<Real> dividends = {0.50, 0.50};
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, 40.0));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot),
qTS, rTS, volTS));
auto engine = ext::make_shared<AnalyticDividendEuropeanEngine>(
stochProcess, DividendVector(dividendDates, dividends));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
Real u = 40.0;
Rate q = 0.0, r = 0.09;
Volatility v = 0.30;
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real calculated = option.NPV();
Real error = std::fabs(calculated-expected);
if (error > tolerance) {
REPORT_FAILURE("value start limit",
payoff, exercise,
u, q, r, today, v,
expected, calculated,
error, tolerance);
}
}
BOOST_AUTO_TEST_CASE(testEuropeanStartLimit) {
BOOST_TEST_MESSAGE(
"Testing dividend European option with a dividend on today's date...");
Real tolerance = 1.0e-5;
Real dividendValue = 10.0;
Option::Type types[] = { Option::Call, Option::Put };
Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.00, 0.10, 0.30 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Integer lengths[] = { 1, 2 };
Volatility vols[] = { 0.05, 0.20, 0.70 };
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
for (auto& type : types) {
for (Real strike : strikes) {
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
std::vector<Date> dividendDates = {today};
std::vector<Real> dividends = {dividendValue};
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
ext::shared_ptr<PricingEngine> ref_engine(new AnalyticEuropeanEngine(stochProcess));
VanillaOption ref_option(payoff, exercise);
ref_option.setPricingEngine(ref_engine);
auto engine = ext::make_shared<AnalyticDividendEuropeanEngine>(
stochProcess, DividendVector(dividendDates, dividends));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
for (Real u : underlyings) {
for (Real m : qRates) {
for (Real n : rRates) {
for (Real v : vols) {
Rate q = m, r = n;
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real calculated = option.NPV();
spot->setValue(u - dividendValue);
Real expected = ref_option.NPV();
Real error = std::fabs(calculated - expected);
if (error > tolerance) {
REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v,
expected, calculated, error, tolerance);
}
}
}
}
}
}
}
}
}
// Doesn't quite work. Need to use discounted values
//BOOST_AUTO_TEST_CASE(testEuropeanEndLimit) {
//
// BOOST_TEST_MESSAGE(
// "Testing dividend European option values with end limits...");
//
// Real tolerance = 1.0e-5;
// Real dividendValue = 10.0;
//
// Option::Type types[] = { Option::Call, Option::Put };
// Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
// Real underlyings[] = { 100.0 };
// Rate qRates[] = { 0.00, 0.10, 0.30 };
// Rate rRates[] = { 0.01, 0.05, 0.15 };
// Integer lengths[] = { 1, 2 };
// Volatility vols[] = { 0.05, 0.20, 0.70 };
//
// DayCounter dc = Actual360();
// Date today = Date::todaysDate();
// Settings::instance().evaluationDate() = today;
//
// ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
// ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
// Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
// ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
// Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
// ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
// Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
//
// for (auto& type : types) {
// for (Real strike : strikes) {
// for (int length : lengths) {
// Date exDate = today + length * Years;
// ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
//
// ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
// new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
//
// std::vector<Date> dividendDates = {exercise->lastDate()};
// std::vector<Real> dividends = {dividendValue};
//
// ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
//
// ext::shared_ptr<StrikedTypePayoff> refPayoff(
// new PlainVanillaPayoff(type, strike + dividendValue));
//
// ext::shared_ptr<PricingEngine> ref_engine(new AnalyticEuropeanEngine(stochProcess));
//
// VanillaOption ref_option(refPayoff, exercise);
// ref_option.setPricingEngine(ref_engine);
//
// QL_DEPRECATED_DISABLE_WARNING
// ext::shared_ptr<PricingEngine> engine1(
// new AnalyticDividendEuropeanEngine(stochProcess));
//
// DividendVanillaOption option1(payoff, exercise, dividendDates, dividends);
// QL_DEPRECATED_ENABLE_WARNING
// option1.setPricingEngine(engine1);
//
// auto engine2 = ext::make_shared<AnalyticDividendEuropeanEngine>(
// stochProcess, DividendVector(dividendDates, dividends));
//
// VanillaOption option2(payoff, exercise);
// option2.setPricingEngine(engine2);
//
// for (Real u : underlyings) {
// for (Real m : qRates) {
// for (Real n : rRates) {
// for (Real v : vols) {
// Rate q = m, r = n;
// spot->setValue(u);
// qRate->setValue(q);
// rRate->setValue(r);
// vol->setValue(v);
//
// Real expected = ref_option.NPV();
// Real calculated = option1.NPV();
// Real error = std::fabs(calculated - expected);
// if (error > tolerance) {
// REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v,
// expected, calculated, error, tolerance);
// }
// calculated = option2.NPV();
// error = std::fabs(calculated - expected);
// if (error > tolerance) {
// REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v,
// expected, calculated, error, tolerance);
// }
// }
// }
// }
// }
// }
// }
// }
//}
BOOST_AUTO_TEST_CASE(testEuropeanGreeks) {
BOOST_TEST_MESSAGE("Testing dividend European option greeks...");
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["vega"] = 1.0e-5;
Option::Type types[] = { Option::Call, Option::Put };
Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.00, 0.10, 0.30 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Integer lengths[] = { 1, 2 };
Volatility vols[] = { 0.05, 0.20, 0.40 };
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
for (auto& type : types) {
for (Real strike : strikes) {
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
std::vector<Date> dividendDates;
std::vector<Real> dividends;
for (Date d = today + 3 * Months; d < exercise->lastDate(); d += 6 * Months) {
dividendDates.push_back(d);
dividends.push_back(5.0);
}
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
auto engine = ext::make_shared<AnalyticDividendEuropeanEngine>(
stochProcess, DividendVector(dividendDates, dividends));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
for (Real u : underlyings) {
for (Real m : qRates) {
for (Real n : rRates) {
for (Real v : vols) {
Rate q = m, r = n;
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["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 risk-free rate and get 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);
// perturb volatility and get vega
Spread 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, expct, calcl, error, tol);
}
}
}
}
}
}
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testFdEuropeanValues) {
BOOST_TEST_MESSAGE(
"Testing finite-difference dividend European option values...");
Real tolerance = 1.0e-2;
Size gridPoints = 400;
Size timeSteps = 40;
Option::Type types[] = { Option::Call, Option::Put };
Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.00, 0.10, 0.30 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Integer lengths[] = { 1, 2 };
Volatility vols[] = { 0.05, 0.20, 0.40 };
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
for (auto& type : types) {
for (Real strike : strikes) {
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
std::vector<Date> dividendDates;
std::vector<Real> dividends;
for (Date d = today + 3 * Months; d < exercise->lastDate(); d += 6 * Months) {
dividendDates.push_back(d);
dividends.push_back(5.0);
}
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
auto ref_engine = ext::make_shared<AnalyticDividendEuropeanEngine>(
stochProcess, DividendVector(dividendDates, dividends));
VanillaOption ref_option(payoff, exercise);
ref_option.setPricingEngine(ref_engine);
ext::shared_ptr<PricingEngine> engine =
MakeFdBlackScholesVanillaEngine(stochProcess)
.withTGrid(timeSteps)
.withXGrid(gridPoints)
.withCashDividends(dividendDates, dividends)
.withCashDividendModel(FdBlackScholesVanillaEngine::Escrowed);
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
for (Real u : underlyings) {
for (Real m : qRates) {
for (Real n : rRates) {
for (Real v : vols) {
Rate q = m, r = n;
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real calculated = option.NPV();
if (calculated > spot->value() * 1.0e-5) {
Real expected = ref_option.NPV();
Real error = std::fabs(calculated - expected);
if (error > tolerance) {
REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v,
expected, calculated, error, tolerance);
}
}
}
}
}
}
}
}
}
}
void testFdGreeks(const Date& today,
const ext::shared_ptr<Exercise>& exercise,
FdBlackScholesVanillaEngine::CashDividendModel model) {
std::map<std::string,Real> calculated, expected, tolerance;
tolerance["delta"] = 5.0e-3;
tolerance["gamma"] = 7.0e-3;
Option::Type types[] = { Option::Call, Option::Put };
Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
Real underlyings[] = { 100.0 };
Rate qRates[] = { 0.00, 0.10, 0.20 };
Rate rRates[] = { 0.01, 0.05, 0.15 };
Volatility vols[] = { 0.05, 0.20, 0.50 };
DayCounter dc = Actual365Fixed();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));
for (auto& type : types) {
for (Real strike : strikes) {
std::vector<Date> dividendDates;
std::vector<Real> dividends;
for (Date d = today + 3*Months;
d < exercise->lastDate();
d += 6*Months) {
dividendDates.push_back(d);
dividends.push_back(5.0);
}
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(Handle<Quote>(spot),
qTS, rTS, volTS));
ext::shared_ptr<PricingEngine> engine =
MakeFdBlackScholesVanillaEngine(stochProcess)
.withCashDividends(dividendDates, dividends)
.withCashDividendModel(model);
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
for (Real u : underlyings) {
for (Real m : qRates) {
for (Real n : rRates) {
for (Real v : vols) {
Rate q = m, r = n;
spot->setValue(u);
qRate->setValue(q);
rRate->setValue(r);
vol->setValue(v);
Real value = option.NPV();
calculated["delta"] = option.delta();
calculated["gamma"] = option.gamma();
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);
// 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, expct, calcl, error, tol);
}
}
}
}
}
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testFdEuropeanGreeks, *precondition(if_speed(Fast))) {
BOOST_TEST_MESSAGE("Testing finite-differences dividend European option greeks...");
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
Integer lengths[] = { 1, 2 };
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
testFdGreeks(today,exercise,FdBlackScholesVanillaEngine::Spot);
testFdGreeks(today,exercise,FdBlackScholesVanillaEngine::Escrowed);
}
}
BOOST_AUTO_TEST_CASE(testFdAmericanGreeks) {
BOOST_TEST_MESSAGE(
"Testing finite-differences dividend American option greeks...");
Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
Integer lengths[] = { 1, 2 };
for (int length : lengths) {
Date exDate = today + length * Years;
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today,exDate));
testFdGreeks(today,exercise,FdBlackScholesVanillaEngine::Spot);
}
}
void testFdDegenerate(const Date& today,
const ext::shared_ptr<Exercise>& exercise,
FdBlackScholesVanillaEngine::CashDividendModel model) {
DayCounter dc = Actual360();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(54.625));
Handle<YieldTermStructure> rTS(flatRate(0.052706, dc));
Handle<YieldTermStructure> qTS(flatRate(0.0, dc));
Handle<BlackVolTermStructure> volTS(flatVol(0.282922, dc));
ext::shared_ptr<BlackScholesMertonProcess> process(
new BlackScholesMertonProcess(Handle<Quote>(spot),
qTS, rTS, volTS));
Size timeSteps = 100;
Size gridPoints = 300;
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, 55.0));
Real tolerance = 1.0e-6;
VanillaOption option(payoff, exercise);
ext::shared_ptr<PricingEngine> engine =
MakeFdBlackScholesVanillaEngine(process)
.withTGrid(timeSteps)
.withXGrid(gridPoints)
.withCashDividendModel(model);
option.setPricingEngine(engine);
Real refValue = option.NPV();
std::vector<Rate> dividends;
std::vector<Date> dividendDates;
engine =
MakeFdBlackScholesVanillaEngine(process)
.withTGrid(timeSteps)
.withXGrid(gridPoints)
.withCashDividends(dividendDates, dividends)
.withCashDividendModel(model);
option.setPricingEngine(engine);
Real value = option.NPV();
if (std::fabs(refValue-value) > tolerance)
BOOST_FAIL("NPV changed by empty dividend set:\n"
<< " previous value: " << value << "\n"
<< " current value: " << refValue << "\n"
<< " change: " << value-refValue);
for (Size i=1; i<=6; i++) {
dividends.push_back(0.0);
dividendDates.push_back(today+i);
engine =
MakeFdBlackScholesVanillaEngine(process)
.withTGrid(timeSteps)
.withXGrid(gridPoints)
.withCashDividends(dividendDates, dividends)
.withCashDividendModel(model);
option.setPricingEngine(engine);
value = option.NPV();
if (std::fabs(refValue-value) > tolerance)
BOOST_FAIL("NPV changed by null dividend :\n"
<< " previous value: " << value << "\n"
<< " current value: " << refValue << "\n"
<< " change: " << value-refValue);
}
}
BOOST_AUTO_TEST_CASE(testFdEuropeanDegenerate) {
BOOST_TEST_MESSAGE(
"Testing degenerate finite-differences dividend European option...");
Date today = Date(27,February,2005);
Settings::instance().evaluationDate() = today;
Date exDate(13,April,2005);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
testFdDegenerate(today,exercise,FdBlackScholesVanillaEngine::Spot);
testFdDegenerate(today,exercise,FdBlackScholesVanillaEngine::Escrowed);
}
BOOST_AUTO_TEST_CASE(testFdAmericanDegenerate) {
BOOST_TEST_MESSAGE(
"Testing degenerate finite-differences dividend American option...");
Date today = Date(27,February,2005);
Settings::instance().evaluationDate() = today;
Date exDate(13,April,2005);
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today,exDate));
testFdDegenerate(today,exercise,FdBlackScholesVanillaEngine::Spot);
testFdDegenerate(today,exercise,FdBlackScholesVanillaEngine::Escrowed);
}
void testFdDividendAtTZero(const Date& today,
const ext::shared_ptr<Exercise>& exercise,
FdBlackScholesVanillaEngine::CashDividendModel model) {
DayCounter dc = Actual360();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(54.625));
Handle<YieldTermStructure> rTS(flatRate(0.0, dc));
Handle<BlackVolTermStructure> volTS(flatVol(0.282922, dc));
ext::shared_ptr<BlackScholesMertonProcess> process(
new BlackScholesMertonProcess(Handle<Quote>(spot),
rTS, rTS, volTS));
Size timeSteps = 50;
Size gridPoints = 400;
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, 55.0));
// today's dividend must by taken into account
std::vector<Rate> dividends(1, 1.0);
std::vector<Date> dividendDates(1, today);
VanillaOption option(payoff, exercise);
ext::shared_ptr<PricingEngine> engine =
MakeFdBlackScholesVanillaEngine(process)
.withTGrid(timeSteps)
.withXGrid(gridPoints)
.withCashDividends(dividendDates, dividends)
.withCashDividendModel(model);
option.setPricingEngine(engine);
Real calculated = option.NPV();
switch(model) {
case FdBlackScholesVanillaEngine::Spot:
BOOST_CHECK_THROW(option.theta(), QuantLib::Error);
break;
case FdBlackScholesVanillaEngine::Escrowed:
BOOST_CHECK_NO_THROW(option.theta());
break;
default:
QL_FAIL("unknown dividend model type");
}
ext::shared_ptr<Exercise> europeanExercise =
ext::make_shared<EuropeanExercise>(exercise->lastDate());
VanillaOption europeanOption(payoff, europeanExercise);
europeanOption.setPricingEngine(
ext::make_shared<AnalyticDividendEuropeanEngine>(process, DividendVector(dividendDates, dividends)));
Real expected = europeanOption.NPV();
const Real tol = 1e-4;
if (std::fabs(calculated-expected) > tol) {
BOOST_ERROR("Can not reproduce reference values "
"from analytic dividend engine :\n"
<< " calculated: " << calculated << "\n"
<< " expected : " << expected << "\n"
<< " diff: " << tol);
}
}
BOOST_AUTO_TEST_CASE(testFdEuropeanWithDividendToday) {
BOOST_TEST_MESSAGE(
"Testing finite-differences dividend European option with dividend on today's date...");
Date today = Date(27,February,2005);
Settings::instance().evaluationDate() = today;
Date exDate(13,April,2005);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
testFdDividendAtTZero(today,exercise,FdBlackScholesVanillaEngine::Spot);
testFdDividendAtTZero(today,exercise,FdBlackScholesVanillaEngine::Escrowed);
}
BOOST_AUTO_TEST_CASE(testFdAmericanWithDividendToday) {
BOOST_TEST_MESSAGE(
"Testing finite-differences dividend American option with dividend on today's date...");
Date today = Date(27,February,2005);
Settings::instance().evaluationDate() = today;
Date exDate(13,April,2005);
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today,exDate));
testFdDividendAtTZero(today,exercise,FdBlackScholesVanillaEngine::Spot);
}
BOOST_AUTO_TEST_CASE(testEscrowedDividendModel) {
BOOST_TEST_MESSAGE("Testing finite-difference European engine "
"with the escrowed dividend model...");
const DayCounter dc = Actual365Fixed();
const Date today = Date(12, October, 2019);
Settings::instance().evaluationDate() = today;
const Handle<Quote> spot(ext::make_shared<SimpleQuote>(100.0));
const Handle<YieldTermStructure> qTS(flatRate(today, 0.063, dc));
const Handle<YieldTermStructure> rTS(flatRate(today, 0.094, dc));
const Handle<BlackVolTermStructure> volTS(flatVol(today, 0.3, dc));
const Date maturity = today + Period(1, Years);
const ext::shared_ptr<BlackScholesMertonProcess> process =
ext::make_shared<BlackScholesMertonProcess>(
spot, qTS, rTS, volTS);
const ext::shared_ptr<PlainVanillaPayoff> payoff(
ext::make_shared<PlainVanillaPayoff>(Option::Put, spot->value()));
const ext::shared_ptr<Exercise> exercise(
ext::make_shared<EuropeanExercise>(maturity));
std::vector<Date> dividendDates = {today + Period(3, Months), today + Period(9, Months)};
std::vector<Real> dividendAmounts = {8.3, 6.8};
VanillaOption ref_option(payoff, exercise);
ref_option.setPricingEngine(
ext::make_shared<AnalyticDividendEuropeanEngine>(process, DividendVector(dividendDates, dividendAmounts)));
const Real analyticNPV = ref_option.NPV();
const Real analyticDelta = ref_option.delta();
VanillaOption option(payoff, exercise);
option.setPricingEngine(
MakeFdBlackScholesVanillaEngine(process)
.withTGrid(50)
.withXGrid(200)
.withDampingSteps(1)
.withCashDividends(dividendDates, dividendAmounts)
.withCashDividendModel(FdBlackScholesVanillaEngine::Escrowed)
);
Real pdeNPV = option.NPV();
Real pdeDelta = option.delta();
const Real tol = 0.0025;
if (std::fabs(pdeNPV - analyticNPV) > tol) {
BOOST_FAIL("Failed to reproduce European option values "
"with the escrowed dividend model and the "