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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003, 2004 Ferdinando Ametrano
Copyright (C) 2005, 2007 StatPro Italia srl
Copyright (C) 2006 Warren Chou
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 "lookbackoptions.hpp"
#include "utilities.hpp"
#include <ql/time/daycounters/actual360.hpp>
#include <ql/instruments/lookbackoption.hpp>
#include <ql/pricingengines/lookback/analyticcontinuousfloatinglookback.hpp>
#include <ql/pricingengines/lookback/analyticcontinuousfixedlookback.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/processes/blackscholesprocess.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
#define REPORT_FAILURE_FLOATING(greekName, minmax, payoff, exercise, \
s, q, r, today, v, \
expected, calculated, error, tolerance) \
BOOST_ERROR( \
exerciseTypeToString(exercise) \
<< payoff->optionType() << " lookback option with " \
<< payoffTypeToString(payoff) << " payoff:\n" \
<< " underlying value: " << s << "\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);
#define REPORT_FAILURE_FIXED(greekName, minmax, payoff, exercise, \
s, q, r, today, v, \
expected, calculated, error, tolerance) \
BOOST_ERROR( \
exerciseTypeToString(exercise) \
<< payoff->optionType() << " lookback option with " \
<< payoffTypeToString(payoff) << " payoff:\n" \
<< " underlying 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);
QL_BEGIN_TEST_LOCALS(LookbackOptionTest)
struct LookbackOptionData {
Option::Type type;
Real strike;
Real minmax;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time t; // time to maturity
Volatility v; // volatility
Real result; // result
Real tol; // tolerance
};
QL_END_TEST_LOCALS(LookbackOptionTest)
void LookbackOptionTest::testAnalyticContinuousFloatingLookback() {
BOOST_MESSAGE(
"Testing analytic continuous floating-strike lookback options...");
LookbackOptionData values[] = {
// data from "Option Pricing Formulas", Haug, 1998, pg.61-62
// type, strike, minmax, s, q, r, t, v, result, tol
{ Option::Call, 0, 100, 120.0, 0.06, 0.10, 0.50, 0.30, 25.3533, 1.0e-4},
// data from "Connecting discrete and continuous path-dependent options",
// Broadie, Glasserman & Kou, 1999, pg.70-74
// type, strike, minmax, s, q, r, t, v, result, tol
{ Option::Call, 0, 100, 100.0, 0.00, 0.05, 1.00, 0.30, 23.7884, 1.0e-4},
{ Option::Call, 0, 100, 100.0, 0.00, 0.05, 0.20, 0.30, 10.7190, 1.0e-4},
{ Option::Call, 0, 100, 110.0, 0.00, 0.05, 0.20, 0.30, 14.4597, 1.0e-4},
{ Option::Put, 0, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 15.3526, 1.0e-4},
{ Option::Put, 0, 110, 100.0, 0.00, 0.10, 0.50, 0.30, 16.8468, 1.0e-4},
{ Option::Put, 0, 120, 100.0, 0.00, 0.10, 0.50, 0.30, 21.0645, 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));
boost::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
boost::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
boost::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
boost::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (Size i=0; i<LENGTH(values); i++) {
Date exDate = today + Integer(values[i].t*360+0.5);
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].v);
boost::shared_ptr<FloatingTypePayoff> payoff(
new FloatingTypePayoff(values[i].type));
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 AnalyticContinuousFloatingLookbackEngine(stochProcess));
ContinuousFloatingLookbackOption option(values[i].minmax,
payoff,
exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = values[i].result;
Real error = std::fabs(calculated-expected);
if (error>values[i].tol) {
REPORT_FAILURE_FLOATING("value", values[i].minmax, payoff,
exercise, values[i].s, values[i].q,
values[i].r, today, values[i].v,
expected, calculated, error,
values[i].tol);
}
}
}
void LookbackOptionTest::testAnalyticContinuousFixedLookback() {
BOOST_MESSAGE(
"Testing analytic continuous fixed-strike lookback options...");
LookbackOptionData values[] = {
// data from "Option Pricing Formulas", Haug, 1998, pg.63-64
// type, strike, minmax, s, q, r, t, v, result, tol
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 13.2687, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 18.9263, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 24.9857, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 8.5126, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 14.1702, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 20.2296, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 4.3908, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 9.8905, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 15.8512, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 18.3241, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 26.0731, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 34.7116, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 13.8000, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 21.5489, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 30.1874, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 9.5445, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 17.2965, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 25.9002, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0.6899, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 4.4448, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 8.9213, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 3.3917, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 8.3177, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 13.1579, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 8.1478, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 13.0739, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 17.9140, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 1.0534, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 6.2813, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 12.2376, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 3.8079, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 10.1294, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 16.3889, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 8.3321, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 14.6536, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 20.9130, 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));
boost::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
boost::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
boost::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
boost::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (Size i=0; i<LENGTH(values); i++) {
Date exDate = today + Integer(values[i].t*360+0.5);
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot ->setValue(values[i].s);
qRate->setValue(values[i].q);
rRate->setValue(values[i].r);
vol ->setValue(values[i].v);
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(values[i].type, values[i].strike));
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 AnalyticContinuousFixedLookbackEngine(stochProcess));
ContinuousFixedLookbackOption option(values[i].minmax,
payoff,
exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = values[i].result;
Real error = std::fabs(calculated-expected);
if (error>values[i].tol) {
REPORT_FAILURE_FIXED("value", values[i].minmax, payoff, exercise,
values[i].s, values[i].q, values[i].r, today,
values[i].v, expected, calculated, error,
values[i].tol);
}
}
}
test_suite* LookbackOptionTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Lookback option tests");
suite->add(BOOST_TEST_CASE(
&LookbackOptionTest::testAnalyticContinuousFloatingLookback));
suite->add(BOOST_TEST_CASE(
&LookbackOptionTest::testAnalyticContinuousFixedLookback));
return suite;
}
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