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lookbackoptions.cpp
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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 "preconditions.hpp"
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/instruments/lookbackoption.hpp>
#include <ql/pricingengines/lookback/analyticcontinuousfixedlookback.hpp>
#include <ql/pricingengines/lookback/analyticcontinuousfloatinglookback.hpp>
#include <ql/pricingengines/lookback/analyticcontinuouspartialfixedlookback.hpp>
#include <ql/pricingengines/lookback/analyticcontinuouspartialfloatinglookback.hpp>
#include <ql/pricingengines/lookback/mclookbackengine.hpp>
#include <ql/processes/blackscholesprocess.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>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(LookbackOptionTests)
#undef REPORT_FAILURE_FLOATING
#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);
#undef REPORT_FAILURE_FIXED
#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);
#undef REPORT_FAILURE_MC
#define REPORT_FAILURE_MC(lookbackType, optionType, analytical, monteCarlo, tolerance) \
BOOST_ERROR( \
"Analytical and MC " << lookbackType << " " << optionType << " values differed by more than tolerance" << "\n" \
<< " Analytical: " << analytical << "\n" \
<< " Monte Carlo: " << monteCarlo << "\n" \
<< " tolerance: " << tolerance << "\n" \
<< " difference: " << std::abs(analytical - monteCarlo));
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
//Partial-time lookback options:
Real l; // level above/below actual extremum
Real t1; // time to start of lookback period
Real result; // result
Real tol; // tolerance
};
BOOST_AUTO_TEST_CASE(testAnalyticContinuousFloatingLookback) {
BOOST_TEST_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, l, t1, result, tol
{ Option::Call, 0, 100, 120.0, 0.06, 0.10, 0.50, 0.30, 0, 0, 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, l, t1, result, tol
{ Option::Call, 0, 100, 100.0, 0.00, 0.05, 1.00, 0.30, 0, 0, 23.7884, 1.0e-4},
{ Option::Call, 0, 100, 100.0, 0.00, 0.05, 0.20, 0.30, 0, 0, 10.7190, 1.0e-4},
{ Option::Call, 0, 100, 110.0, 0.00, 0.05, 0.20, 0.30, 0, 0, 14.4597, 1.0e-4},
{ Option::Put, 0, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 15.3526, 1.0e-4},
{ Option::Put, 0, 110, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 16.8468, 1.0e-4},
{ Option::Put, 0, 120, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 21.0645, 1.0e-4},
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
ext::shared_ptr<FloatingTypePayoff> payoff(new FloatingTypePayoff(value.type));
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 AnalyticContinuousFloatingLookbackEngine(stochProcess));
ContinuousFloatingLookbackOption option(value.minmax, payoff, exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE_FLOATING("value", values[i].minmax, payoff, exercise, value.s, value.q,
value.r, today, value.v, expected, calculated, error,
value.tol);
}
}
}
BOOST_AUTO_TEST_CASE(testAnalyticContinuousFixedLookback) {
BOOST_TEST_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, l, t1, result, tol
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 13.2687, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 18.9263, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 24.9857, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 8.5126, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 14.1702, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 20.2296, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 4.3908, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 9.8905, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 15.8512, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 18.3241, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 26.0731, 1.0e-4},
{ Option::Call, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 34.7116, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 13.8000, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 21.5489, 1.0e-4},
{ Option::Call, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 30.1874, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 9.5445, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 17.2965, 1.0e-4},
{ Option::Call, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 25.9002, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 0.6899, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 4.4448, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 8.9213, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 3.3917, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 8.3177, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 13.1579, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.10, 0, 0, 8.1478, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.20, 0, 0, 13.0739, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 0.50, 0.30, 0, 0, 17.9140, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 1.0534, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 6.2813, 1.0e-4},
{ Option::Put, 95, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 12.2376, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 3.8079, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 10.1294, 1.0e-4},
{ Option::Put, 100, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 16.3889, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.10, 0, 0, 8.3321, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.20, 0, 0, 14.6536, 1.0e-4},
{ Option::Put, 105, 100, 100.0, 0.00, 0.10, 1.00, 0.30, 0, 0, 20.9130, 1.0e-4}
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(value.type, value.strike));
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 AnalyticContinuousFixedLookbackEngine(stochProcess));
ContinuousFixedLookbackOption option(value.minmax, payoff, exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE_FIXED("value", values[i].minmax, payoff, exercise, value.s, value.q,
value.r, today, value.v, expected, calculated, error, value.tol);
}
}
}
BOOST_AUTO_TEST_CASE(testAnalyticContinuousPartialFloatingLookback) {
BOOST_TEST_MESSAGE(
"Testing analytic continuous partial floating-strike lookback options...");
LookbackOptionData values[] = {
// data from "Option Pricing Formulas, Second Edition", Haug, 2006, pg.146
//type, strike, minmax, s, q, r, t, v, l, t1, result, tol
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.25, 8.6524, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.5, 9.2128, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.75, 9.5567, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.25, 10.5751, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.5, 11.2601, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.75, 11.6804, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.25, 13.3402, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.5, 14.5121, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.75, 15.314, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.25, 16.3047, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.5, 17.737, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.75, 18.7171, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.25, 17.9831, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.5, 19.6618, 1.0e-4},
{ Option::Call, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.75, 20.8493, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.25, 21.9793, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.5, 24.0311, 1.0e-4},
{ Option::Call, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.75, 25.4825, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.25, 2.7189, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.5, 3.4639, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.1, 1, 0.75, 4.1912, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.25, 3.3231, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.5, 4.2336, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.1, 1, 0.75, 5.1226, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.25, 7.9153, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.5, 9.5825, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.2, 1, 0.75, 11.0362, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.25, 9.6743, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.5, 11.7119, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.2, 1, 0.75, 13.4887, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.25, 13.4719, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.5, 16.1495, 1.0e-4},
{ Option::Put, 0, 90, 90, 0, 0.06, 1, 0.3, 1, 0.75, 18.4071, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.25, 16.4657, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.5, 19.7383, 1.0e-4},
{ Option::Put, 0, 110, 110, 0, 0.06, 1, 0.3, 1, 0.75, 22.4976, 1.0e-4}
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
ext::shared_ptr<FloatingTypePayoff> payoff(new FloatingTypePayoff(value.type));
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 AnalyticContinuousPartialFloatingLookbackEngine(stochProcess));
Date lookbackEnd = today + timeToDays(value.t1);
ContinuousPartialFloatingLookbackOption option(value.minmax, value.l, lookbackEnd, payoff,
exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE_FLOATING("value", values[i].minmax, payoff, exercise, value.s, value.q,
value.r, today, value.v, expected, calculated, error,
value.tol);
}
}
}
BOOST_AUTO_TEST_CASE(testAnalyticContinuousPartialFixedLookback) {
BOOST_TEST_MESSAGE(
"Testing analytic continuous fixed-strike lookback options...");
LookbackOptionData values[] = {
// data from "Option Pricing Formulas, Second Edition", Haug, 2006, pg.148
//type, strike, minmax, s, q, r, t, v, l, t1, result, tol
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.25, 20.2845, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.5, 19.6239, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.75, 18.6244, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.25, 4.0432, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.5, 3.958, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.75, 3.7015, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.25, 27.5385, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.5, 25.8126, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.75, 23.4957, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.25, 11.4895, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.5, 10.8995, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.75, 9.8244, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.25, 35.4578, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.5, 32.7172, 1.0e-4},
{ Option::Call, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.75, 29.1473, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.25, 19.725, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.5, 18.4025, 1.0e-4},
{ Option::Call, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.75, 16.2976, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.25, 0.4973, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.5, 0.4632, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.1, 0, 0.75, 0.3863, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.25, 12.6978, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.5, 10.9492, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.1, 0, 0.75, 9.1555, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.25, 4.5863, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.5, 4.1925, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.2, 0, 0.75, 3.5831, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.25, 19.0255, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.5, 16.9433, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.2, 0, 0.75, 14.6505, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.25, 9.9348, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.5, 9.1111, 1.0e-4},
{ Option::Put, 90, 0, 100, 0, 0.06, 1, 0.3, 0, 0.75, 7.9267, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.25, 25.2112, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.5, 22.8217, 1.0e-4},
{ Option::Put, 110, 0, 100, 0, 0.06, 1, 0.3, 0, 0.75, 20.0566, 1.0e-4}
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vol->setValue(value.v);
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(value.type, value.strike));
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 AnalyticContinuousPartialFixedLookbackEngine(stochProcess));
Date lookbackStart = today + timeToDays(value.t1);
ContinuousPartialFixedLookbackOption option(lookbackStart,
payoff,
exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE_FIXED("value", values[i].minmax, payoff, exercise, value.s, value.q,
value.r, today, value.v, expected, calculated, error, value.tol);
}
}
}
BOOST_AUTO_TEST_CASE(testMonteCarloLookback, *precondition(if_speed(Slow))) {
BOOST_TEST_MESSAGE("Testing Monte Carlo engines for lookback options...");
Real tolerance = 0.1;
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Real strike = 90;
Real t = 1;
Real t1= 0.25;
Date exDate = today + timeToDays(t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
spot ->setValue(100);
qRate->setValue(0);
rRate->setValue(0.06);
vol ->setValue(0.1);
ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
new BlackScholesMertonProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
Option::Type types[] = { Option::Call, Option::Put };
for (auto type : types) {
ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
/**
* Partial Fixed
* **/
Date lookbackStart = today + timeToDays(t1);
ContinuousPartialFixedLookbackOption partialFixedLookback(lookbackStart,
payoff,
exercise);
ext::shared_ptr<PricingEngine> engine(
new AnalyticContinuousPartialFixedLookbackEngine(stochProcess));
partialFixedLookback.setPricingEngine(engine);
Real analytical = partialFixedLookback.NPV();
ext::shared_ptr<PricingEngine> mcpartialfixedengine =
MakeMCLookbackEngine<ContinuousPartialFixedLookbackOption, PseudoRandom>
(stochProcess)
.withSteps(2000)
.withAntitheticVariate()
.withSeed(1)
.withAbsoluteTolerance(tolerance);
partialFixedLookback.setPricingEngine(mcpartialfixedengine);
Real monteCarlo = partialFixedLookback.NPV();
Real diff = std::abs(analytical - monteCarlo);
if (diff > tolerance){
REPORT_FAILURE_MC("Partial Fixed", type, analytical, monteCarlo, tolerance);
}
/**
* Fixed
* **/
Real minMax = 100;
ContinuousFixedLookbackOption fixedLookback(minMax,
payoff,
exercise);
ext::shared_ptr<PricingEngine> analyticalfixedengine(
new AnalyticContinuousFixedLookbackEngine(stochProcess));
fixedLookback.setPricingEngine(analyticalfixedengine);
analytical = fixedLookback.NPV();
ext::shared_ptr<PricingEngine> mcfixedengine =
MakeMCLookbackEngine<ContinuousFixedLookbackOption, PseudoRandom>
(stochProcess)
.withSteps(2000)
.withAntitheticVariate()
.withSeed(1)
.withAbsoluteTolerance(tolerance);
fixedLookback.setPricingEngine(mcfixedengine);
monteCarlo = fixedLookback.NPV();
diff = std::abs(analytical - monteCarlo);
if (diff > tolerance){
REPORT_FAILURE_MC("Fixed", type, analytical, monteCarlo, tolerance);
}
/**
* Partial Floating
* **/
Real lambda = 1;
Date lookbackEnd = today + timeToDays(t1);
ext::shared_ptr<FloatingTypePayoff> floatingPayoff(new FloatingTypePayoff(type));
ContinuousPartialFloatingLookbackOption partialFloating(minMax,
lambda,
lookbackEnd,
floatingPayoff,
exercise);
ext::shared_ptr<PricingEngine> analyticalpartialFloatingengine(
new AnalyticContinuousPartialFloatingLookbackEngine(stochProcess));
partialFloating.setPricingEngine(analyticalpartialFloatingengine);
analytical = partialFloating.NPV();
ext::shared_ptr<PricingEngine> mcpartialfloatingengine =
MakeMCLookbackEngine<ContinuousPartialFloatingLookbackOption, PseudoRandom>
(stochProcess)
.withSteps(2000)
.withAntitheticVariate()
.withSeed(1)
.withAbsoluteTolerance(tolerance);
partialFloating.setPricingEngine(mcpartialfloatingengine);
monteCarlo = partialFloating.NPV();
diff = std::abs(analytical - monteCarlo);
if (diff > tolerance){
REPORT_FAILURE_MC("Partial Floating", type, analytical, monteCarlo, tolerance);
}
/**
* Floating
* **/
ContinuousFloatingLookbackOption floating(minMax,
floatingPayoff,
exercise);
ext::shared_ptr<PricingEngine> analyticalFloatingengine(
new AnalyticContinuousFloatingLookbackEngine(stochProcess));
floating.setPricingEngine(analyticalFloatingengine);
analytical = floating.NPV();
ext::shared_ptr<PricingEngine> mcfloatingengine =
MakeMCLookbackEngine<ContinuousFloatingLookbackOption, PseudoRandom>
(stochProcess)
.withSteps(2000)
.withAntitheticVariate()
.withSeed(1)
.withAbsoluteTolerance(tolerance);
floating.setPricingEngine(mcfloatingengine);
monteCarlo = floating.NPV();
diff = std::abs(analytical - monteCarlo);
if (diff > tolerance){
REPORT_FAILURE_MC("Floating", type, analytical, monteCarlo, tolerance);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()