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basketoption.cpp
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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003, 2004, 2005, 2008 StatPro Italia srl
Copyright (C) 2004 Ferdinando Ametrano
Copyright (C) 2004 Neil Firth
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/basketoption.hpp>
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/math/randomnumbers/sobolbrownianbridgersg.hpp>
#include <ql/pricingengines/basket/bjerksundstenslandspreadengine.hpp>
#include <ql/pricingengines/basket/fd2dblackscholesvanillaengine.hpp>
#include <ql/pricingengines/basket/fdndimblackscholesvanillaengine.hpp>
#include <ql/pricingengines/basket/kirkengine.hpp>
#include <ql/pricingengines/basket/choibasketengine.hpp>
#include <ql/pricingengines/basket/mcamericanbasketengine.hpp>
#include <ql/pricingengines/basket/mceuropeanbasketengine.hpp>
#include <ql/pricingengines/basket/operatorsplittingspreadengine.hpp>
#include <ql/pricingengines/basket/singlefactorbsmbasketengine.hpp>
#include <ql/pricingengines/basket/denglizhoubasketengine.hpp>
#include <ql/pricingengines/basket/stulzengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/processes/stochasticprocessarray.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/volatility/equityfx/hestonblackvolsurface.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/yearfractiontodate.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/math/statistics/incrementalstatistics.hpp>
#include <cmath>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(BasketOptionTests)
#undef REPORT_FAILURE_2
#define REPORT_FAILURE_2(greekName, basketType, payoff, exercise, \
s1, s2, q1, q2, r, today, v1, v2, rho, \
expected, calculated, error, tolerance) \
BOOST_ERROR( \
exerciseTypeToString(exercise) << " " \
<< payoff->optionType() << " option on " \
<< basketTypeToString(basketType) \
<< " with " << payoffTypeToString(payoff) << " payoff:\n" \
<< "1st underlying value: " << s1 << "\n" \
<< "2nd underlying value: " << s2 << "\n" \
<< " strike: " << payoff->strike() << "\n" \
<< " 1st dividend yield: " << io::rate(q1) << "\n" \
<< " 2nd dividend yield: " << io::rate(q2) << "\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " maturity: " << exercise->lastDate() << "\n" \
<< "1st asset volatility: " << io::volatility(v1) << "\n" \
<< "2nd asset volatility: " << io::volatility(v2) << "\n" \
<< " correlation: " << rho << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance);
#undef REPORT_FAILURE_3
#define REPORT_FAILURE_3(greekName, basketType, payoff, exercise, \
s1, s2, s3, r, today, v1, v2, v3, rho, \
expected, calculated, error, tolerance) \
BOOST_ERROR( \
exerciseTypeToString(exercise) << " " \
<< payoff->optionType() << " option on " \
<< basketTypeToString(basketType) \
<< " with " << payoffTypeToString(payoff) << " payoff:\n" \
<< "1st underlying value: " << s1 << "\n" \
<< "2nd underlying value: " << s2 << "\n" \
<< "3rd underlying value: " << s3 << "\n" \
<< " strike: " << payoff->strike() <<"\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " maturity: " << exercise->lastDate() << "\n" \
<< "1st asset volatility: " << io::volatility(v1) << "\n" \
<< "2nd asset volatility: " << io::volatility(v2) << "\n" \
<< "3rd asset volatility: " << io::volatility(v3) << "\n" \
<< " correlation: " << rho << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance);
enum BasketType { MinBasket, MaxBasket, SpreadBasket };
std::string basketTypeToString(BasketType basketType) {
switch (basketType) {
case MinBasket:
return "MinBasket";
case MaxBasket:
return "MaxBasket";
case SpreadBasket:
return "Spread";
}
QL_FAIL("unknown basket option type");
}
ext::shared_ptr<BasketPayoff> basketTypeToPayoff(BasketType basketType,
const ext::shared_ptr<Payoff> &p) {
switch (basketType) {
case MinBasket:
return ext::shared_ptr<BasketPayoff>(new MinBasketPayoff(p));
case MaxBasket:
return ext::shared_ptr<BasketPayoff>(new MaxBasketPayoff(p));
case SpreadBasket:
return ext::shared_ptr<BasketPayoff>(new SpreadBasketPayoff(p));
}
QL_FAIL("unknown basket option type");
}
struct BasketOptionOneData {
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
};
struct BasketOptionTwoData {
BasketType basketType;
Option::Type type;
Real strike;
Real s1;
Real s2;
Rate q1;
Rate q2;
Rate r;
Time t; // years
Volatility v1;
Volatility v2;
Real rho;
Real result;
Real tol;
};
struct BasketOptionThreeData {
BasketType basketType;
Option::Type type;
Real strike;
Real s1;
Real s2;
Real s3;
Rate r;
Time t; // months
Volatility v1;
Volatility v2;
Volatility v3;
Real rho;
Real euroValue;
Real amValue;
};
BasketOptionOneData oneDataValues[] = {
// type, strike, spot, q, r, t, vol, value, tol
{ Option::Put, 100.00, 80.00, 0.0, 0.06, 0.5, 0.4, 21.6059, 1e-2 },
{ Option::Put, 100.00, 85.00, 0.0, 0.06, 0.5, 0.4, 18.0374, 1e-2 },
{ Option::Put, 100.00, 90.00, 0.0, 0.06, 0.5, 0.4, 14.9187, 1e-2 },
{ Option::Put, 100.00, 95.00, 0.0, 0.06, 0.5, 0.4, 12.2314, 1e-2 },
{ Option::Put, 100.00, 100.00, 0.0, 0.06, 0.5, 0.4, 9.9458, 1e-2 },
{ Option::Put, 100.00, 105.00, 0.0, 0.06, 0.5, 0.4, 8.0281, 1e-2 },
{ Option::Put, 100.00, 110.00, 0.0, 0.06, 0.5, 0.4, 6.4352, 1e-2 },
{ Option::Put, 100.00, 115.00, 0.0, 0.06, 0.5, 0.4, 5.1265, 1e-2 },
{ Option::Put, 100.00, 120.00, 0.0, 0.06, 0.5, 0.4, 4.0611, 1e-2 },
// Longstaff Schwartz 1D example
// use constant and three Laguerre polynomials
// 100,000 paths and 50 timesteps per year
{ Option::Put, 40.00, 36.00, 0.0, 0.06, 1.0, 0.2, 4.478, 1e-2 },
{ Option::Put, 40.00, 36.00, 0.0, 0.06, 2.0, 0.2, 4.840, 1e-2 },
{ Option::Put, 40.00, 36.00, 0.0, 0.06, 1.0, 0.4, 7.101, 1e-2 },
{ Option::Put, 40.00, 36.00, 0.0, 0.06, 2.0, 0.4, 8.508, 1e-2 },
{ Option::Put, 40.00, 38.00, 0.0, 0.06, 1.0, 0.2, 3.250, 1e-2 },
{ Option::Put, 40.00, 38.00, 0.0, 0.06, 2.0, 0.2, 3.745, 1e-2 },
{ Option::Put, 40.00, 38.00, 0.0, 0.06, 1.0, 0.4, 6.148, 1e-2 },
{ Option::Put, 40.00, 38.00, 0.0, 0.06, 2.0, 0.4, 7.670, 1e-2 },
{ Option::Put, 40.00, 40.00, 0.0, 0.06, 1.0, 0.2, 2.314, 1e-2 },
{ Option::Put, 40.00, 40.00, 0.0, 0.06, 2.0, 0.2, 2.885, 1e-2 },
{ Option::Put, 40.00, 40.00, 0.0, 0.06, 1.0, 0.4, 5.312, 1e-2 },
{ Option::Put, 40.00, 40.00, 0.0, 0.06, 2.0, 0.4, 6.920, 1e-2 },
{ Option::Put, 40.00, 42.00, 0.0, 0.06, 1.0, 0.2, 1.617, 1e-2 },
{ Option::Put, 40.00, 42.00, 0.0, 0.06, 2.0, 0.2, 2.212, 1e-2 },
{ Option::Put, 40.00, 42.00, 0.0, 0.06, 1.0, 0.4, 4.582, 1e-2 },
{ Option::Put, 40.00, 42.00, 0.0, 0.06, 2.0, 0.4, 6.248, 1e-2 },
{ Option::Put, 40.00, 44.00, 0.0, 0.06, 1.0, 0.2, 1.110, 1e-2 },
{ Option::Put, 40.00, 44.00, 0.0, 0.06, 2.0, 0.2, 1.690, 1e-2 },
{ Option::Put, 40.00, 44.00, 0.0, 0.06, 1.0, 0.4, 3.948, 1e-2 },
{ Option::Put, 40.00, 44.00, 0.0, 0.06, 2.0, 0.4, 5.647, 1e-2 }
};
BOOST_AUTO_TEST_CASE(testEuroTwoValues) {
BOOST_TEST_MESSAGE("Testing two-asset European basket options...");
/*
Data from:
Excel spreadsheet www.maths.ox.ac.uk/~firth/computing/excel.shtml
and
"Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag 56-58
European two asset max basket options
*/
BasketOptionTwoData values[] = {
// basketType, optionType, strike, s1, s2, q1, q2, r, t, v1, v2, rho, result, tol
// data from http://www.maths.ox.ac.uk/~firth/computing/excel.shtml
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.90, 10.898, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.70, 8.483, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.50, 6.844, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 5.531, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.10, 4.413, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.50, 0.70, 0.00, 4.981, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.50, 0.30, 0.00, 4.159, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.50, 0.10, 0.00, 2.597, 1.0e-3},
{MinBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.50, 0.10, 0.50, 4.030, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.90, 17.565, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.70, 19.980, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.50, 21.619, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 22.932, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.10, 24.049, 1.1e-3},
{MaxBasket, Option::Call, 100.0, 80.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 16.508, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 80.0, 80.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 8.049, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 80.0, 120.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 30.141, 1.0e-3},
{MaxBasket, Option::Call, 100.0, 120.0, 120.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 42.889, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.90, 11.369, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.70, 12.856, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.50, 13.890, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 14.741, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.10, 15.485, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 0.50, 0.30, 0.30, 0.10, 11.893, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 0.25, 0.30, 0.30, 0.10, 8.881, 1.0e-3},
{MinBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 2.00, 0.30, 0.30, 0.10, 19.268, 1.0e-3},
{MaxBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.90, 7.339, 1.0e-3},
{MaxBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.70, 5.853, 1.0e-3},
{MaxBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.50, 4.818, 1.0e-3},
{MaxBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.30, 3.967, 1.1e-3},
{MaxBasket, Option::Put, 100.0, 100.0, 100.0, 0.00, 0.00, 0.05, 1.00, 0.30, 0.30, 0.10, 3.223, 1.0e-3},
// basketType, optionType, strike, s1, s2, q1, q2, r, t, v1, v2, rho, result, tol
// data from "Option pricing formulas" VB code + spreadsheet
{MinBasket, Option::Call, 98.0, 100.0, 105.0, 0.00, 0.00, 0.05, 0.50, 0.11, 0.16, 0.63, 4.8177, 1.0e-4},
{MaxBasket, Option::Call, 98.0, 100.0, 105.0, 0.00, 0.00, 0.05, 0.50, 0.11, 0.16, 0.63, 11.6323, 1.0e-4},
{MinBasket, Option::Put, 98.0, 100.0, 105.0, 0.00, 0.00, 0.05, 0.50, 0.11, 0.16, 0.63, 2.0376, 1.0e-4},
{MaxBasket, Option::Put, 98.0, 100.0, 105.0, 0.00, 0.00, 0.05, 0.50, 0.11, 0.16, 0.63, 0.5731, 1.0e-4},
{MinBasket, Option::Call, 98.0, 100.0, 105.0, 0.06, 0.09, 0.05, 0.50, 0.11, 0.16, 0.63, 2.9340, 1.0e-4},
{MinBasket, Option::Put, 98.0, 100.0, 105.0, 0.06, 0.09, 0.05, 0.50, 0.11, 0.16, 0.63, 3.5224, 1.0e-4},
// data from "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag 58
{MaxBasket, Option::Call, 98.0, 100.0, 105.0, 0.06, 0.09, 0.05, 0.50, 0.11, 0.16, 0.63, 8.0701, 1.0e-4},
{MaxBasket, Option::Put, 98.0, 100.0, 105.0, 0.06, 0.09, 0.05, 0.50, 0.11, 0.16, 0.63, 1.2181, 1.0e-4},
/* "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag 59-60
Kirk approx. for a european spread option on two futures*/
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.20, -0.5, 4.7530, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.20, 0.0, 3.7970, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.20, 0.5, 2.5537, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.25, 0.20, -0.5, 5.4275, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.25, 0.20, 0.0, 4.3712, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.25, 0.20, 0.5, 3.0086, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.25, -0.5, 5.4061, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.25, 0.0, 4.3451, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.1, 0.20, 0.25, 0.5, 2.9723, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.20, -0.5,10.7517, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.20, 0.0, 8.7020, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.20, 0.5, 6.0257, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.25, 0.20, -0.5,12.1941, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.25, 0.20, 0.0, 9.9340, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.25, 0.20, 0.5, 7.0067, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.25, -0.5,12.1483, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.25, 0.0, 9.8780, 1.0e-3},
{SpreadBasket, Option::Call, 3.0, 122.0, 120.0, 0.0, 0.0, 0.10, 0.5, 0.20, 0.25, 0.5, 6.9284, 1.0e-3}
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot1(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> spot2(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate1(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS1 = flatRate(today, qRate1, dc);
ext::shared_ptr<SimpleQuote> qRate2(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS2 = flatRate(today, qRate2, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol1(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);
ext::shared_ptr<SimpleQuote> vol2(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS2 = flatVol(today, vol2, dc);
const Real mcRelativeErrorTolerance = 0.01;
const Real fdRelativeErrorTolerance = 0.01;
for (auto& value : values) {
ext::shared_ptr<PlainVanillaPayoff> payoff(
new PlainVanillaPayoff(value.type, value.strike));
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
spot1->setValue(value.s1);
spot2->setValue(value.s2);
qRate1->setValue(value.q1);
qRate2->setValue(value.q2);
rRate->setValue(value.r);
vol1->setValue(value.v1);
vol2->setValue(value.v2);
ext::shared_ptr<PricingEngine> analyticEngine;
ext::shared_ptr<GeneralizedBlackScholesProcess> p1, p2;
switch (value.basketType) {
case MaxBasket:
case MinBasket:
p1 = ext::shared_ptr<GeneralizedBlackScholesProcess>(new BlackScholesMertonProcess(
Handle<Quote>(spot1), Handle<YieldTermStructure>(qTS1),
Handle<YieldTermStructure>(rTS), Handle<BlackVolTermStructure>(volTS1)));
p2 = ext::shared_ptr<GeneralizedBlackScholesProcess>(new BlackScholesMertonProcess(
Handle<Quote>(spot2), Handle<YieldTermStructure>(qTS2),
Handle<YieldTermStructure>(rTS), Handle<BlackVolTermStructure>(volTS2)));
analyticEngine = ext::shared_ptr<PricingEngine>(new StulzEngine(p1, p2, value.rho));
break;
case SpreadBasket:
p1 = ext::shared_ptr<GeneralizedBlackScholesProcess>(
new BlackProcess(Handle<Quote>(spot1), Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS1)));
p2 = ext::shared_ptr<GeneralizedBlackScholesProcess>(
new BlackProcess(Handle<Quote>(spot2), Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS2)));
analyticEngine = ext::shared_ptr<PricingEngine>(
new KirkEngine(ext::dynamic_pointer_cast<BlackProcess>(p1),
ext::dynamic_pointer_cast<BlackProcess>(p2), value.rho));
break;
default:
QL_FAIL("unknown basket type");
}
std::vector<ext::shared_ptr<StochasticProcess1D> > procs = { p1, p2 };
Matrix correlationMatrix(2, 2, value.rho);
for (Integer j=0; j < 2; j++) {
correlationMatrix[j][j] = 1.0;
}
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(procs,correlationMatrix));
ext::shared_ptr<PricingEngine> mcEngine =
MakeMCEuropeanBasketEngine<PseudoRandom, Statistics>(process)
.withStepsPerYear(1)
.withSamples(10000)
.withSeed(42);
ext::shared_ptr<PricingEngine> fdEngine(
new Fd2dBlackScholesVanillaEngine(p1, p2, value.rho, 50, 50, 15));
BasketOption basketOption(basketTypeToPayoff(value.basketType, payoff), exercise);
// analytic engine
basketOption.setPricingEngine(analyticEngine);
Real calculated = basketOption.NPV();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol) {
REPORT_FAILURE_2("value", value.basketType, payoff, exercise, value.s1, value.s2,
value.q1, value.q2, value.r, today, value.v1, value.v2, value.rho,
value.result, calculated, error, value.tol);
}
// fd engine
basketOption.setPricingEngine(fdEngine);
calculated = basketOption.NPV();
Real relError = relativeError(calculated, expected, expected);
if (relError > mcRelativeErrorTolerance ) {
REPORT_FAILURE_2("FD value", value.basketType, payoff, exercise, value.s1, value.s2,
value.q1, value.q2, value.r, today, value.v1, value.v2, value.rho,
value.result, calculated, relError, fdRelativeErrorTolerance);
}
// mc engine
basketOption.setPricingEngine(mcEngine);
calculated = basketOption.NPV();
relError = relativeError(calculated, expected, value.s1);
if (relError > mcRelativeErrorTolerance ) {
REPORT_FAILURE_2("MC value", value.basketType, payoff, exercise, value.s1, value.s2,
value.q1, value.q2, value.r, today, value.v1, value.v2, value.rho,
value.result, calculated, relError, mcRelativeErrorTolerance);
}
}
}
BOOST_AUTO_TEST_CASE(testBarraquandThreeValues, *precondition(if_speed(Slow))) {
BOOST_TEST_MESSAGE("Testing three-asset basket options "
"against Barraquand's values...");
/*
Data from:
"Numerical Valuation of High Dimensional American Securities"
Barraquand, J. and Martineau, D.
Journal of Financial and Quantitative Analysis 1995 3(30) 383-405
*/
BasketOptionThreeData values[] = {
// time in months is with 30 days to the month..
// basketType, optionType, strike, s1, s2, s3, r, t, v1, v2, v3, rho, euro, american,
// Table 2
// not using 4 month case to speed up test
/*
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 8.59, 8.59},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 3.84, 3.84},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 0.89, 0.89},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 12.55, 12.55},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 7.87, 7.87},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 4.26, 4.26},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 15.29, 15.29},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 10.72, 10.72},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 6.96, 6.96},
*/
/*
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 7.78, 7.78},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 3.18, 3.18},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 0.82, 0.82},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 10.97, 10.97},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 6.69, 6.69},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 3.70, 3.70},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 13.23, 13.23},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 9.11, 9.11},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 5.98, 5.98},
*/
/*
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 6.53, 6.53},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 2.38, 2.38},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 0.74, 0.74},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 8.51, 8.51},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 4.92, 4.92},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 2.97, 2.97},
{MaxBasket, Option::Call, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 10.04, 10.04},
{MaxBasket, Option::Call, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 6.64, 6.64},
{MaxBasket, Option::Call, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 4.61, 4.61},
*/
// Table 3
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 0.00, 0.00},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 0.13, 0.23},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.0, 2.26, 5.00},
//{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 0.01, 0.01},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 0.25, 0.44},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.0, 1.55, 5.00},
//{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 0.03, 0.04},
//{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 0.31, 0.57},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.0, 1.41, 5.00},
/*
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 0.00, 0.00},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 0.38, 0.48},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 0.5, 3.00, 5.00},
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 0.07, 0.09},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 0.72, 0.93},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 0.5, 2.65, 5.00},
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 0.17, 0.20},
*/
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 0.91, 1.19},
/*
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 0.5, 2.63, 5.00},
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 0.01, 0.01},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 0.84, 0.08},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 1.00, 0.20, 0.30, 0.50, 1.0, 4.18, 5.00},
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 0.19, 0.19},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 1.51, 1.56},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 4.00, 0.20, 0.30, 0.50, 1.0, 4.49, 5.00},
{MaxBasket, Option::Put, 35.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 0.41, 0.42},
{MaxBasket, Option::Put, 40.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 1.87, 1.96},
{MaxBasket, Option::Put, 45.0, 40.0, 40.0, 40.0, 0.05, 7.00, 0.20, 0.30, 0.50, 1.0, 4.70, 5.20}
*/
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot1(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> spot2(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> spot3(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> vol1(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);
ext::shared_ptr<SimpleQuote> vol2(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS2 = flatVol(today, vol2, dc);
ext::shared_ptr<SimpleQuote> vol3(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS3 = flatVol(today, vol3, dc);
for (auto& value : values) {
ext::shared_ptr<PlainVanillaPayoff> payoff(
new PlainVanillaPayoff(value.type, value.strike));
Date exDate = today + Integer(value.t) * 30;
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
ext::shared_ptr<Exercise> amExercise(new AmericanExercise(today,
exDate));
spot1->setValue(value.s1);
spot2->setValue(value.s2);
spot3->setValue(value.s3);
rRate->setValue(value.r);
vol1->setValue(value.v1);
vol2->setValue(value.v2);
vol3->setValue(value.v3);
ext::shared_ptr<StochasticProcess1D> stochProcess1(new
BlackScholesMertonProcess(Handle<Quote>(spot1),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS1)));
ext::shared_ptr<StochasticProcess1D> stochProcess2(new
BlackScholesMertonProcess(Handle<Quote>(spot2),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS2)));
ext::shared_ptr<StochasticProcess1D> stochProcess3(new
BlackScholesMertonProcess(Handle<Quote>(spot3),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS3)));
std::vector<ext::shared_ptr<StochasticProcess1D> > procs
= {stochProcess1, stochProcess2, stochProcess3 };
Matrix correlation(3, 3, value.rho);
for (Integer j=0; j < 3; j++) {
correlation[j][j] = 1.0;
}
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(procs,correlation));
// use a 3D sobol sequence...
// Think long and hard before moving to more than 1 timestep....
ext::shared_ptr<PricingEngine> mcQuasiEngine =
MakeMCEuropeanBasketEngine<LowDiscrepancy>(process)
.withStepsPerYear(1)
.withSamples(8091)
.withSeed(42);
BasketOption euroBasketOption(basketTypeToPayoff(value.basketType, payoff), exercise);
euroBasketOption.setPricingEngine(mcQuasiEngine);
Real expected = value.euroValue;
Real calculated = euroBasketOption.NPV();
Real relError = relativeError(calculated, expected, value.s1);
Real mcRelativeErrorTolerance = 0.01;
if (relError > mcRelativeErrorTolerance ) {
REPORT_FAILURE_3("MC Quasi value", value.basketType, payoff, exercise, value.s1,
value.s2, value.s3, value.r, today, value.v1, value.v2, value.v3,
value.rho, value.euroValue, calculated, relError,
mcRelativeErrorTolerance);
}
Size requiredSamples = 1000;
Size timeSteps = 500;
BigNatural seed = 1;
ext::shared_ptr<PricingEngine> mcLSMCEngine =
MakeMCAmericanBasketEngine<>(process)
.withSteps(timeSteps)
.withAntitheticVariate()
.withSamples(requiredSamples)
.withCalibrationSamples(requiredSamples/4)
.withSeed(seed);
BasketOption amBasketOption(basketTypeToPayoff(value.basketType, payoff), amExercise);
amBasketOption.setPricingEngine(mcLSMCEngine);
expected = value.amValue;
calculated = amBasketOption.NPV();
relError = relativeError(calculated, expected, value.s1);
Real mcAmericanRelativeErrorTolerance = 0.01;
if (relError > mcAmericanRelativeErrorTolerance) {
REPORT_FAILURE_3("MC LSMC Value", value.basketType, payoff, exercise, value.s1,
value.s2, value.s3, value.r, today, value.v1, value.v2, value.v3,
value.rho, value.amValue, calculated, relError,
mcRelativeErrorTolerance);
}
}
}
BOOST_AUTO_TEST_CASE(testTavellaValues) {
BOOST_TEST_MESSAGE("Testing three-asset American basket options "
"against Tavella's values...");
/*
Data from:
"Quantitative Methods in Derivatives Pricing"
Tavella, D. A. - Wiley (2002)
*/
BasketOptionThreeData values[] = {
// time in months is with 30 days to the month..
// basketType, optionType, strike, s1, s2, s3, r, t, v1, v2, v3, rho, euroValue, american Value,
{MaxBasket, Option::Call, 100, 100, 100, 100, 0.05, 3.00, 0.20, 0.20, 0.20, 0.0, -999, 18.082}
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot1(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> spot2(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> spot3(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.1));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.05));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol1(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);
ext::shared_ptr<SimpleQuote> vol2(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS2 = flatVol(today, vol2, dc);
ext::shared_ptr<SimpleQuote> vol3(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS3 = flatVol(today, vol3, dc);
Real mcRelativeErrorTolerance = 0.01;
Size requiredSamples = 10000;
Size timeSteps = 20;
BigNatural seed = 0;
ext::shared_ptr<PlainVanillaPayoff> payoff(new
PlainVanillaPayoff(values[0].type, values[0].strike));
Date exDate = today + timeToDays(values[0].t);
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today, exDate));
spot1 ->setValue(values[0].s1);
spot2 ->setValue(values[0].s2);
spot3 ->setValue(values[0].s3);
vol1 ->setValue(values[0].v1);
vol2 ->setValue(values[0].v2);
vol3 ->setValue(values[0].v3);
ext::shared_ptr<StochasticProcess1D> stochProcess1(new
BlackScholesMertonProcess(Handle<Quote>(spot1),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS1)));
ext::shared_ptr<StochasticProcess1D> stochProcess2(new
BlackScholesMertonProcess(Handle<Quote>(spot2),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS2)));
ext::shared_ptr<StochasticProcess1D> stochProcess3(new
BlackScholesMertonProcess(Handle<Quote>(spot3),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS3)));
std::vector<ext::shared_ptr<StochasticProcess1D> > procs = {stochProcess1,
stochProcess2,
stochProcess3};
Matrix correlation(3,3, 0.0);
for (Integer j=0; j < 3; j++) {
correlation[j][j] = 1.0;
}
correlation[1][0] = -0.25;
correlation[0][1] = -0.25;
correlation[2][0] = 0.25;
correlation[0][2] = 0.25;
correlation[2][1] = 0.3;
correlation[1][2] = 0.3;
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(procs,correlation));
ext::shared_ptr<PricingEngine> mcLSMCEngine =
MakeMCAmericanBasketEngine<>(process)
.withSteps(timeSteps)
.withAntitheticVariate()
.withSamples(requiredSamples)
.withCalibrationSamples(requiredSamples/4)
.withSeed(seed);
BasketOption basketOption(basketTypeToPayoff(values[0].basketType,
payoff),
exercise);
basketOption.setPricingEngine(mcLSMCEngine);
Real calculated = basketOption.NPV();
Real expected = values[0].amValue;
Real errorEstimate = basketOption.errorEstimate();
Real relError = relativeError(calculated, expected, values[0].s1);
if (relError > mcRelativeErrorTolerance ) {
REPORT_FAILURE_3("MC LSMC Tavella value", values[0].basketType,
payoff, exercise, values[0].s1, values[0].s2,
values[0].s3, values[0].r, today, values[0].v1,
values[0].v2, values[0].v3, values[0].rho,
values[0].amValue, calculated, errorEstimate,
mcRelativeErrorTolerance);
}
}
BOOST_AUTO_TEST_SUITE(BasketOptionAmericanTest, *precondition(if_speed(Fast)))
struct sliceOne { static const int from{0}, to{5}; };
struct sliceTwo { static const int from{5}, to{11}; };
struct sliceThree { static const int from{11}, to{17}; };
struct sliceFour { static const int from{17}, to{23}; };
struct sliceFive { static const int from{23}, to{29}; };
using slices = boost::mpl::vector<sliceOne, sliceTwo, sliceThree, sliceFour, sliceFive>;
BOOST_AUTO_TEST_CASE_TEMPLATE(testOneDAmericanValues, T, slices) {
const int from = T::from;
const int to = T::to;
BOOST_TEST_MESSAGE("Testing basket American options against 1-D case "
"from " << from << " to " << to - 1 << "...");
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot1(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(0.05));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol1(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);
Size requiredSamples = 10000;
Size timeSteps = 52;
BigNatural seed = 0;
ext::shared_ptr<StochasticProcess1D> stochProcess1(new
BlackScholesMertonProcess(Handle<Quote>(spot1),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS1)));
std::vector<ext::shared_ptr<StochasticProcess1D>> procs = {stochProcess1};
Matrix correlation(1, 1, 1.0);
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(procs, correlation));
ext::shared_ptr<PricingEngine> mcLSMCEngine =
MakeMCAmericanBasketEngine<>(process)
.withSteps(timeSteps)
.withAntitheticVariate()
.withSamples(requiredSamples)
.withCalibrationSamples(requiredSamples / 4)
.withSeed(seed);
for (Size i = from; i < to; i++) {
ext::shared_ptr<PlainVanillaPayoff> payoff(
new PlainVanillaPayoff(oneDataValues[i].type, oneDataValues[i].strike));
Date exDate = today + timeToDays(oneDataValues[i].t);
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today, exDate));
spot1 ->setValue(oneDataValues[i].s);
vol1 ->setValue(oneDataValues[i].v);
rRate ->setValue(oneDataValues[i].r);
qRate ->setValue(oneDataValues[i].q);
BasketOption basketOption( // process,
basketTypeToPayoff(MaxBasket, payoff), exercise);
basketOption.setPricingEngine(mcLSMCEngine);
Real calculated = basketOption.NPV();
Real expected = oneDataValues[i].result;
// Real errorEstimate = basketOption.errorEstimate();
Real relError = relativeError(calculated, expected, oneDataValues[i].s);
// Real error = std::fabs(calculated-expected);
if (relError > oneDataValues[i].tol) {
BOOST_FAIL("expected value: " << oneDataValues[i].result << "\n"
<< "calculated: " << calculated);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
/* This unit test is a regression test to check for a crash in
monte carlo if the required sample is odd. The crash occurred
because the samples array size was off by one when antithetic
paths were added.
*/
BOOST_AUTO_TEST_CASE(testOddSamples) {
BOOST_TEST_MESSAGE("Testing antithetic engine using odd sample number...");
Size requiredSamples = 10001; // The important line
Size timeSteps = 53;
BasketOptionOneData values[] = {
// type, strike, spot, q, r, t, vol, value, tol
{ Option::Put, 100.00, 80.00, 0.0, 0.06, 0.5, 0.4, 21.6059, 1e-2 }
};
DayCounter dc = Actual360();
Date today = Date::todaysDate();
ext::shared_ptr<SimpleQuote> spot1(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(0.05));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<SimpleQuote> vol1(new SimpleQuote(0.0));
ext::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);
BigNatural seed = 0;
ext::shared_ptr<StochasticProcess1D> stochProcess1(new
BlackScholesMertonProcess(Handle<Quote>(spot1),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS1)));
std::vector<ext::shared_ptr<StochasticProcess1D> > procs = {stochProcess1};
Matrix correlation(1, 1, 1.0);
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(procs,correlation));
ext::shared_ptr<PricingEngine> mcLSMCEngine =
MakeMCAmericanBasketEngine<>(process)
.withSteps(timeSteps)
.withAntitheticVariate()
.withSamples(requiredSamples)
.withCalibrationSamples(requiredSamples/4)
.withSeed(seed);
for (auto& value : values) {
ext::shared_ptr<PlainVanillaPayoff> payoff(
new PlainVanillaPayoff(value.type, value.strike));
Date exDate = today + timeToDays(value.t);
ext::shared_ptr<Exercise> exercise(new AmericanExercise(today,
exDate));
spot1->setValue(value.s);
vol1->setValue(value.v);
rRate->setValue(value.r);
qRate->setValue(value.q);
BasketOption basketOption(// process,
basketTypeToPayoff(MaxBasket, payoff),
exercise);
basketOption.setPricingEngine(mcLSMCEngine);
Real calculated = basketOption.NPV();
Real expected = value.result;
// Real errorEstimate = basketOption.errorEstimate();
Real relError = relativeError(calculated, expected, value.s);
// Real error = std::fabs(calculated-expected);
if (relError > value.tol) {
BOOST_FAIL("expected value: " << value.result << "\n"
<< "calculated: " << calculated);
}
}
}
BOOST_AUTO_TEST_CASE(testLocalVolatilitySpreadOption) {
BOOST_TEST_MESSAGE("Testing 2D local-volatility spread-option pricing...");
const DayCounter dc = Actual360();
const Date today = Date(21, September, 2017);
const Date maturity = today + Period(3, Months);
const Handle<YieldTermStructure> riskFreeRate(flatRate(today, 0.07, dc));
const Handle<YieldTermStructure> dividendYield(flatRate(today, 0.03, dc));
const Handle<Quote> s1(ext::make_shared<SimpleQuote>(100));
const Handle<Quote> s2(ext::make_shared<SimpleQuote>(110));
const ext::shared_ptr<HestonModel> hm1(
ext::make_shared<HestonModel>(
ext::make_shared<HestonProcess>(
riskFreeRate, dividendYield,
s1, 0.09, 1.0, 0.06, 0.6, -0.75)));
const ext::shared_ptr<HestonModel> hm2(
ext::make_shared<HestonModel>(
ext::make_shared<HestonProcess>(
riskFreeRate, dividendYield,
s2, 0.1, 2.0, 0.07, 0.8, 0.85)));
const Handle<BlackVolTermStructure> vol1(
ext::make_shared<HestonBlackVolSurface>(Handle<HestonModel>(hm1)));
const Handle<BlackVolTermStructure> vol2(
ext::make_shared<HestonBlackVolSurface>(Handle<HestonModel>(hm2)));
BasketOption basketOption(
basketTypeToPayoff(
SpreadBasket,
ext::make_shared<PlainVanillaPayoff>(
Option::Call, s2->value() - s1->value())),
ext::make_shared<EuropeanExercise>(maturity));
const Real rho = -0.6;
const ext::shared_ptr<GeneralizedBlackScholesProcess> bs2(
ext::make_shared<GeneralizedBlackScholesProcess>(
s2, dividendYield, riskFreeRate, vol2));
const ext::shared_ptr<GeneralizedBlackScholesProcess> bs1(
ext::make_shared<GeneralizedBlackScholesProcess>(
s1, dividendYield, riskFreeRate, vol1));
basketOption.setPricingEngine(
ext::make_shared<Fd2dBlackScholesVanillaEngine>(
bs1, bs2, rho, 11, 11, 6, 0,
FdmSchemeDesc::Hundsdorfer(), true, 0.25));
const Real tolerance = 0.01;
const Real expected = 2.561;
const Real calculated = basketOption.NPV();
if (std::fabs(expected - calculated) > tolerance) {
BOOST_ERROR("Failed to reproduce expected local volatility price"
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< "\n tolerance: " << tolerance);
}
}
BOOST_AUTO_TEST_CASE(test2DPDEGreeks) {
BOOST_TEST_MESSAGE("Testing Greeks of two-dimensional PDE engine...");
const Real s1 = 100;
const Real s2 = 100;
const Real r = 0.013;