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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Warren Chou
Copyright (C) 2007, 2008 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
<https://www.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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/quotes/simplequote.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/instruments/varianceswap.hpp>
#include <ql/pricingengines/forward/replicatingvarianceswapengine.hpp>
#include <ql/pricingengines/forward/mcvarianceswapengine.hpp>
#include <ql/math/randomnumbers/rngtraits.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancecurve.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancesurface.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/processes/blackscholesprocess.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(VarianceSwapTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, isLong, varStrike, nominal, s, q, r, today, \
exDate, v, expected, calculated, error, tolerance) \
BOOST_ERROR( \
" variance swap with " \
<< " underlying value: " << s << "\n" \
<< " strike: " << varStrike << "\n" \
<< " nominal: " << nominal << "\n" \
<< " dividend yield: " << io::rate(q) << "\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " maturity: " << exDate << "\n" \
<< " volatility: " << io::volatility(v) << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance);
struct MCVarianceSwapData {
Position::Type type;
Real varStrike;
Real nominal;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time t1; // intermediate time
Time t; // time to maturity
Volatility v1; // volatility at t1
Volatility v; // volatility at t
Real result; // result
Real tol; // tolerance
};
struct ReplicatingVarianceSwapData {
Position::Type type;
Real varStrike;
Real nominal;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time t; // time to maturity
Volatility v; // volatility at t
Real result; // result
Real tol; // tolerance
};
struct Datum {
Option::Type type;
Real strike;
Volatility v;
};
BOOST_AUTO_TEST_CASE(testReplicatingVarianceSwap) {
BOOST_TEST_MESSAGE("Testing variance swap with replicating cost engine...");
ReplicatingVarianceSwapData values[] = {
// data from "A Guide to Volatility and Variance Swaps",
// Derman, Kamal & Zou, 1999
// with maturity t corrected from 0.25 to 0.246575
// corresponding to Jan 1, 1999 to Apr 1, 1999
//type, varStrike, nominal, s, q, r, t, v, result, tol
{ Position::Long, 0.04, 50000, 100.0, 0.00, 0.05, 0.246575, 0.20, 0.04189, 1.0e-4}
};
Datum replicatingOptionData[] = {
// data from "A Guide to Volatility and Variance Swaps",
// Derman, Kamal & Zou, 1999
//Option::Type, strike, v
{ Option::Put, 50, 0.30 },
{ Option::Put, 55, 0.29 },
{ Option::Put, 60, 0.28 },
{ Option::Put, 65, 0.27 },
{ Option::Put, 70, 0.26 },
{ Option::Put, 75, 0.25 },
{ Option::Put, 80, 0.24 },
{ Option::Put, 85, 0.23 },
{ Option::Put, 90, 0.22 },
{ Option::Put, 95, 0.21 },
{ Option::Put, 100, 0.20 },
{ Option::Call, 100, 0.20 },
{ Option::Call, 105, 0.19 },
{ Option::Call, 110, 0.18 },
{ Option::Call, 115, 0.17 },
{ Option::Call, 120, 0.16 },
{ Option::Call, 125, 0.15 },
{ Option::Call, 130, 0.14 },
{ Option::Call, 135, 0.13 }
};
DayCounter dc = Actual365Fixed();
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);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t, 365);
std::vector<Date> dates(1);
dates[0] = exDate;
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
Size options = std::size(replicatingOptionData);
std::vector<Real> callStrikes, putStrikes, callVols, putVols;
// Assumes ascending strikes and same min call and max put strikes
Size j;
for (j=0; j<options; j++) {
if (replicatingOptionData[j].type == Option::Call) {
callStrikes.push_back(replicatingOptionData[j].strike);
callVols.push_back(replicatingOptionData[j].v);
} else if (replicatingOptionData[j].type == Option::Put) {
putStrikes.push_back(replicatingOptionData[j].strike);
putVols.push_back(replicatingOptionData[j].v);
} else {
QL_FAIL("unknown option type");
}
}
Matrix vols(options-1, 1);
std::vector<Real> strikes;
for (j=0; j<putVols.size(); j++) {
vols[j][0] = putVols[j];
strikes.push_back(putStrikes[j]);
}
for (Size k=1; k<callVols.size(); k++) {
Size j = putVols.size()-1;
vols[j+k][0] = callVols[k];
strikes.push_back(callStrikes[k]);
}
ext::shared_ptr<BlackVolTermStructure> volTS(new
BlackVarianceSurface(today, NullCalendar(),
dates, strikes, vols, dc));
ext::shared_ptr<GeneralizedBlackScholesProcess> stochProcess(
new BlackScholesMertonProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
ext::shared_ptr<PricingEngine> engine(
new ReplicatingVarianceSwapEngine(stochProcess, 5.0,
callStrikes,
putStrikes));
VarianceSwap varianceSwap(value.type, value.varStrike, value.nominal, today, exDate);
varianceSwap.setPricingEngine(engine);
Real calculated = varianceSwap.variance();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol)
REPORT_FAILURE("value", values[i].type, value.varStrike, value.nominal, value.s,
value.q, value.r, today, exDate, value.v, expected, calculated, error,
value.tol);
}
}
BOOST_AUTO_TEST_CASE(testMCVarianceSwap) {
BOOST_TEST_MESSAGE("Testing variance swap with Monte Carlo engine...");
MCVarianceSwapData values[] = {
// data from "A Guide to Volatility and Variance Swaps",
// Derman, Kamal & Zou, 1999
// with maturity t corrected from 0.25 to 0.246575
// corresponding to Jan 1, 1999 to Apr 1, 1999
// exercising code using BlackVarianceCurve because BlackVarianceSurface is unreliable
// Result should be v*v for arbitrary t1 and v1 (as long as 0<=t1<t and 0<=v1<v)
//type, varStrike, nominal, s, q, r, t1, t, v1, v, result, tol
{ Position::Long, 0.04, 50000, 100.0, 0.00, 0.05, 0.1, 0.246575, 0.1, 0.20, 0.04, 3.0e-4}
};
DayCounter dc = Actual365Fixed();
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);
std::vector<Volatility> vols(2);
std::vector<Date> dates(2);
for (auto& value : values) {
Date exDate = today + timeToDays(value.t, 365);
Date intermDate = today + timeToDays(value.t1, 365);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
dates[0] = intermDate;
dates[1] = exDate;
spot->setValue(value.s);
qRate->setValue(value.q);
rRate->setValue(value.r);
vols[0] = value.v1;
vols[1] = value.v;
ext::shared_ptr<BlackVolTermStructure> volTS(
new BlackVarianceCurve(today, dates, vols, dc, true));
ext::shared_ptr<GeneralizedBlackScholesProcess> stochProcess(
new BlackScholesMertonProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
ext::shared_ptr<PricingEngine> engine;
engine =
MakeMCVarianceSwapEngine<PseudoRandom>(stochProcess)
.withStepsPerYear(250)
.withSamples(1023)
.withSeed(42);
VarianceSwap varianceSwap(value.type, value.varStrike, value.nominal, today, exDate);
varianceSwap.setPricingEngine(engine);
Real calculated = varianceSwap.variance();
Real expected = value.result;
Real error = std::fabs(calculated-expected);
if (error > value.tol)
REPORT_FAILURE("value", values[i].type, value.varStrike, value.nominal, value.s,
value.q, value.r, today, exDate, value.v, expected, calculated, error,
value.tol);
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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