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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*!
Copyright (C) 2006, 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
<[email protected]>. 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.
*/
/* This example showcases the CompositeInstrument class. Such class
is used to build a static replication of a down-and-out barrier
option, as outlined in Section 10.2 of Mark Joshi's "The Concepts
and Practice of Mathematical Finance" to which we refer the
reader.
*/
#include <ql/qldefines.hpp>
#if !defined(BOOST_ALL_NO_LIB) && defined(BOOST_MSVC)
# include <ql/auto_link.hpp>
#endif
#include <ql/instruments/compositeinstrument.hpp>
#include <ql/instruments/barrieroption.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/pricingengines/barrier/analyticbarrierengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/exercise.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <iostream>
#include <iomanip>
using namespace QuantLib;
int main(int, char* []) {
try {
std::cout << std::endl;
Date today(29, May, 2006);
Settings::instance().evaluationDate() = today;
// the option to replicate
Barrier::Type barrierType = Barrier::DownOut;
Real barrier = 70.0;
Real rebate = 0.0;
Option::Type type = Option::Put;
Real underlyingValue = 100.0;
auto underlying = ext::make_shared<SimpleQuote>(underlyingValue);
Real strike = 100.0;
auto riskFreeRate = ext::make_shared<SimpleQuote>(0.04);
auto volatility = ext::make_shared<SimpleQuote>(0.20);
Date maturity = today + 1*Years;
std::cout << std::endl ;
// write column headings
Size widths[] = { 45, 15, 15 };
Size totalWidth = widths[0]+widths[1]+widths[2];
std::string rule(totalWidth, '-'), dblrule(totalWidth, '=');
std::cout << dblrule << std::endl;
std::cout << "Initial market conditions" << std::endl;
std::cout << dblrule << std::endl;
std::cout << std::setw(widths[0]) << std::left << "Option"
<< std::setw(widths[1]) << std::left << "NPV"
<< std::setw(widths[2]) << std::left << "Error"
<< std::endl;
std::cout << rule << std::endl;
// bootstrap the yield/vol curves
DayCounter dayCounter = Actual365Fixed();
Handle<Quote> h1(riskFreeRate);
Handle<Quote> h2(volatility);
Handle<YieldTermStructure> flatRate(
ext::make_shared<FlatForward>(0, NullCalendar(), h1, dayCounter));
Handle<BlackVolTermStructure> flatVol(
ext::make_shared<BlackConstantVol>(0, NullCalendar(), h2, dayCounter));
// instantiate the option
auto exercise = ext::make_shared<EuropeanExercise>(maturity);
auto payoff = ext::make_shared<PlainVanillaPayoff>(type, strike);
auto bsProcess = ext::make_shared<BlackScholesProcess>(
Handle<Quote>(underlying), flatRate, flatVol);
auto barrierEngine = ext::make_shared<AnalyticBarrierEngine>(bsProcess);
auto europeanEngine = ext::make_shared<AnalyticEuropeanEngine>(bsProcess);
BarrierOption referenceOption(barrierType, barrier, rebate,
payoff, exercise);
referenceOption.setPricingEngine(barrierEngine);
Real referenceValue = referenceOption.NPV();
std::cout << std::setw(widths[0]) << std::left
<< "Original barrier option"
<< std::fixed
<< std::setw(widths[1]) << std::left << referenceValue
<< std::setw(widths[2]) << std::left << "N/A"
<< std::endl;
// Replicating portfolios
CompositeInstrument portfolio1, portfolio2, portfolio3;
// Final payoff first (the same for all portfolios):
// as shown in Joshi, a put struck at K...
auto put1 = ext::make_shared<EuropeanOption>(payoff, exercise);
put1->setPricingEngine(europeanEngine);
portfolio1.add(put1);
portfolio2.add(put1);
portfolio3.add(put1);
// ...minus a digital put struck at B of notional K-B...
auto digitalPayoff = ext::make_shared<CashOrNothingPayoff>(Option::Put, barrier, 1.0);
auto digitalPut = ext::make_shared<EuropeanOption>(digitalPayoff, exercise);
digitalPut->setPricingEngine(europeanEngine);
portfolio1.subtract(digitalPut, strike-barrier);
portfolio2.subtract(digitalPut, strike-barrier);
portfolio3.subtract(digitalPut, strike-barrier);
// ...minus a put option struck at B.
auto lowerPayoff = ext::make_shared<PlainVanillaPayoff>(Option::Put, barrier);
auto put2 = ext::make_shared<EuropeanOption>(lowerPayoff, exercise);
put2->setPricingEngine(europeanEngine);
portfolio1.subtract(put2);
portfolio2.subtract(put2);
portfolio3.subtract(put2);
// Now we use puts struck at B to kill the value of the
// portfolio on a number of points (B,t). For the first
// portfolio, we'll use 12 dates at one-month's distance.
Integer i;
for (i=12; i>=1; i--) {
// First, we instantiate the option...
Date innerMaturity = today + i*Months;
auto innerExercise = ext::make_shared<EuropeanExercise>(innerMaturity);
auto innerPayoff = ext::make_shared<PlainVanillaPayoff>(Option::Put, barrier);
auto putn = ext::make_shared<EuropeanOption>(innerPayoff, innerExercise);
putn->setPricingEngine(europeanEngine);
// ...second, we evaluate the current portfolio and the
// latest put at (B,t)...
Date killDate = today + (i-1)*Months;
Settings::instance().evaluationDate() = killDate;
underlying->setValue(barrier);
Real portfolioValue = portfolio1.NPV();
Real putValue = putn->NPV();
// ...finally, we estimate the notional that kills the
// portfolio value at that point...
Real notional = portfolioValue/putValue;
// ...and we subtract from the portfolio a put with such
// notional.
portfolio1.subtract(putn, notional);
}
// The portfolio being complete, we return to today's market...
Settings::instance().evaluationDate() = today;
underlying->setValue(underlyingValue);
// ...and output the value.
Real portfolioValue = portfolio1.NPV();
Real error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (12 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
// For the second portfolio, we'll use 26 dates at two-weeks'
// distance.
for (i=52; i>=2; i-=2) {
// Same as above.
Date innerMaturity = today + i*Weeks;
auto innerExercise = ext::make_shared<EuropeanExercise>(innerMaturity);
auto innerPayoff = ext::make_shared<PlainVanillaPayoff>(Option::Put, barrier);
auto putn = ext::make_shared<EuropeanOption>(innerPayoff, innerExercise);
putn->setPricingEngine(europeanEngine);
Date killDate = today + (i-2)*Weeks;
Settings::instance().evaluationDate() = killDate;
underlying->setValue(barrier);
Real portfolioValue = portfolio2.NPV();
Real putValue = putn->NPV();
Real notional = portfolioValue/putValue;
portfolio2.subtract(putn, notional);
}
Settings::instance().evaluationDate() = today;
underlying->setValue(underlyingValue);
portfolioValue = portfolio2.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (26 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
// For the third portfolio, we'll use 52 dates at one-week's
// distance.
for (i=52; i>=1; i--) {
// Same as above.
Date innerMaturity = today + i*Weeks;
auto innerExercise = ext::make_shared<EuropeanExercise>(innerMaturity);
auto innerPayoff = ext::make_shared<PlainVanillaPayoff>(Option::Put, barrier);
auto putn = ext::make_shared<EuropeanOption>(innerPayoff, innerExercise);
putn->setPricingEngine(europeanEngine);
Date killDate = today + (i-1)*Weeks;
Settings::instance().evaluationDate() = killDate;
underlying->setValue(barrier);
Real portfolioValue = portfolio3.NPV();
Real putValue = putn->NPV();
Real notional = portfolioValue/putValue;
portfolio3.subtract(putn, notional);
}
Settings::instance().evaluationDate() = today;
underlying->setValue(underlyingValue);
portfolioValue = portfolio3.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (52 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
// Now we modify the market condition to see whether the
// replication holds. First, we change the underlying value so
// that the option is out of the money.
std::cout << dblrule << std::endl;
std::cout << "Modified market conditions: out of the money"
<< std::endl;
std::cout << dblrule << std::endl;
std::cout << std::setw(widths[0]) << std::left << "Option"
<< std::setw(widths[1]) << std::left << "NPV"
<< std::setw(widths[2]) << std::left << "Error"
<< std::endl;
std::cout << rule << std::endl;
underlying->setValue(110.0);
referenceValue = referenceOption.NPV();
std::cout << std::setw(widths[0]) << std::left
<< "Original barrier option"
<< std::fixed
<< std::setw(widths[1]) << std::left << referenceValue
<< std::setw(widths[2]) << std::left << "N/A"
<< std::endl;
portfolioValue = portfolio1.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (12 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
portfolioValue = portfolio2.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (26 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
portfolioValue = portfolio3.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (52 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
// Next, we change the underlying value so that the option is
// in the money.
std::cout << dblrule << std::endl;
std::cout << "Modified market conditions: in the money" << std::endl;
std::cout << dblrule << std::endl;
std::cout << std::setw(widths[0]) << std::left << "Option"
<< std::setw(widths[1]) << std::left << "NPV"
<< std::setw(widths[2]) << std::left << "Error"
<< std::endl;
std::cout << rule << std::endl;
underlying->setValue(90.0);
referenceValue = referenceOption.NPV();
std::cout << std::setw(widths[0]) << std::left
<< "Original barrier option"
<< std::fixed
<< std::setw(widths[1]) << std::left << referenceValue
<< std::setw(widths[2]) << std::left << "N/A"
<< std::endl;
portfolioValue = portfolio1.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (12 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
portfolioValue = portfolio2.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (26 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
portfolioValue = portfolio3.NPV();
error = portfolioValue - referenceValue;
std::cout << std::setw(widths[0]) << std::left
<< "Replicating portfolio (52 dates)"
<< std::fixed
<< std::setw(widths[1]) << std::left << portfolioValue
<< std::setw(widths[2]) << std::left << error
<< std::endl;
// Finally, a word of warning for those (shame on them) who
// run the example but do not read the code.
std::cout << dblrule << std::endl;
std::cout
<< std::endl
<< "The replication seems to be less robust when volatility and \n"
<< "risk-free rate are changed. Feel free to experiment with \n"
<< "the example and contribute a patch if you spot any errors."
<< std::endl;
return 0;
} catch (std::exception& e) {
std::cerr << e.what() << std::endl;
return 1;
} catch (...) {
std::cerr << "unknown error" << std::endl;
return 1;
}
}