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/*!
Copyright (C) 2000, 2001, 2002 RiskMap 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 ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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.
*/
//! $Id: EuropeanOption.cpp,v 1.15 2002/01/16 14:40:40 nando Exp $
#include <ql/quantlib.hpp>
using namespace QuantLib;
using QuantLib::Pricers::EuropeanOption;
using QuantLib::Pricers::McEuropean;
using QuantLib::Pricers::FdEuropean;
// helper function for option payoff: MAX((stike-underlying),0), etc.
using QuantLib::Pricers::ExercisePayoff;
// This will be included in the library after a bit of redesign
class Payoff : public QL::ObjectiveFunction{
public:
Payoff(Time maturity,
double strike,
double s0,
double sigma,
Rate r)
: maturity_(maturity),
strike_(strike),
s0_(s0),
sigma_(sigma),r_(r){}
double operator()(double x) const {
double nuT = (r_-0.5*sigma_*sigma_)*maturity_;
return QL_EXP(-r_*maturity_)
*ExercisePayoff(Option::Call, s0_*QL_EXP(x), strike_)
*QL_EXP(-(x - nuT)*(x -nuT)/(2*sigma_*sigma_*maturity_))
/QL_SQRT(2.0*3.141592*sigma_*sigma_*maturity_);
}
private:
Time maturity_;
double strike_;
double s0_;
double sigma_;
Rate r_;
};
int main(int argc, char* argv[])
{
try {
// our option
double underlying = 102;
double strike = 100; // at the money
Spread dividendYield = 0.0; // no dividends
Rate riskFreeRate = 0.05; // 5%
Time maturity = 0.25; // 3 months
double volatility = 0.20; // 20%
std::cout << "Time to maturity = " << maturity
<< std::endl;
std::cout << "Underlying price = " << underlying
<< std::endl;
std::cout << "Strike = " << strike
<< std::endl;
std::cout << "Risk-free interest rate = " << riskFreeRate
<< std::endl;
std::cout << "Volatility = " << volatility
<< std::endl;
std::cout << std::endl;
// write column headings
std::cout << "Method\t\tValue\tEstimatedError\tDiscrepancy"
"\tRel. Discr." << std::endl;
// first method: Black Scholes analytic solution
std::string method ="Black Scholes";
double value = EuropeanOption(Option::Call, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility).value();
double estimatedError = 0.0;
double discrepancy = 0.0;
double relativeDiscrepancy = 0.0;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< DoubleFormatter::toString(estimatedError, 4) << "\t\t"
<< DoubleFormatter::toString(discrepancy, 6) << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
// store the Black Scholes value as the correct one
double rightValue = value;
// second method: Call-Put parity
method ="Call-Put parity";
value = EuropeanOption(Option::Put, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility).value()
+ underlying - strike*QL_EXP(- riskFreeRate*maturity);
discrepancy = QL_FABS(value-rightValue);
relativeDiscrepancy = discrepancy/rightValue;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< "N/A\t\t"
<< discrepancy << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
// third method: Integral
method ="Integral";
using QuantLib::Math::SegmentIntegral;
Payoff po(maturity, strike, underlying, volatility, riskFreeRate);
SegmentIntegral integrator(5000);
double nuT = (riskFreeRate - 0.5*volatility*volatility)*maturity;
double infinity = 10.0*volatility*QL_SQRT(maturity);
value = integrator(po, nuT-infinity, nuT+infinity);
discrepancy = QL_FABS(value-rightValue);
relativeDiscrepancy = discrepancy/rightValue;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< "N/A\t\t"
<< DoubleFormatter::toString(discrepancy, 6) << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
// fourth method: Finite Differences
method ="Finite Diff.";
Size grid = 100;
value = FdEuropean(Option::Call, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility, grid).value();
discrepancy = QL_FABS(value-rightValue);
relativeDiscrepancy = discrepancy/rightValue;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< "N/A\t\t"
<< DoubleFormatter::toString(discrepancy, 6) << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
// fifth method: Monte Carlo (crude)
method ="MC (crude)";
bool antitheticVariance = false;
McEuropean mcEur(Option::Call, underlying, strike, dividendYield,
riskFreeRate, maturity, volatility, antitheticVariance);
// let's require a tolerance of 0.002%
value = mcEur.value(0.002);
estimatedError = mcEur.errorEstimate();
discrepancy = QL_FABS(value-rightValue);
relativeDiscrepancy = discrepancy/rightValue;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< DoubleFormatter::toString(estimatedError, 4) << "\t\t"
<< DoubleFormatter::toString(discrepancy, 6) << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
// sixth method: Monte Carlo with antithetic variance reduction
method ="MC (antithetic)";
// let's use the same number of samples as in the crude Monte Carlo
Size nSamples = mcEur.sampleAccumulator().samples();
antitheticVariance = true;
McEuropean mcEur2(Option::Call, underlying, strike, dividendYield,
riskFreeRate, maturity, volatility, antitheticVariance);
value = mcEur2.valueWithSamples(nSamples);
estimatedError = mcEur2.errorEstimate();
discrepancy = QL_FABS(value-rightValue);
relativeDiscrepancy = discrepancy/rightValue;
std::cout << method << "\t"
<< DoubleFormatter::toString(value, 4) << "\t"
<< DoubleFormatter::toString(estimatedError, 4) << "\t\t"
<< DoubleFormatter::toString(discrepancy, 6) << "\t"
<< DoubleFormatter::toString(relativeDiscrepancy, 6)
<< std::endl;
return 0;
} catch (std::exception& e) {
std::cout << e.what() << std::endl;
return 1;
} catch (...) {
std::cout << "unknown error" << std::endl;
return 1;
}
}
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