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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004 Ferdinando Ametrano
Copyright (C) 2003 Neil Firth
Copyright (C) 2000, 2001, 2002, 2003 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
<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 <ql/pricingengines/vanilla/mcdigitalengine.hpp>
namespace QuantLib {
DigitalPathPricer::DigitalPathPricer(
const boost::shared_ptr<CashOrNothingPayoff>& payoff,
const boost::shared_ptr<AmericanExercise>& exercise,
const Handle<YieldTermStructure>& discountTS,
const boost::shared_ptr<StochasticProcess1D>& diffProcess,
const PseudoRandom::ursg_type& sequenceGen)
: payoff_(payoff), exercise_(exercise), diffProcess_(diffProcess),
sequenceGen_(sequenceGen), discountTS_(discountTS) {}
Real DigitalPathPricer::operator()(const Path& path) const {
Size n = path.length();
QL_REQUIRE(n>1, "the path cannot be empty");
Real log_asset_price = std::log(path.front());
Real x, y;
Volatility vol;
TimeGrid timeGrid = path.timeGrid();
Time dt;
std::vector<Real> u = sequenceGen_.nextSequence().value;
Real log_strike = std::log(payoff_->strike());
Size i;
switch (payoff_->optionType()) {
case Option::Call:
for (i=0; i<n-1; i++) {
x = std::log(path[i+1]/path[i]);
// terminal or initial vol?
vol = diffProcess_->diffusion(timeGrid[i+1],
std::exp(log_asset_price));
// vol = diffProcess_->diffusion(timeGrid[i+2],
// std::exp(log_asset_price+x));
dt = timeGrid.dt(i);
y = log_asset_price +
0.5*(x + std::sqrt(x*x-2*vol*vol*dt*std::log((1-u[i]))));
// cross the strike
if (y >= log_strike) {
if (exercise_->payoffAtExpiry()) {
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid().back());
} else {
// the discount should be calculated at the exercise
// time between path.timeGrid()[i+1] and
// path.timeGrid()[i+2]
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid()[i+1]);
}
}
log_asset_price += x;
}
break;
case Option::Put:
for (i=0; i<n-1; i++) {
x = std::log(path[i+1]/path[i]);
// terminal or initial vol?
// initial (timeGrid[i+1]) for the time being
vol = diffProcess_->diffusion(timeGrid[i+1],
std::exp(log_asset_price));
// vol = diffProcess_->diffusion(timeGrid[i+2],
// std::exp(log_asset_price+x));
dt = timeGrid.dt(i);
y = log_asset_price +
0.5*(x - std::sqrt(x*x - 2*vol*vol*dt*std::log(u[i])));
if (y <= log_strike) {
if (exercise_->payoffAtExpiry()) {
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid().back());
} else {
// the discount should be calculated at the exercise
// time between path.timeGrid()[i+1] and
// path.timeGrid()[i+2]
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid()[i+1]);
}
}
log_asset_price += x;
}
break;
default:
QL_FAIL("unknown option type");
}
return 0.0;
}
}
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