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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004 Ferdinando Ametrano
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/americanpayoffatexpiry.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
namespace QuantLib {
AmericanPayoffAtExpiry::AmericanPayoffAtExpiry(
Real spot, DiscountFactor discount, DiscountFactor dividendDiscount,
Real variance, const boost::shared_ptr<StrikedTypePayoff>& payoff)
: spot_(spot), discount_(discount), dividendDiscount_(dividendDiscount),
variance_(variance) {
QL_REQUIRE(spot_>0.0,
"positive spot_ value required");
forward_ = spot_ * dividendDiscount_ / discount_;
QL_REQUIRE(discount_>0.0,
"positive discount required");
QL_REQUIRE(dividendDiscount_>0.0,
"positive dividend discount_ required");
QL_REQUIRE(variance_>=0.0,
"negative variance_ not allowed");
stdDev_ = std::sqrt(variance_);
Option::Type type = payoff->optionType();
strike_ = payoff->strike();
mu_ = std::log(dividendDiscount_/discount_)/variance_ - 0.5;
// binary cash-or-nothing payoff?
boost::shared_ptr<CashOrNothingPayoff> coo =
boost::dynamic_pointer_cast<CashOrNothingPayoff>(payoff);
if (coo) {
K_ = coo->cashPayoff();
DKDstrike_ = 0.0;
}
// binary asset-or-nothing payoff?
boost::shared_ptr<AssetOrNothingPayoff> aoo =
boost::dynamic_pointer_cast<AssetOrNothingPayoff>(payoff);
if (aoo) {
K_ = forward_;
DKDstrike_ = 0.0;
mu_ += 1.0;
}
log_H_S_ = std::log(strike_/spot_);
Real n_d1, n_d2;
Real cum_d1_, cum_d2_;
if (variance_>=QL_EPSILON) {
D1_ = log_H_S_/stdDev_ + mu_*stdDev_;
D2_ = D1_ - 2.0*mu_*stdDev_;
CumulativeNormalDistribution f;
cum_d1_ = f(D1_);
cum_d2_ = f(D2_);
n_d1 = f.derivative(D1_);
n_d2 = f.derivative(D2_);
} else {
if (log_H_S_>0) {
cum_d1_= 1.0;
cum_d2_= 1.0;
} else {
cum_d1_= 0.0;
cum_d2_= 0.0;
}
n_d1 = 0.0;
n_d2 = 0.0;
}
switch (type) {
// up-and-in cash-(at-hit)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
case Option::Call:
if (strike_>spot_) {
alpha_ = 1.0-cum_d2_;// N(-d2)
DalphaDd1_ = - n_d2; // -n( d2)
beta_ = 1.0-cum_d1_;// N(-d1)
DbetaDd2_ = - n_d1; // -n( d1)
} else {
alpha_ = 0.5;
DalphaDd1_ = 0.0;
beta_ = 0.5;
DbetaDd2_ = 0.0;
}
break;
// down-and-in cash-(at-hit)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
case Option::Put:
if (strike_<spot_) {
alpha_ = cum_d2_;// N(d2)
DalphaDd1_ = n_d2; // n(d2)
beta_ = cum_d1_;// N(d1)
DbetaDd2_ = n_d1; // n(d1)
} else {
alpha_ = 0.5;
DalphaDd1_ = 0.0;
beta_ = 0.5;
DbetaDd2_ = 0.0;
}
break;
default:
QL_FAIL("invalid option type");
}
inTheMoney_ = (type==Option::Call && strike_<spot_) ||
(type==Option::Put && strike_>spot_);
if (inTheMoney_) {
Y_ = 1.0;
X_ = 1.0;
DYDstrike_ = 0.0;
DXDstrike_ = 0.0;
} else {
Y_ = 1.0;
X_ = std::pow(Real(strike_/spot_), Real(2.0*mu_));
// DXDstrike_ = ......;
}
}
}
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