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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
<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 <ql/pricingengines/americanpayoffatexpiry.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
namespace QuantLib {
AmericanPayoffAtExpiry::AmericanPayoffAtExpiry(
Real spot, DiscountFactor discount, DiscountFactor dividendDiscount,
Real variance, const ext::shared_ptr<StrikedTypePayoff>& payoff,
bool knock_in)
: spot_(spot), discount_(discount), dividendDiscount_(dividendDiscount),
variance_(variance), knock_in_(knock_in) {
QL_REQUIRE(spot_>0.0,
"positive spot value required");
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();
forward_ = spot_ * dividendDiscount_ / discount_;
mu_ = std::log(dividendDiscount_/discount_)/variance_ - 0.5;
// binary cash-or-nothing payoff?
ext::shared_ptr<CashOrNothingPayoff> coo =
ext::dynamic_pointer_cast<CashOrNothingPayoff>(payoff);
if (coo != nullptr) {
K_ = coo->cashPayoff();
}
// binary asset-or-nothing payoff?
ext::shared_ptr<AssetOrNothingPayoff> aoo =
ext::dynamic_pointer_cast<AssetOrNothingPayoff>(payoff);
if (aoo != nullptr) {
K_ = forward_;
mu_ += 1.0;
}
log_H_S_ = std::log(strike_/spot_);
Real log_S_H_ = std::log(spot_/strike_);
double eta;
double phi;
switch (type) {
case Option::Call:
if (knock_in_) {
// up-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
eta = -1.0;
phi = 1.0;
} else {
// up-and-out cash-(at-expiry)-or-nothing option
eta = -1.0;
phi = -1.0;
}
break;
case Option::Put:
if (knock_in_) {
// down-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
eta = 1.0;
phi = -1.0;
} else {
// down-and-out cash-(at-expiry)-or-nothing option
eta = 1.0;
phi = 1.0;
}
break;
default:
QL_FAIL("invalid option type");
}
if (variance_>=QL_EPSILON) {
D1_ = phi*(log_S_H_/stdDev_ + mu_*stdDev_);
D2_ = eta*(log_H_S_/stdDev_ + 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_S_H_ * phi >0)
cum_d1_= 1.0;
else
cum_d1_= 0.0;
if (log_H_S_ * eta >0)
cum_d2_= 1.0;
else
cum_d2_= 0.0;
n_d1_ = 0.0;
n_d2_ = 0.0;
}
switch (type) {
case Option::Call:
if (strike_<=spot_) {
if (knock_in_) {
// up-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
cum_d1_ = 0.5;
cum_d2_ = 0.5;
} else {
// up-and-out cash-(at-expiry)-or-nothing option
// already knocked out
cum_d1_ = 0.0;
cum_d2_ = 0.0;
}
n_d1_ = 0.0;
n_d2_ = 0.0;
}
break;
case Option::Put:
if (strike_>=spot_) {
if (knock_in_) {
// down-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
cum_d1_ = 0.5;
cum_d2_ = 0.5;
} else {
// down-and-out cash-(at-expiry)-or-nothing option
// already knocked out
cum_d1_ = 0.0;
cum_d2_ = 0.0;
}
n_d1_ = 0.0;
n_d2_ = 0.0;
}
break;
default:
QL_FAIL("invalid option type");
}
inTheMoney_ = (type==Option::Call && strike_<spot_) ||
(type==Option::Put && strike_>spot_);
if (inTheMoney_) {
X_ = 1.0;
Y_ = 1.0;
} else {
X_ = 1.0;
if (cum_d2_ == 0.0)
Y_ = 0.0; // check needed on some extreme cases
else
Y_ = std::pow(Real(strike_/spot_), Real(2.0*mu_));
}
if (!knock_in_)
Y_ *= -1.0;
}
}
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