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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 Klaus Spanderen
Copyright (C) 2014 Ralph Schreyer
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 <algorithm>
#include <ql/math/interpolations/bilinearinterpolation.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsimplestoragecondition.hpp>
#include <utility>
namespace QuantLib {
FdmSimpleStorageCondition::FdmSimpleStorageCondition(
std::vector<Time> exerciseTimes,
ext::shared_ptr<FdmMesher> mesher,
ext::shared_ptr<FdmInnerValueCalculator> calculator,
Real changeRate)
: exerciseTimes_(std::move(exerciseTimes)), mesher_(std::move(mesher)),
calculator_(std::move(calculator)), changeRate_(changeRate) {
x_.reserve(mesher_->layout()->dim()[0]);
y_.reserve(mesher_->layout()->dim()[1]);
for (const auto& iter : *mesher_->layout()) {
if (iter.coordinates()[1] == 0U) {
x_.push_back(mesher_->location(iter, 0));
}
if (iter.coordinates()[0] == 0U) {
y_.push_back(mesher_->location(iter, 1));
}
}
}
void FdmSimpleStorageCondition::applyTo(Array& a, Time t) const {
const auto iter
= std::find(exerciseTimes_.begin(), exerciseTimes_.end(), t);
if (iter != exerciseTimes_.end()) {
Array retVal(a.size());
Matrix m(y_.size(), x_.size());
std::copy(a.begin(), a.end(), m.begin());
BilinearInterpolation interpl(x_.begin(), x_.end(),
y_.begin(), y_.end(), m);
QL_REQUIRE(mesher_->layout()->size() == a.size(),
"inconsistent array dimensions");
for (const auto& iter : *mesher_->layout()) {
const std::vector<Size>& coor = iter.coordinates();
const Real x = x_[coor[0]];
const Real y = y_[coor[1]];
const Real price = calculator_->innerValue(iter, t);
const Real maxWithDraw = std::min(y-y_.front(), changeRate_);
const Real sellPrice = interpl(x, y-maxWithDraw);
const Real maxInject = std::min(y_.back()-y, changeRate_);
const Real buyPrice = interpl(x, y+maxInject);
// bang-bang-wait strategy
Real currentValue = std::max({
a[iter.index()],
Real(buyPrice - price*maxInject),
Real(sellPrice + price*maxWithDraw)
});
// check if intermediate grid points give a better value
auto yIter = std::upper_bound(y_.begin(), y_.end(), y - maxWithDraw);
while (yIter != y_.end() && *yIter < y + maxInject) {
if (*yIter != y) {
const Real change = *yIter - y;
const Real storagePrice(interpl(x, *yIter));
currentValue = std::max(currentValue,
storagePrice - change*price);
}
++yIter;
}
retVal[iter.index()] = currentValue;
}
a = retVal;
}
}
}
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