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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2022 Klaus Spanderen
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.
*/
/*! \file qdplusamericanengine.hpp
*/
#ifndef quantlib_qd_plus_american_engine_hpp
#define quantlib_qd_plus_american_engine_hpp
#include <ql/utilities/null.hpp>
#include <ql/instruments/vanillaoption.hpp>
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
namespace QuantLib {
class Interpolation;
class ChebyshevInterpolation;
class QdPlusBoundaryEvaluator;
namespace detail {
class QdPutCallParityEngine: public VanillaOption::engine {
public:
explicit QdPutCallParityEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process);
void calculate() const override;
protected:
virtual Real calculatePut(
Real S, Real K, Rate r, Rate q, Volatility vol, Time T) const = 0;
const ext::shared_ptr<GeneralizedBlackScholesProcess> process_;
private:
Real calculatePutWithEdgeCases(
Real S, Real K, Rate r, Rate q, Volatility vol, Time T) const;
};
class QdPlusAddOnValue {
public:
QdPlusAddOnValue(Time T,
Real S,
Real K,
Rate r,
Rate q,
Volatility vol,
Real xmax,
ext::shared_ptr<Interpolation> q_z);
Real operator()(Real z) const;
private:
const Time T_;
const Real S_, K_, xmax_;
const Rate r_, q_;
const Volatility vol_;
const ext::shared_ptr<Interpolation> q_z_;
const CumulativeNormalDistribution Phi_;
};
}
//! American engine based on the QD+ approximation to the exercise boundary.
/*! The main purpose of this engine is to provide a good initial guess to the exercise
boundary for the superior fixed point American engine QdFpAmericanEngine
References:
Li, M. (2009), “Analytical Approximations for the Critical Stock Prices
of American Options: A Performance Comparison,”
Working paper, Georgia Institute of Technology.
https://mpra.ub.uni-muenchen.de/15018/1/MPRA_paper_15018.pdf
*/
class QdPlusAmericanEngine: public detail::QdPutCallParityEngine {
public:
enum SolverType {Brent, Newton, Ridder, Halley, SuperHalley};
explicit QdPlusAmericanEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess>,
Size interpolationPoints = 8,
SolverType solverType = Halley,
Real eps = 1e-6,
Size maxIter = Null<Size>());
std::pair<Size, Real> putExerciseBoundaryAtTau(
Real S, Real K, Rate r, Rate q,
Volatility vol, Time T, Time tau) const;
ext::shared_ptr<ChebyshevInterpolation> getPutExerciseBoundary(
Real S, Real K, Rate r, Rate q, Volatility vol, Time T) const;
static Real xMax(Real K, Rate r, Rate q);
protected:
Real calculatePut(
Real S, Real K, Rate r, Rate q, Volatility vol, Time T) const override;
private:
template <class Solver>
Real buildInSolver(
const QdPlusBoundaryEvaluator& eval,
Solver solver, Real S, Real strike, Size maxIter,
Real guess = Null<Real>()) const;
const Size interpolationPoints_;
const SolverType solverType_;
const Real eps_;
const Size maxIter_;
};
}
#endif
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