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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006, 2007, 2015 Ferdinando Ametrano
Copyright (C) 2006 Cristina Duminuco
Copyright (C) 2007 Giorgio Facchinetti
Copyright (C) 2015 Paolo Mazzocchi
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.
*/
#ifndef quantlib_abcd_math_function_hpp
#define quantlib_abcd_math_function_hpp
#include <ql/types.hpp>
#include <ql/errors.hpp>
#include <vector>
namespace QuantLib {
//! %Abcd functional form
/*! \f[ f(t) = [ a + b*t ] e^{-c*t} + d \f]
following Rebonato's notation. */
class AbcdMathFunction {
public:
AbcdMathFunction(Real a = 0.002,
Real b = 0.001,
Real c = 0.16,
Real d = 0.0005);
AbcdMathFunction(std::vector<Real> abcd);
//! function value at time t: \f[ f(t) \f]
Real operator()(Time t) const;
//! time at which the function reaches maximum (if any)
Time maximumLocation() const;
//! maximum value of the function
Real maximumValue() const;
//! function value at time +inf: \f[ f(\inf) \f]
Real longTermValue() const { return d_; }
/*! first derivative of the function at time t
\f[ f'(t) = [ (b-c*a) + (-c*b)*t) ] e^{-c*t} \f] */
Real derivative(Time t) const;
/*! indefinite integral of the function at time t
\f[ \int f(t)dt = [ (-a/c-b/c^2) + (-b/c)*t ] e^{-c*t} + d*t \f] */
Real primitive(Time t) const;
/*! definite integral of the function between t1 and t2
\f[ \int_{t1}^{t2} f(t)dt \f] */
Real definiteIntegral(Time t1, Time t2) const;
/*! Inspectors */
Real a() const { return a_; }
Real b() const { return b_; }
Real c() const { return c_; }
Real d() const { return d_; }
const std::vector<Real>& coefficients() { return abcd_; }
const std::vector<Real>& derivativeCoefficients() { return dabcd_; }
// the primitive is not abcd
/*! coefficients of a AbcdMathFunction defined as definite
integral on a rolling window of length tau, with tau = t2-t */
std::vector<Real> definiteIntegralCoefficients(Time t,
Time t2) const;
/*! coefficients of a AbcdMathFunction defined as definite
derivative on a rolling window of length tau, with tau = t2-t */
std::vector<Real> definiteDerivativeCoefficients(Time t,
Time t2) const;
static void validate(Real a,
Real b,
Real c,
Real d);
protected:
Real a_, b_, c_, d_;
private:
void initialize_();
std::vector<Real> abcd_;
std::vector<Real> dabcd_;
Real da_, db_;
Real pa_, pb_, K_;
Real dibc_, diacplusbcc_;
};
// inline AbcdMathFunction
inline Real AbcdMathFunction::operator()(Time t) const {
//return (a_ + b_*t)*std::exp(-c_*t) + d_;
return t<0 ? 0.0 : Real((a_ + b_*t)*std::exp(-c_*t) + d_);
}
inline Real AbcdMathFunction::derivative(Time t) const {
//return (da_ + db_*t)*std::exp(-c_*t);
return t<0 ? 0.0 : Real((da_ + db_*t)*std::exp(-c_*t));
}
inline Real AbcdMathFunction::primitive(Time t) const {
//return (pa_ + pb_*t)*std::exp(-c_*t) + d_*t + K_;
return t<0 ? 0.0 : Real((pa_ + pb_*t)*std::exp(-c_*t) + d_*t + K_);
}
inline Real AbcdMathFunction::maximumValue() const {
if (b_==0.0 || a_<=0.0)
return d_;
return (*this)(maximumLocation());
}
}
#endif
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