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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Allen Kuo
Copyright (C) 2010 Alessandro Roveda
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 nonlinearfittingmethods.hpp
\brief nonlinear methods to fit a bond discount function
*/
#ifndef quantlib_nonlinear_fitting_methods_hpp
#define quantlib_nonlinear_fitting_methods_hpp
#include <ql/termstructures/yield/fittedbonddiscountcurve.hpp>
#include <ql/math/bspline.hpp>
#include <ql/shared_ptr.hpp>
namespace QuantLib {
//! Exponential-splines fitting method
/*! Fits a discount function to the exponential form
\f[
d(t) = \sum_{i=1}^9 c_i e^{-\kappa_i t}
\f]
where the constants \f$ c_i \f$ and \f$ \kappa \f$ are to be
determined. See:Li, B., E. DeWetering, G. Lucas, R. Brenner
and A. Shapiro (2001): "Merrill Lynch Exponential Spline
Model." Merrill Lynch Working Paper
\f$ \kappa \f$ can be passed a fixed value, in which case it
is excluded from optimization.
\warning convergence may be slow
*/
class ExponentialSplinesFitting
: public FittedBondDiscountCurve::FittingMethod {
public:
ExponentialSplinesFitting(bool constrainAtZero = true,
const Array& weights = Array(),
const ext::shared_ptr<OptimizationMethod>& optimizationMethod = {},
const Array& l2 = Array(),
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Size numCoeffs = 9,
Real fixedKappa = Null<Real>(),
Constraint constraint = NoConstraint());
ExponentialSplinesFitting(bool constrainAtZero,
const Array& weights,
const Array& l2,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Size numCoeffs = 9,
Real fixedKappa = Null<Real>(),
Constraint constraint = NoConstraint());
ExponentialSplinesFitting(bool constrainAtZero,
Size numCoeffs,
Real fixedKappa,
const Array& weights = Array(),
Constraint constraint = NoConstraint());
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
private:
Natural numCoeffs_;
Real fixedKappa_;
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
};
//! Nelson-Siegel fitting method
/*! Fits a discount function to the form
\f$ d(t) = e^{-r t}, \f$ where the zero rate \f$r\f$ is defined as
\f[
r \equiv c_0 + (c_1 + c_2) \left( \frac{1 - e^{-\kappa t}}{\kappa t} \right) -
c_2 e^{ - \kappa t}.
\f]
See: Nelson, C. and A. Siegel (1985): "Parsimonious modeling of yield
curves for US Treasury bills." NBER Working Paper Series, no 1594.
*/
class NelsonSiegelFitting
: public FittedBondDiscountCurve::FittingMethod {
public:
NelsonSiegelFitting(const Array& weights = Array(),
const ext::shared_ptr<OptimizationMethod>& optimizationMethod = {},
const Array& l2 = Array(),
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
NelsonSiegelFitting(const Array& weights,
const Array& l2,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
private:
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
};
//! Svensson Fitting method
/*! Fits a discount function to the form
\f$ d(t) = e^{-r t}, \f$ where the zero rate \f$r\f$ is defined as
\f[
r \equiv c_0 + (c_1 + c_2) \left( \frac {1 - e^{-\kappa t}}{\kappa t} \right)
- c_2 e^{ - \kappa t}
+ c_3 \left( \frac{1 - e^{-\kappa_1 t}}{\kappa_1 t} -e^{-\kappa_1 t} \right).
\f]
See: Svensson, L. (1994). Estimating and interpreting forward
interest rates: Sweden 1992-4.
Discussion paper, Centre for Economic Policy Research(1051).
*/
class SvenssonFitting
: public FittedBondDiscountCurve::FittingMethod {
public:
SvenssonFitting(const Array& weights = Array(),
const ext::shared_ptr<OptimizationMethod>& optimizationMethod = {},
const Array& l2 = Array(),
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
SvenssonFitting(const Array& weights,
const Array& l2,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
private:
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
};
//! CubicSpline B-splines fitting method
/*! Fits a discount function to a set of cubic B-splines
\f$ N_{i,3}(t) \f$, i.e.,
\f[
d(t) = \sum_{i=0}^{n} c_i \times N_{i,3}(t)
\f]
See: McCulloch, J. 1971, "Measuring the Term Structure of
Interest Rates." Journal of Business, 44: 19-31
McCulloch, J. 1975, "The tax adjusted yield curve."
Journal of Finance, XXX811-30
\warning "The results are extremely sensitive to the number
and location of the knot points, and there is no
optimal way of selecting them." James, J. and
N. Webber, "Interest Rate Modelling" John Wiley,
2000, pp. 440.
*/
class CubicBSplinesFitting
: public FittedBondDiscountCurve::FittingMethod {
public:
CubicBSplinesFitting(const std::vector<Time>& knotVector,
bool constrainAtZero = true,
const Array& weights = Array(),
const ext::shared_ptr<OptimizationMethod>& optimizationMethod = {},
const Array& l2 = Array(),
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
CubicBSplinesFitting(const std::vector<Time>& knotVector,
bool constrainAtZero,
const Array& weights,
const Array& l2,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
//! cubic B-spline basis functions
Real basisFunction(Integer i, Time t) const;
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
private:
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
BSpline splines_;
Size size_;
//! N_th basis function coefficient to solve for when d(0)=1
Natural N_;
};
//! Simple polynomial fitting method
/*! Fits a discount function to the simple polynomial form:
\f[
d(t) = \sum_{i=0}^{degree} c_i t^{i}
\f]
where the constants \f$ c_i \f$ are to be determined.
This is a simple/crude, but fast and robust, means of fitting
a yield curve.
*/
class SimplePolynomialFitting
: public FittedBondDiscountCurve::FittingMethod {
public:
SimplePolynomialFitting(Natural degree,
bool constrainAtZero = true,
const Array& weights = Array(),
const ext::shared_ptr<OptimizationMethod>& optimizationMethod = {},
const Array& l2 = Array(),
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
SimplePolynomialFitting(Natural degree,
bool constrainAtZero,
const Array& weights,
const Array& l2,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL,
Constraint constraint = NoConstraint());
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
private:
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
Size size_;
};
//! Spread fitting method helper
/*! Fits a spread curve on top of a discount function according
to the given parametric method
*/
class SpreadFittingMethod
: public FittedBondDiscountCurve::FittingMethod {
public:
SpreadFittingMethod(const ext::shared_ptr<FittingMethod>& method,
Handle<YieldTermStructure> discountCurve,
Real minCutoffTime = 0.0,
Real maxCutoffTime = QL_MAX_REAL);
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override;
protected:
void init() override;
private:
Size size() const override;
DiscountFactor discountFunction(const Array& x, Time t) const override;
// underlying parametric method
ext::shared_ptr<FittingMethod> method_;
// adjustment in case underlying discount curve has different reference date
DiscountFactor rebase_;
// discount curve from on top of which the spread will be calculated
Handle<YieldTermStructure> discountingCurve_;
};
}
#endif
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