CubicSpline B-splines fitting method. More...

#include <nonlinearfittingmethods.hpp>

Inheritance diagram for CubicBSplinesFitting:

Collaboration diagram for CubicBSplinesFitting:

Public Member Functions
	CubicBSplinesFitting (const std::vector< Time > &knotVector, bool constrainAtZero=true, const Array &weights=Array(), const ext::shared_ptr< OptimizationMethod > &optimizationMethod=ext::shared_ptr< OptimizationMethod >(), const Array &l2=Array(), Real minCutoffTime=0.0, Real maxCutoffTime=QL_MAX_REAL)

	CubicBSplinesFitting (const std::vector< Time > &knotVector, bool constrainAtZero, const Array &weights, const Array &l2, Real minCutoffTime=0.0, Real maxCutoffTime=QL_MAX_REAL)

Real	basisFunction (Integer i, Time t) const
	cubic B-spline basis functions More...

std::unique_ptr< FittedBondDiscountCurve::FittingMethod >	clone () const override
	clone of the current object More...

Public Member Functions inherited from FittedBondDiscountCurve::FittingMethod
virtual	~FittingMethod ()=default

virtual Size	size () const =0
	total number of coefficients to fit/solve for More...

Array	solution () const
	output array of results of optimization problem More...

Integer	numberOfIterations () const
	final number of iterations used in the optimization problem More...

Real	minimumCostValue () const
	final value of cost function after optimization More...

EndCriteria::Type	errorCode () const
	error code of the optimization More...

virtual std::unique_ptr< FittingMethod >	clone () const =0
	clone of the current object More...

bool	constrainAtZero () const
	return whether there is a constraint at zero More...

Array	weights () const
	return weights being used More...

Array	l2 () const
	return l2 penalties being used More...

ext::shared_ptr< OptimizationMethod >	optimizationMethod () const
	return optimization method being used More...

DiscountFactor	discount (const Array &x, Time t) const
	open discountFunction to public More...

Private Member Functions
Size	size () const override
	total number of coefficients to fit/solve for More...

DiscountFactor	discountFunction (const Array &x, Time t) const override
	discount function called by FittedBondDiscountCurve More...

Private Attributes
BSpline	splines_

Size	size_

Natural	N_
	N_th basis function coefficient to solve for when d(0)=1. More...

Additional Inherited Members
Protected Member Functions inherited from FittedBondDiscountCurve::FittingMethod
	FittingMethod (bool constrainAtZero=true, const Array &weights=Array(), ext::shared_ptr< OptimizationMethod > optimizationMethod=ext::shared_ptr< OptimizationMethod >(), Array l2=Array(), Real minCutoffTime=0.0, Real maxCutoffTime=QL_MAX_REAL)
	constructors More...

virtual void	init ()
	rerun every time instruments/referenceDate changes More...

virtual DiscountFactor	discountFunction (const Array &x, Time t) const =0
	discount function called by FittedBondDiscountCurve More...

Protected Attributes inherited from FittedBondDiscountCurve::FittingMethod
bool	constrainAtZero_
	constrains discount function to unity at \( T=0 \), if true More...

FittedBondDiscountCurve *	curve_
	internal reference to the FittedBondDiscountCurve instance More...

Array	solution_
	solution array found from optimization, set in calculate() More...

Array	guessSolution_
	optional guess solution to be passed into constructor. More...

ext::shared_ptr< FittingCost >	costFunction_
	base class sets this cost function used in the optimization routine More...

Detailed Description

CubicSpline B-splines fitting method.

Fits a discount function to a set of cubic B-splines \( N_{i,3}(t) \), i.e.,

\[ d(t) = \sum_{i=0}^{n} c_i * N_{i,3}(t) \]

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.

Examples: FittedBondCurve.cpp.

Definition at line 164 of file nonlinearfittingmethods.hpp.

Constructor & Destructor Documentation

◆ CubicBSplinesFitting() [1/2]

CubicBSplinesFitting	(	const std::vector< Time > &	knotVector,
		bool	constrainAtZero = `true`,
		const Array &	weights = `Array()`,
		const ext::shared_ptr< OptimizationMethod > &	optimizationMethod = `ext::shared_ptr<OptimizationMethod>()`,
		const Array &	l2 = `Array()`,
		Real	minCutoffTime = `0.0`,
		Real	maxCutoffTime = `QL_MAX_REAL`
	)

Definition at line 180 of file nonlinearfittingmethods.cpp.

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◆ CubicBSplinesFitting() [2/2]

CubicBSplinesFitting	(	const std::vector< Time > &	knotVector,
		bool	constrainAtZero,
		const Array &	weights,
		const Array &	l2,
		Real	minCutoffTime = `0.0`,
		Real	maxCutoffTime = `QL_MAX_REAL`
	)