Single-factor Hull-White (extended Vasicek) model class. More...

#include <hullwhite.hpp>

Inheritance diagram for HullWhite:

Collaboration diagram for HullWhite:

Classes
class	Dynamics
	Short-rate dynamics in the Hull-White model. More...

class	FittingParameter
	Analytical term-structure fitting parameter \( \varphi(t) \). More...

Public Member Functions
	HullWhite (const Handle< YieldTermStructure > &termStructure, Real a=0.1, Real sigma=0.01)

ext::shared_ptr< Lattice >	tree (const TimeGrid &grid) const override
	Return by default a trinomial recombining tree. More...

ext::shared_ptr< ShortRateDynamics >	dynamics () const override
	returns the short-rate dynamics More...

Real	discountBondOption (Option::Type type, Real strike, Time maturity, Time bondMaturity) const override

Real	discountBondOption (Option::Type type, Real strike, Time maturity, Time bondStart, Time bondMaturity) const override

Public Member Functions inherited from Vasicek
	Vasicek (Rate r0=0.05, Real a=0.1, Real b=0.05, Real sigma=0.01, Real lambda=0.0)

Real	discountBondOption (Option::Type type, Real strike, Time maturity, Time bondMaturity) const override

ext::shared_ptr< ShortRateDynamics >	dynamics () const override
	returns the short-rate dynamics More...

Real	a () const

Real	b () const

Real	lambda () const

Real	sigma () const

Real	r0 () const

Public Member Functions inherited from OneFactorAffineModel
	OneFactorAffineModel (Size nArguments)

Real	discountBond (Time now, Time maturity, Array factors) const override

Real	discountBond (Time now, Time maturity, Rate rate) const

DiscountFactor	discount (Time t) const override
	Implied discount curve. More...

Public Member Functions inherited from OneFactorModel
	OneFactorModel (Size nArguments)

	~OneFactorModel () override=default

virtual ext::shared_ptr< ShortRateDynamics >	dynamics () const =0
	returns the short-rate dynamics More...

ext::shared_ptr< Lattice >	tree (const TimeGrid &grid) const override
	Return by default a trinomial recombining tree. More...

Public Member Functions inherited from ShortRateModel
	ShortRateModel (Size nArguments)

virtual ext::shared_ptr< Lattice >	tree (const TimeGrid &) const =0

Public Member Functions inherited from CalibratedModel
	CalibratedModel (Size nArguments)

void	update () override

virtual void	calibrate (const std::vector< ext::shared_ptr< CalibrationHelper > > &, OptimizationMethod &method, const EndCriteria &endCriteria, const Constraint &constraint=Constraint(), const std::vector< Real > &weights=std::vector< Real >(), const std::vector< bool > &fixParameters=std::vector< bool >())
	Calibrate to a set of market instruments (usually caps/swaptions) More...

Real	value (const Array &params, const std::vector< ext::shared_ptr< CalibrationHelper > > &)

const ext::shared_ptr< Constraint > &	constraint () const

EndCriteria::Type	endCriteria () const
	Returns end criteria result. More...

const Array &	problemValues () const
	Returns the problem values. More...

Array	params () const
	Returns array of arguments on which calibration is done. More...

virtual void	setParams (const Array &params)

Integer	functionEvaluation () const

Public Member Functions inherited from Observer
	Observer ()=default

	Observer (const Observer &)

Observer &	operator= (const Observer &)

virtual	~Observer ()

std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)

void	registerWithObservables (const ext::shared_ptr< Observer > &)

Size	unregisterWith (const ext::shared_ptr< Observable > &)

void	unregisterWithAll ()

virtual void	update ()=0

virtual void	deepUpdate ()

Public Member Functions inherited from Observable
	Observable ()

	Observable (const Observable &)

Observable &	operator= (const Observable &)

	Observable (Observable &&)=delete

Observable &	operator= (Observable &&)=delete

virtual	~Observable ()=default

void	notifyObservers ()

virtual DiscountFactor	discount (Time t) const =0
	Implied discount curve. More...

virtual Real	discountBond (Time now, Time maturity, Array factors) const =0

virtual Real	discountBondOption (Option::Type type, Real strike, Time maturity, Time bondMaturity) const =0

virtual Real	discountBondOption (Option::Type type, Real strike, Time maturity, Time bondStart, Time bondMaturity) const

Public Member Functions inherited from TermStructureConsistentModel
	TermStructureConsistentModel (Handle< YieldTermStructure > termStructure)

const Handle< YieldTermStructure > &	termStructure () const

Static Public Member Functions
static Rate	convexityBias (Real futurePrice, Time t, Time T, Real sigma, Real a)

static std::vector< bool >	FixedReversion ()

Protected Member Functions
void	generateArguments () override

Real	A (Time t, Time T) const override

Protected Member Functions inherited from Vasicek
Real	A (Time t, Time T) const override

Real	B (Time t, Time T) const override

virtual Real	A (Time t, Time T) const =0

virtual Real	B (Time t, Time T) const =0

virtual void	generateArguments ()

Private Attributes
Parameter	phi_

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator

Protected Attributes inherited from Vasicek
Real	r0_

Parameter &	a_

Parameter &	b_

Parameter &	sigma_

Parameter &	lambda_

Protected Attributes inherited from CalibratedModel
std::vector< Parameter >	arguments_

ext::shared_ptr< Constraint >	constraint_

EndCriteria::Type	shortRateEndCriteria_ = EndCriteria::None

Array	problemValues_

Integer	functionEvaluation_

Detailed Description

Single-factor Hull-White (extended Vasicek) model class.

This class implements the standard single-factor Hull-White model defined by

\[ dr_t = (\theta(t) - \alpha r_t)dt + \sigma dW_t \]

where \( \alpha \) and \( \sigma \) are constants.

Tests:: calibration results are tested against cached values

Bug:: When the term structure is relinked, the r0 parameter of the underlying Vasicek model is not updated.

Definition at line 49 of file hullwhite.hpp.

Constructor & Destructor Documentation

◆ HullWhite()

HullWhite	(	const Handle< YieldTermStructure > &	termStructure,
		Real	a = `0.1`,
		Real	sigma = `0.01`
	)

Definition at line 31 of file hullwhite.cpp.

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Member Function Documentation

◆ tree()

ext::shared_ptr< Lattice > tree ( const TimeGrid & grid ) const

overridevirtual

Return by default a trinomial recombining tree.

Reimplemented from OneFactorModel.

Definition at line 43 of file hullwhite.cpp.

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◆ dynamics()

ext::shared_ptr< OneFactorModel::ShortRateDynamics > dynamics ( ) const

overridevirtual

returns the short-rate dynamics

Implements OneFactorModel.

Definition at line 163 of file hullwhite.hpp.

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◆ discountBondOption() [1/2]

Real discountBondOption	(	Option::Type	type,
		Real	strike,
		Time	maturity,
		Time	bondMaturity
	)		const

overridevirtual

Implements AffineModel.

Definition at line 89 of file hullwhite.cpp.

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◆ discountBondOption() [2/2]

Real discountBondOption	(	Option::Type	type,
		Real	strike,
		Time	maturity,
		Time	bondStart,
		Time	bondMaturity
	)		const

overridevirtual

Reimplemented from AffineModel.

Definition at line 107 of file hullwhite.cpp.

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◆ convexityBias()

Rate convexityBias	(	Real	futurePrice,
		Time	t,
		Time	T,
		Real	sigma,
		Real	a
	)

static

Futures convexity bias (i.e., the difference between futures implied rate and forward rate) calculated as in G. Kirikos, D. Novak, "Convexity Conundrums", Risk Magazine, March 1997.

Note: t and T should be expressed in yearfraction using deposit day counter, F_quoted is futures' market price.

Definition at line 133 of file hullwhite.cpp.

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◆ FixedReversion()

static std::vector< bool > FixedReversion ( )

static

Definition at line 83 of file hullwhite.hpp.

◆ generateArguments()

void generateArguments ( )

overrideprotectedvirtual

Reimplemented from CalibratedModel.

Definition at line 85 of file hullwhite.cpp.

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◆ A()

Real A	(	Time	t,
		Time	T
	)		const

overrideprotectedvirtual

Implements OneFactorAffineModel.

Definition at line 75 of file hullwhite.cpp.

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Member Data Documentation

◆ phi_

Parameter phi_

private

Definition at line 98 of file hullwhite.hpp.

Classes

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HullWhite()

Member Function Documentation

◆ tree()

◆ dynamics()

◆ discountBondOption() [1/2]

◆ discountBondOption() [2/2]

◆ convexityBias()

◆ FixedReversion()

◆ generateArguments()

◆ A()

Member Data Documentation

◆ phi_