HullWhite Class Reference

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

#include <ql/models/shortrate/onefactormodels/hullwhite.hpp>

Inheritance 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
ext::shared_ptr< ShortRateDynamics >	dynamics () const override
	returns the short-rate dynamics
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
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.
Public Member Functions inherited from OneFactorModel
	OneFactorModel (Size nArguments)
ext::shared_ptr< Lattice >	tree (const TimeGrid &grid) const override
	Return by default a trinomial recombining tree.
Public Member Functions inherited from ShortRateModel
	ShortRateModel (Size nArguments)
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)
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.
const Array &	problemValues () const
	Returns the problem values.
Array	params () const
	Returns array of arguments on which calibration is done.
virtual void	setParams (const Array &params)
Integer	functionEvaluation () const
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const 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	deepUpdate ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()
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

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.

Member Function Documentation

tree()

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

overridevirtual

Implements ShortRateModel.

dynamics()

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

overridevirtual

returns the short-rate dynamics

Implements OneFactorModel.

discountBondOption() [1/2]

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

overridevirtual

Implements AffineModel.

discountBondOption() [2/2]

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

overridevirtual

Reimplemented from AffineModel.

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.

generateArguments()

void generateArguments ( )

overrideprotectedvirtual

Reimplemented from CalibratedModel.

A()

Real A ( Time t, Time T ) const

overrideprotectedvirtual

Implements OneFactorAffineModel.