# QuantLib_HullWhite man page

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

## Synopsis

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

Inherits **Vasicek**, and **TermStructureConsistentModel**.

### Classes

classDynamics

Short-rate dynamics in the Hull-White model.

classFittingParameter

Analytical term-structure fitting parameter $ varphi(t) $.

### Public Member Functions

HullWhite(constHandle<YieldTermStructure> &termStructure,Reala=0.1,Realsigma=0.01)

boost::shared_ptr<Lattice>tree(constTimeGrid&grid) const

Return by default a trinomial recombining tree.

boost::shared_ptr<ShortRateDynamics>dynamics() const

returns the short-rate dynamicsReal discountBondOption(Option::Type type,Realstrike,Timematurity,TimebondMaturity) constReal discountBondOption(Option::Type type,Realstrike,Timematurity,TimebondStart,TimebondMaturity) const

### Static Public Member Functions

staticRate convexityBias(RealfuturePrice,Timet,TimeT,Realsigma,Reala)

static std::vector< bool >FixedReversion()

### Protected Member Functions

voidgenerateArguments()Real A(Timet,TimeT) const

### Additional Inherited Members

## Detailed Description

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

This class implements the standard single-factor Hull-White model defined by [ dr_t = ( heta(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.

**Examples:** **BermudanSwaption.cpp**, and **CallableBonds.cpp**.

## Member Function Documentation

### static 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.

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

FixedReversion(3) and HullWhite(3) are aliases of QuantLib_HullWhite(3).