# 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

class **Dynamics**

Short-rate dynamics in the Hull-White model.

class **FittingParameter**

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

### Public Member Functions

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

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

Return by default a trinomial recombining tree.

boost::shared_ptr< **ShortRateDynamics** > **dynamics** () const

returns the short-rate dynamics **Real discountBondOption** (Option::Type type, **Real** strike, **Time** maturity, **Time** bondMaturity) const**Real discountBondOption** (Option::Type type, **Real** strike, **Time** maturity, **Time** bondStart, **Time** bondMaturity) 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** ()**Real A** (**Time** t, **Time** T) 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).