quantlib.models.shortrate.onefactormodels.hullwhite.HullWhite

class HullWhite(YieldTermStructure term_structure=YieldTermStructure(), Real a=0, Real sigma=0)

Bases: Vasicek

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

The standard single-factor Hull-White model is defined by

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

where \alpha and \sigma are constants.

Warning

When the term structure is relinked the r_0 parameter of the underlying Vasicek model is not updated:

__init__(*args, **kwargs)

Methods

__init__(*args, **kwargs)

calibrate(self, list helpers, ...)

convexity_bias(Real future_price, Time t, ...)

Futures convexity bias

discount_bound(self, Time now, ...)

params(self)

set_params(self, Array params)

Attributes

Lambda

a

b

dynamics

r0

sigma

calibrate(self, list helpers, OptimizationMethod method, EndCriteria end_criteria, Constraint constraint=Constraint(), vector[Real] weights=[], vector[bool] fix_parameters=[])
static convexity_bias(Real future_price, Time t, Time T, Real sigma, Real a)

Futures convexity bias

i.e., the difference between futures implied rate and forward rate calculated as in [1].

Parameters:

  • t (float) – maturity date of the futures contract

  • T (float) – maturity of the underlying Libor deposit

  • sigma (float) – annual volatility of the short rate

  • a – mean-reversion parameter

Notes

t and T should be expressed in yearfraction using deposit day counter, future_price is futures’ market price.