BlackKarasinski::Dynamics Class Reference

Short-rate dynamics in the Black-Karasinski model. More...

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

Inheritance diagram for BlackKarasinski::Dynamics:

Public Member Functions
	Dynamics (Parameter fitting, Real alpha, Real sigma)
Real	variable (Time t, Rate r) const override
	Compute state variable from short rate.
Real	shortRate (Time t, Real x) const override
	Compute short rate from state variable.
Public Member Functions inherited from OneFactorModel::ShortRateDynamics
	ShortRateDynamics (ext::shared_ptr< StochasticProcess1D > process)
const ext::shared_ptr< StochasticProcess1D > &	process ()
	Returns the risk-neutral dynamics of the state variable.

Detailed Description

Short-rate dynamics in the Black-Karasinski model.

The short-rate is here

\[ r_t = e^{\varphi(t) + x_t} \]

where \( \varphi(t) \) is the deterministic time-dependent parameter (which can not be determined analytically) used for term-structure fitting and \( x_t \) is the state variable following an Ornstein-Uhlenbeck process.

Member Function Documentation

variable()

Real variable ( Time t, Rate r ) const

overridevirtual

Compute state variable from short rate.

Implements OneFactorModel::ShortRateDynamics.

shortRate()

Real shortRate ( Time t, Real variable ) const

overridevirtual

Compute short rate from state variable.

Implements OneFactorModel::ShortRateDynamics.