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:

List of all members.

Public Member Functions

 Dynamics (const Parameter &fitting, Real alpha, Real sigma)
Real variable (Time t, Rate r) const
 Compute state variable from short rate.
Real shortRate (Time t, Real x) const
 Compute short rate from 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.