A free/open-source library for quantitative finance
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 (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. | |
 Public Member Functions inherited from OneFactorModel::ShortRateDynamics | |
| ShortRateDynamics (const boost::shared_ptr< StochasticProcess1D > &process) | |
|
const boost::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
![\[ r_t = e^{\varphi(t) + x_t} \]](form_293.png)
where 
is the deterministic time-dependent parameter (which can not be determined analytically) used for term-structure fitting and 
is the state variable following an Ornstein-Uhlenbeck process.