QuantLib: BlackKarasinski::Dynamics Class Reference

A free/open-source library for quantitative finance Reference manual - version 1.12

Public Member Functions | List of all members
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:
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## 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

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

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.