Dynamics of the short-rate under the Cox-Ingersoll-Ross model More...
#include <ql/models/shortrate/onefactormodels/coxingersollross.hpp>
Public Member Functions | |
Dynamics (Real theta, Real k, Real sigma, Real x0) | |
virtual Real | variable (Time, Rate r) const |
Compute state variable from short rate. | |
virtual Real | shortRate (Time, Real y) const |
Compute short rate from state variable. | |
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ShortRateDynamics (const ext::shared_ptr< StochasticProcess1D > &process) | |
const ext::shared_ptr< StochasticProcess1D > & | process () |
Returns the risk-neutral dynamics of the state variable. | |
Dynamics of the short-rate under the Cox-Ingersoll-Ross model
The state variable \( y_t \) will here be the square-root of the short-rate. It satisfies the following stochastic equation
\[ dy_t=\left[ (\frac{k\theta }{2}+\frac{\sigma ^2}{8})\frac{1}{y_t}- \frac{k}{2}y_t \right] d_t+ \frac{\sigma }{2}dW_{t} \]
.