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
$$
dy_t=\left[
(\frac{k\theta }{2}+\frac{\sigma ^2}{8})\frac{1}{y_t}-
\frac{k}{2}y_t \right] d_t+ \frac{\sigma }{2}dW_{t}
$$.
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 $$ dy_t=\left[ (\frac{k\theta }{2}+\frac{\sigma ^2}{8})\frac{1}{y_t}- \frac{k}{2}y_t \right] d_t+ \frac{\sigma }{2}dW_{t} $$.