# Extended CIR and discretization

Did someone know how to discretize this process efficiently :

$dX(t) = \kappa [\theta(t)-X(t)]dt + \sigma \sqrt{X(t)}dW(t)$

I am looking for something more sophisticated than the trivial Euler Schema :

$X(t_{k+1}) =X(t_{k}) + \kappa[\theta(t_k)-X(t_{k})]\Delta t + \sigma \sqrt{X(t_{k})}\Delta_k W$

• Changed the typo $\frac{\partial\Sigma(t,X_t)}{\partial t}$ to $\frac{\partial\Sigma(t,X_t)}{\partial X_t}$. Jul 3 '15 at 15:03