The CIR model for spot rate $r_t$ is:
$$dr_t=(\eta-\gamma r_t)dt+\sqrt{\alpha r_t} dW_t$$
where $\eta, \gamma, \alpha$ are constants.
How to express this SDE in discrete form using Milstein scheme?
The one I derived is:
$$r_{t+1}=r_t+(\eta-\gamma r_t)\delta t+\sqrt{\alpha r_t}\cdot\sqrt{\delta t}\phi +\frac{1}{2}\sqrt{\alpha r_t}\cdot\left(\frac{1}{2}\frac{\alpha}{\alpha r_t}\right)[\delta t(\phi^2-1)]$$
where $\phi$ is normal RV.
Can anyone help me to identify my error? Or is it correct?