Likelihood ratio and pathwise sensitivity method for coupled SDEs

I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\ \end{align*} where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data are $S_0$ and $V_0$ , $a(\cdot)$ and $b(\cdot)$ are sufficiently well-behaved, and I use an Euler-Maruyama discretisation with $N$ timesteps. How exactly should one calculate the derivative of a payoff function $\mathbb{E}f(S)$ with respect to $S_0$ in this case? In particular, I am confused as to h