Consider the following model
$$\begin{cases} dS_t=r_tS_tdt+\sigma S_tdW_t, \\ dr_t=adt+\eta dW_t\\ \end{cases} $$ where $W$ is a Brownian motion and $\sigma, a ,b, \eta$ are positive constants.
I have to find a formula of the price of a call option:
$$E \left[ e^{-\int_0^T r_s ds}(S_T-K)^+ \right]. $$
Is it $$BS(S_0,K,-\frac{1}{T}\int_0^T r_s ds,T,\sigma) \quad ?$$
Can I obtain a more explicit formula?
