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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?


marked as duplicate by Quantuple, LocalVolatility, JejeBelfort, Community Dec 19 '17 at 13:51

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