Imagine that space Z is exposed to the FX risk (i.e., currency exchange rate risk ), and we aim to provide a hedging solution for that. One choice is to consider a currency-forward contract. I wonder how I can derive the value of the forward contract when the spot domestic and foreign rates are a stochastic process, for example, following a Vasicek model. How should I discount the payoff of the forward contract in order to obtain a fair price? I think the final price should be a function of the forward rate.
If my understanding is correct, for the payoff function, we have something like this. Denote $S_T$ the spot FX rate at time T, K the strike rate at which we exchange the currencies. Then we have that
payoff= $S_T - K$
or I should consider
payoff= $S_T -F(t, T)$
where $F(t, T)$ stands for the forward exchange rate.