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I assume the forward contract matures at time $S$ and $0 \leq t < S < T.$ Let $F_t(S,T)$ be the price that makes the forward contract be worth zero at time $t$. Then by the risk-neutral valuation formula we obtain $$0= \mathbb E^{\mathbb Q} \left[(B_S(T) - F_t(S,T))e^{-\int_t^S r(u)du} | \mathcal F_t \right].$$ Since $ F_t(S,T))e^{-\int_t^S r(u)du}$ is ...


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