The forward contract initiated at $t$ has payoff $S_T-F_t^T$ and zero value. Pricing under the <T-forward measure> gives
$$
0=B_t^T\mathbb E_{Q^T}[S_T-F_t^T\mid\mathcal F_t].
$$
Because $F_t^T$ is $\mathcal F_t$-measurable and $B_t^T>0$,
$$
F_t^T=\mathbb E_{Q^T}[S_T\mid\mathcal F_t].
$$
The <tower property of conditional expectation> therefore makes $(F_t^T)_{t<T}$ a $Q^T$-martingale.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 211 / 2 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-211/2/b/solution