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I would like to know whether my reasoning is correct or not.

Let $\pi_t$ be the price of a financial product $P$.

The forward associated to a forward contract on $P$ that settles at time $T$ is given by : $$F_{t}=\mathbb{E}^{T}\left(\left.\pi_{T}\right|\mathbb{F}_{t}\right)\\ =\mathbb{E}^{T}\left(\left.\frac{\pi_{T}}{B(T,T)}\right|\mathbb{F}_{t}\right)\\=\frac{\pi_{t}}{B(t,T)}$$

Since $\frac{\pi_{t}}{B(t,T)}$ is a martingal for $0\leq t\leq T$ under the $T$-forward mesure.

If not, under which conditions on $P$ this expression is correct ?

Thanks!

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