# Forward contract on a given financial product $P$

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!