If an interest rate model with the following $P$-dynamics for the short rate.
$$dr(t)=\mu(t,r(t))dt+\sigma(t,r(t))d\bar{W}(t)$$
Now consider a $T$-claim of the form $\chi = \Phi(r(T))$ with corresponding price process $Π(t)$.
Can anyone help me to find stochastic differential of $Π(t)$ ?
and show that the normalized price process
$$Z(t)=\frac{\Pi(t)}{B(t)}$$
is a $Q$-martingale.?
I appreciate any help.
Thanks.