Consider the following notation:
$P(T_j,T_2)$ is the price of a zero-coupon bond at $T_j$ with maturity $T_2$.
$F(t,T_h,T_2)$ is the price of a forward contract at time $t$ on the above $T_2$-maturity zero-coupon bond with the forward contract delivery date $T_h$.
The payoff function of this forward contract ON the delivery date $T_1$ is:
My question is:
Does the forward price change with respect to $t$? In other words, if we know the delivery date and the maturity of the underlying, the forward changes as $t$ gets closers to the maturtiy, correct?
If the answer is yes to #1, then wouldn't it be more appropriate to denote $\pi$ in terms of $\pi(t)$?