# Payoff of Forward Contract

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:

$$\pi=P(T_1,T_2)-F(t,T_1,T_2).$$

My question is:

1. 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?

2. If the answer is yes to #1, then wouldn't it be more appropriate to denote $$\pi$$ in terms of $$\pi(t)$$?

• The forward you will use is the forward price you agreed to on trade date. This will not change in that you agreed to this price on the day you traded. – AlRacoon Nov 21 '19 at 22:31

Delivery price at maturity is a constant, $$K$$. Thus $$\pi = P-K$$ for a long position, and $$\pi = K-P$$ for a short position.