Forward Contract Payoff Uses the Fixed Delivery Price

Summary

This short exchange clarifies the payoff notation for a forward contract on a zero-coupon bond. Although the forward price quoted before delivery can vary over time as market conditions and remaining time change, the delivery price agreed when the contract is initiated is fixed. At delivery, the long position’s payoff is the bond’s market price minus that fixed delivery price; the short position has the opposite payoff.

The answer gives the essential distinction between a forward price observed at an earlier time and the contract’s locked-in delivery price. It does not derive how the forward price evolves before delivery or discuss discounting, financing, or bond-market conventions. The takeaway is limited to interpreting the maturity payoff and choosing notation for the agreed price.

Key ideas

• The delivery price agreed at trade inception is fixed for the life of the forward.
• At delivery, a long forward on the bond receives its market value less the fixed delivery price.
• The short position’s payoff is the negative of the long position’s payoff.
• The exchange does not explain how the forward price changes before delivery.

Tags

# Payoff of Forward Contract


# 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:

- 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 $\pi(t)$?

## Answer by user18399 (score 1)

https://quant.stackexchange.com/a/49861

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

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.