The Forward Payoff

The Forward Payoff

A long forward payoff is a straight line in the terminal spot price.

highlighted = computed this step

Locked delivery price

A long forward locks in delivery at $105.00 and pays terminal spot minus the forward price at maturity. It has zero cost to enter in this model.

long payoff=ST−F0\text{long payoff}=S_T-F_0

Straight-line payoff

At terminal spot $90.00 the payoff is a loss of $15.00; at $105.00 it is $0.00; at $120.00 it is a gain of $15.00. The line crosses zero at the forward price.

ST−F0∈{−$15.00,$0.00,$15.00}S_T-F_0\in\{-\$15.00,\$0.00,\$15.00\}
Long forward payoffThe synthetic long call and short put line recomputes the forward payoff.Long forward payoffK=$105$80$105$120$-29.00$+0.00$+19.00Underlying price at expiryPayofflong call + short put = forward (S - K)

Put-call parity tie-back

The diagram reuses the payoff primitive from Option Payoffs. A long call and short put at the same strike make the same straight-line payoff by put-call parity.

C−P=S−KC-P=S-K