Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S9 / 1 / 2 / Solution

Let $S_T$ be the terminal asset price and $K$ a common strike or forward delivery price. A long European call and put have expiry payoffsThe call is zero below $K$ and then rises with slope one; the put falls with slope minus one below $K$ and is zero above it. A long forward instead has $\boxed{F_T^{\mathrm{long}}=S_T-K}$ and a short forward has $\boxed{F_T^{\mathrm{short}}=K-S_T}$. Both are straight lines crossing zero at $K$, with negative as well as positive outcomes.

The option's exercise right truncates the unfavourable side, whereas the forward is an obligation. These are payoffs, not total profits: an option premium and its financing cost have not been subtracted. A newly agreed fair forward may have zero initial value while still having a nonzero future delivery price.