= 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 payoffs
$$
\boxed{C_T=(S_T-K)^+,\qquad P_T=(K-S_T)^+.}
$$
The 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 $\boxed{F_T^{\rm long}=S_T-K}$ and a short forward has $\boxed{F_T^{\rm short}=K-S_T}$. 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 \b[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.
\Image[/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-expiry-payoffs.png]
{title=Original European call and put payoffs compared with long and short forward-contract payoffs}
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