Option Payoff Diagrams

An option is a contract that gives its holder the right - but never the obligation - to buy or sell an asset at a fixed price, the strike $K$, on or before an expiry date. A call is the right to buy; a put is the right to sell. Because the holder walks away whenever exercising would lose money, an option can never be worth less than zero at expiry.

Let $S$ be the underlying price at expiry. A call is exercised only when $S > K$ (buy cheap at $K$, sell at $S$), so it pays $\max(S-K,0)$. A put is exercised only when $S < K$ (sell high at $K$), so it pays $\max(K-S,0)$. Plotted against $S$, each is a flat line that suddenly bends - the hockey stick.

The holder paid a premium for the option up front. Profit is the payoff minus that premium, which simply slides the whole hockey stick down by the premium. The price at which profit crosses zero is the breakeven: for a long call it is $K + \text{premium}$; for a long put it is $K - \text{premium}$.