Lesson 5 of 7 · 12 min

Put payoffs and the four option positions

A put pays off when the price falls below the exercise price; because a price cannot drop below zero, every put position has a limited best and worst case, unlike a short call.

In short

A put buyer exercises only if $S_T < X$ . Payoff: $p_T = \max(0, X - S_T)$ .
Long put profit: $\max(0, X - S_T) - p_0$ . Breakeven $X - p_0$ . Max loss $p_0$ ; max gain $X - p_0$ , reached if the price falls to zero.
Short put profit: $-\max(0, X - S_T) + p_0$ . Max gain $p_0$ ; max loss $X - p_0$ .
A put buyer earns a positive profit only if $S_T < X - p_0$ , not merely if $S_T < X$ .
Of the four basic positions, only the short call has an unlimited loss.

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