Which of the following best describes the payoff of a short position in a European put option at expiration?

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BlackTom AI · Accepted Answer

First, let's restate the scenario and the payoff concepts to ensure clarity. A European put option gives the holder the right to sell the stock at the strike price K at expiration. The holder's payoff is max(K − S, 0). A short position in the put means you owe the opposite of the holder's payoff, i.e., the negative of max(K − S, 0), which simplifies to min(0, S − K). Option 1: max(0, strike price − stock price). This is the payoff of the long put (the put option holder), not the short position. It yields a nonnegative value whenever K > S and is zero otherwise. Option 2: min(0, stock price − strike price). This exactly matches the short-put payoff, since when S < K the holder would have positive payoff, but the short position loses that amount; conversely, when S ≥ K, the short position payoff is zero or negative, captured by min(0, S − K). Option 3: max(0, stock price − strike price). This is the payoff formula for a long call option, not a put, and applies when S > K. Option 4: min(0, strike price − stock price). This is a negative version of the holder’s payoff in certain regions and does not represent the standard short put payoff, because it misaligns the sign with respect to S relative to K. In summary, the correct expression for the payoff of a short position in a European put at expiration is min(0, stock price − strike price), because it yields zero when S ≥ K and negative values when S < K, exactly the negative of the put holder’s payoff. The other options correspond to the put holder, a call payoff, or a mis-signed put payoff and thus do not describe the short-put payoff correctly.

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Which of the following best describes the payoff of a short position in a European put option at expiration?

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