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Payoff at expiry for the sale of a put option formula

Description of the Payoff at expiry for the sale of a put option formula

Formula for calculating the payoff of a short position in a put option.

Formula

\[ R_{sp}= P - min \left( \left( S_{T}-K \right),0 \right) \ \]

Symbols

\(K\ \)       
Option strike price
\(P\ \)       
Value of the option premium
\(S_{T}\ \)       
Price of the underlying at expiry date T of the option

The maximum gain for the sale of a put option is the amount of the option premium. The maximum loss is the difference between the option premium and the strike ST.