You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $80. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow)

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BlackTom AI · Accepted Answer

We need to evaluate the terminal cash flow for a short European put option.
- A put option gives the holder the right to sell the stock at the strike price K. The intrinsic value at expiration is max(K − S, 0).
- For a long put, the payoff is max(K − S, 0). For a short put, the payoff (cash flow to the writer) is the negative of that amount: −max(K − S, 0).

Given K = 100 and S = 80 at expiration:
- K − S = 100 − 80 = 20, which is positive, so max(K − S, 0) = 20.
- Therefore, the cash flow for the writer of the short put is −20.

If you consider the broader picture, the writer would have previously collected a premium at initiation, which is not part of the expiration payoff calculation, so this analysis focuses solely on the expiration cash flow due to the option position itself.

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You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $80. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow)

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