Question at position 4 You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $75. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow) Answer You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $75. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow) [input]简答题
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Question

Question at position 4 You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $75. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow) Answer You sell (short) a European put option with strike $100. On the expiration date the price of the underlying stock is $75. What is your cash flow at expiration? (Please use a minus sign to indicate a negative cash flow) [input]简答题

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BlackTom AI · Accepted Answer

Shorting a put obligates you to buy the underlying at the strike if the option is exercised, so your payoff is the negative of the long put payoff.

1. Relevant knowledge points and concepts
- Long European put payoff at expiration: max(K − S_T, 0), where K is strike and S_T is stock price at expiration.
- Short (sold) put payoff is the opposite sign: −max(K − S_T, 0). European means exercise only at expiration.
- If S_T < K, the put is exercised and has positive intrinsic value K − S_T; if S_T ≥ K, the put expires worthless.

2. Step-by-step reasoning
- Given K = 100 and S_T = 75. Since 75 < 100, the put is in-the-money and will be exercised at expiration.
- Compute the intrinsic value for the long put: K − S_T = 100 − 75.

3. Calculations (all intermediate steps)
- K − S_T = 100 − 75 = 25.
- Long put payoff = max(25, 0) = 25.
- Short put payoff = −(long put payoff) = −25.

4. Why the correct answer is correct
- As the seller of the put, you must pay the holder the intrinsic value when exercised. The holder receives $25; therefore you have a cash outflow of $25 at expiration. That outflow is represented as −25.

5. Why other answers would be incorrect
- +25 would indicate you receive $25, which would be true for a long put holder, not the seller. 0 would be incorrect because the option is in-the-money (S_T < K) so it does not expire worthless. Any other value not equal to −25 contradicts the formula −max(K − S_T, 0).

6. Conclusion
- The cash flow at expiration for the short European put with K = 100 when S_T = 75 is −25, which matches the provided answer: -25.

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