Consider a put option and a call option written on the same stock and with the same strike price. Which of the following is true?

Question

BlackTom AI · Accepted Answer

A call option is in the money when the stock price S is greater than the strike K (S > K), because the call payoff is max(S − K, 0). A put option is in the money when S < K, because the put payoff is max(K − S, 0). At-the-money means S = K; strictly in-the-money or strictly out-of-the-money require strict inequalities. 1) Relevant concepts - Call payoff = max(S − K, 0). Call is: in-the-money if S > K, at-the-money if S = K, out-of-the-money if S < K. - Put payoff = max(K − S, 0). Put is: in-the-money if S < K, at-the-money if S = K, out-of-the-money if S > K. 2) Step-by-step reasoning with inequalities - For both options to be strictly in the money you would need S > K (call in-the-money) and S < K (put in-the-money) simultaneously. That implies S > K and S < K at once, which is impossible. - For both to be strictly out of the money you would need S < K (call out-of-the-money) and S > K (put out-of-the-money) simultaneously. That also is impossible. - For one option to be strictly in the money in all cases would require either S > K or S < K always; but if S = K neither option is strictly in-the-money, so “one must be strictly in the money” is false. - If S = K, then call and put are both at-the-money simultaneously. This is a consistent, attainable case. 3) Intermediate “calculations” (inequalities shown) - Call ITM: S − K > 0 → S > K. Put ITM: K − S > 0 → S < K. - Both ITM: require S > K and S < K → contradiction. - Both ATM: S = K → both have zero intrinsic value and are at-the-money. 4) Why the correct answer is correct When the stock price equals the strike (S = K) both options satisfy the at-the-money condition simultaneously. This is a possible and common scenario. 5) Why other choices are incorrect - “Both strictly in the money”: impossible because it requires S > K and S < K together. - “Both strictly out of the money”: impossible for the same reason (contradictory inequalities). - “One of the options must be strictly in the money”: false because at S = K neither is strictly in the money. Conclusion: It is possible for both options to be at the money (when S = K). This matches the provided correct answer.

Consider a put option and a call option written on the same stock and with the same strike price. Which of the following is true?单项选择题

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