You could answer this question using your intuition for option pricing. You are comparing the value of options which only differ in terms of their strike price (all other key inputs are identical). Which of the following is true?

Question

BlackTom AI · Accepted Answer

A call’s payoff max(S − K, 0) decreases as K increases, while a put’s payoff max(K − S, 0) increases as K increases.

Relevant concepts:
- Call option: right to buy at strike K; payoff at expiry = max(S − K, 0).
- Put option: right to sell at strike K; payoff at expiry = max(K − S, 0).
- If all other inputs (S, volatility, time to expiry, interest rates) are identical, option prices preserve the monotonicity of payoffs.

Step-by-step reasoning:
1. Let K1 < K2 be two strikes. For any terminal stock price S:
   - Call payoffs: max(S − K1, 0) ≥ max(S − K2, 0) because subtracting a larger K2 can only reduce S − K and hence cannot increase the payoff. Thus the call with lower strike (K1) always has payoff at least as large as the call with higher strike (K2).
   - Put payoffs: max(K1 − S, 0) ≤ max(K2 − S, 0) because a larger strike K2 increases K − S, so the put with higher strike (K2) has payoff at least as large.
2. Since option prices are expected discounted values of payoffs under the risk-neutral measure (and both options share identical other parameters), the inequalities for payoffs translate directly to prices:
   - Call price C(K1) ≥ C(K2) → call price decreases as strike increases.
   - Put price P(K1) ≤ P(K2) → put price increases as strike increases.

Optional algebraic support: Put-call parity C(K) − P(K) = S − Ke^{−rT}. Differentiating with respect to K gives C'(K) − P'(K) = −e^{−rT} < 0, consistent with C'(K) ≤ 0 and P'(K) ≥ 0.

Why the other options are wrong:
- “Higher strike lower value for both” is wrong because puts become more valuable with higher K.
- “Higher strike higher value for both” is wrong because calls become less valuable with higher K.
- “Calls with higher strike more valuable, puts less valuable” is the reverse of the true monotonicities.

Conclusion: Calls with higher strike are less valuable, while puts with higher strikes are more valuable — which matches the provided correct answer.

You could answer this question using your intuition for option pricing. You are comparing the value of options which only differ in terms of their strike price (all other key inputs are identical). Which of the following is true?单项选择题

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