You buy a European put option with strike
𝐾
1
and short a European put option with strike
𝐾
2

𝐾
1
on the same underlying asset with the same expiration at T. If
𝑆
𝑇

𝐾
2
, do you make an overall profit?

Question

You buy a European put option with strike 
𝐾
1
 and short a European put option with strike 
𝐾
2
>
𝐾
1
 on the same underlying asset with the same expiration at T. If 
𝑆
𝑇
>
𝐾
2
, do you make an overall profit?

BlackTom AI · Accepted Answer

The question describes a position consisting of a long European put with strike K1 and a short European put with strike K2, where K2 > K1, both expiring at T, and asks about profit when ST > K2.
Option 1: 'No, you make a loss' — This would require the combined payoff to be negative. However, when ST > K2 > K1, the long put with strike K1 has payoff max(K1 − ST, 0) = 0, and the short put with strike K2 has payoff −max(K2 − ST, 0) = −0 = 0. The total payoff is 0, not negative, so this option misstates the outcome.
Option 2: 'There is not enough information to answer this question' — Given the explicit condition ST > K2, we can determine the payoff deterministically: both puts expire worthless, yielding zero net payoff. Therefore, there is enough information to answer, and this option is incorrect.
Option 3: 'Yes, you make a profit' — Since both put options expire worthless in this scenario, there is no profit. The long put pays 0 and the short put also pays 0, so the net outcome is not a profit. This option is incorrect as stated.
In this setup, the actual realized payoff is 0 (break-even) when ST > K2, because each put finishes out of the money. The provided options do not include a statement that reflects a zero payoff (break-even) outcome, which is the precise result under ST > K2. Consequently, all listed choices mischaracterize the payoff in this scenario.

You buy a European put option with strike 𝐾 1 and short a European put option with strike 𝐾 2 > 𝐾 1 on the same underlying asset with the same expiration at T. If 𝑆 𝑇 > 𝐾 2 , do you make an overall profit? 单项选择题

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