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 . When you set up the position at
𝑡
, do you receive a cash inflow or a cash outflow?

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 . When you set up the position at 
𝑡
, do you receive a cash inflow or a cash outflow?

BlackTom AI · Accepted Answer

We need to assess the cash flow at time t when constructing the position described.
Option 1: 'A cash inflow' — Start by recalling how option premia behave with strike level. For European puts on the same underlying and same maturity, higher strike puts have higher intrinsic and time value (all else equal) than lower strike puts, so P(K2) > P(K1) when K2 > K1.
Since you are long a put with strike K1 and short a put with strike K2, the cash you receive upfront is the premium from selling the higher-strike put minus the premium you pay for buying the lower-strike put. That is, cash flow = P(K2) − P(K1).
Because P(K2) > P(K1), this net amount is positive, implying an inflow at initiation.

Option 2: 'A cash outflow' — This would require P(K1) > P(K2) or a scenario where you pay more than you receive upfront. Given the monotonicity of put prices with strike, the opposite holds, so this option is inconsistent with standard put pricing.

Option 3: 'There is not enough information to answer this question' — In typical arbitrage-free pricing, with the same underlying and expiry, the relation P(K2) > P(K1) holds for a higher strike put. Therefore, there is enough information to conclude the sign of the cash flow, making this option incorrect.

To summarize the intuition behind the pricing: higher strike puts are more valuable because they have a greater range of underlying prices at which they will be in the money at expiration and thus contribute more time value. When you buy the lower-strike put and sell the higher-strike put, you are effectively collecting the premium spread between the two options, which is positive under normal conditions. This leads to a net cash inflow at the setup time rather than a net outflow.

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 . When you set up the position at 𝑡 , do you receive a cash inflow or a cash outflow?单项选择题

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