You long one European put with maturity at T with strike 50. You also long one European put with maturity at T with strike 100. You also short two European puts with strikes 75. STS_T is the price of the underlying asset at maturity. What is the cashflow of your portfolio at time T (not accounting for any costs of purchasing the portfolio) if

a) STS_T=80? [Fill in the blank],

b) STS_T=65? [Fill in the blank],

Please type in a single number as your answer. Use a minus sign to indicate a negative cashflow.

Question

You long one European put with maturity at T with strike 50. You also long one European put with maturity at T with strike 100. You also short two European puts with strikes 75. STS_T is the price of the underlying asset at maturity. What is the cashflow of your portfolio at time T (not accounting for any costs of purchasing the portfolio) if

a) STS_T=80? [Fill in the blank],

b) STS_T=65? [Fill in the blank],

Please type in a single number as your answer. Use a minus sign to indicate a negative cashflow.

BlackTom AI · Accepted Answer

We need to evaluate the payoff of the given option portfolio at two different underlying prices, at maturity T. The portfolio consists of: a long put with strike 50, a long put with strike 100, and a short two puts with strike 75. Each put payoff is max(strike - S_T, 0), and the short puts contribute minus that amount for each contract. We'll sum the payoffs across all components for each scenario.

First scenario: S_T = 80
- The 50-strike put payoff: max(50 - 80, 0) = max(-30, 0) = 0.
- The 100-strike put payoff: max(100 - 80, 0) = max(20, 0) = 20.
- The two 75-strike puts payoff: each is max(75 - 80, 0) = max(-5, 0) = 0, so two of them sum to 0; since these are short puts, their contribution is -0 = 0.
- Total payoff: 0 + 20 + 0 = 20.

Second scenario: S_T = 65
- The 50-strike put payoff: max(50 - 65, 0) = max(-15, 0) = 0.
- The 100-strike put payoff: max(100 - 65, 0) = max(35, 0) = 35.
- The two 75-strike puts payoff: each is max(75 - 65, 0) = max(10, 0) = 10, so two of them sum to 20; since we are short them, their contribution is -20.
- Total payoff: 0 + 35 - 20 = 15.

Thus, the cashflows at time T are 20 when S_T = 80 and 15 when S_T = 65. Note that these results are purely the payoff components of the options (ignoring any initial costs or funding considerations).

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