Question: Let C gap (K 1 , K 2 ) and P gap (K 1 , K 2 ) be the current prices of a T-year

Let C^gap(K₁, K₂) and P^gap(K₁, K₂) be the current prices of a T-year European gap call option and a T-year European gap put option, respectively, both with a strike price of K₁ and a payment trigger of K₂. Prove that

Identify K^∗.

Cgap (K, K) - pgap (K, K) = FT(S) - K*e-T.

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