Consider a market with one stock and one bond, with the same assumptions on parameters as in the derivation of the Black-Scholes formula given in class. Consider a contingent claim whose payoff depends on two dates T1 and T2, with T2 > T1 > 0, and two numbers K1 > 0 and K2 > 0. The maturity date is T2. The buyer of this claim can buy 1 share of stock at time T2 at the price K2, but only if the price of the stock was higher than K1 at time T1. If the price of the stock was lower than K1 at time T1, she cannot buy anything. Find a formula for the price of this contingent claim at time t = 0. The formula has to be explicit in the sense that one could feed it into a computer program, just like the Black-Scholes formula. The formula may contain integrals. It is not necessary to simplify the formula.