# Question

Suppose that S1 and S2 are correlated, non-dividend-paying assets that follow geometric Brownian motion. Specifically, let S1(0) = S2(0) = $100, r = 0.06, σ1 = 0.35, σ2 = 0.25, ρ = 0.40 and T = 1. Verify that the following two procedures for valuing an outperformance option give a price of approximately $13.464.

a. Use Monte Carlo simulation to simulate both S1(T ) and S2(T ) to value the payoff max(0, S1(T)− S2(T ))

b. Use Monte Carlo simulation to simulate only S1(T )/S2(T ), and value the payoff S2(0) max(0, S1(T )/S2(T ) − 1)

a. Use Monte Carlo simulation to simulate both S1(T ) and S2(T ) to value the payoff max(0, S1(T)− S2(T ))

b. Use Monte Carlo simulation to simulate only S1(T )/S2(T ), and value the payoff S2(0) max(0, S1(T )/S2(T ) − 1)

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