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)