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, 1 0 35, 2 0 25, 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 ...

For the first part of the exercise ...

Suppose that S1 and S2 are correlated, non-dividend-paying assets that follow geometric Brownian motion. Specifically, let S1(0)

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 to simulate both S1(T ) and S2(T ) to value the payoff max(0, S1(T)− S2(T ))
b. Use to simulate only S1(T )/S2(T ), and value the payoff S2(0) max(0, S1(T )/S2(T ) − 1) Monte Carlo simulation
Monte Carlo simulation is a technique used to understand the impact of risk and uncertainty in financial, project management, cost, and other forecasting models. A Monte Carlo simulator helps one visualize most or all of the potential outcomes to...