Exercise 2.8 Suppose that two stocks satisfy the Black-Scholes model with parameters 1 = 0.04, 2 =

Exercise 2.8 Suppose that two stocks satisfy the Black-Scholes model with parameters

μ1 = 0.04, μ2 = 0.09, σ1 = 0.25, σ2 = 0.35, and R12 = 0.25. We want to price an exchange option whose payoff at maturity is max(3S1 − 2S2, 0).

(a) Why would an investor be interested by this derivative?

(b) Write the expressions for σ, D1, D2 and C(t, s1, s2).

(c) Today, S1 = $43 and S2 = $65. Compute the value of the exchange option if it expires in 6 months. Assume that the risk-free rate is 2%.

(d) Compute the (bivariate) delta of the option.

(d) What is the impact of a change in the risk-free interest rate for this option, from a hedging point of view?