Let S = $40, σ = 0.30, r = 0.08, T = 1, and δ = 0. Also let Q = $40, σQ = 0.30, δQ = 0, and ρ = 1. Consider an exchange call with S as the price of the underlying asset and Q as the price of the strike asset.
a. What is the price of an exchange call with S as the underlying asset and Q as the strike price?
b. Now suppose σQ
= 0.40. What is the price of the exchange call?
c. Explain your answers to (a) and (b).