Assume the Black-Scholes framework. For j = 1, 2 and t ≥ 0, let S_j(t) denote the time-t price of Stock j.

(a) Consider a T-year European contingent claim whose payoff is the maximum of the two stocks, max(S₁(T), S₂(T)). Show that the time-0 price of such a claim can be written as

where 

Give the second term of the pricing formula. How does it compare with the first term? 

(b) Repeat part (a) for the T-year European contingent claim whose payoff is the minimum of the two stocks, min(S₁(T), S₂(T)).  

Vmax = FT(S1) N In Fr(S1)/FT(S2)] + (02/2)T) (1), (8 +