A (K1, t1, K2, t2 ) double call option is one that can be exercised either at time t1 with strike price K1 or at time t2 (t2 > t1) with strike price K2.

(a) Argue that you would never exercise at time t1 if K1 > e^-r(t2-t1) K2.

(b) Assume that K1 < e^-r(t2-t1) K2. Argue that there is a value x such that the option should be exercised at time t1 if S(t1) > x and not exercised if S(t1) < x.