Suppose that c1, c2, and c3 are the prices of European call options with strike prices K1, K2, and

K3, respectively, where K3 > K2 > K1 and K3 K2 = K2 K1. All options have the same maturity.

Show that c2 <(c1+c3)/2 must hold for all such combinations of strike prices that satisfy the

above-stated conditions.

(Hint: Consider a portfolio that is long one option with strike price K1, long one option with

strike price K3, and short two options with strike price K2.)