In this question, do not make any assumptions on the price process of the underlying. (a)...

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In this question, do not make any assumptions on the price process of the underlying. (a) [15 marks] Let C(K) be the price of a European call option with strike price K. Consider strike prices K1, K2 (with K < K2) and Kx defined by K = \K + (1 )K2, where 0 < < 1. Show that C(Kx) XC (K) + (1 A)C(K2), i.e. the call price is convex in the strike price. (b) [10 marks] Using the result in part (a), establish the analogous result for European puts. In this question, do not make any assumptions on the price process of the underlying. (a) [15 marks] Let C(K) be the price of a European call option with strike price K. Consider strike prices K1, K2 (with K < K2) and Kx defined by K = \K + (1 )K2, where 0 < < 1. Show that C(Kx) XC (K) + (1 A)C(K2), i.e. the call price is convex in the strike price. (b) [10 marks] Using the result in part (a), establish the analogous result for European puts.