Exercise 14.17 Consider a European call option with strike price K and maturity T. From (14.47), the option premium is given by

Note: It is known that the distribution function F(S, x) is non-increasing in S for all x > 0 if the stock price process is a diffusion. Hence, c′(K) is nonincreasing in S, so that the delta cS is non-increasing in the strike K in the case of diffusion. See Kijima (2002) for details.

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c(K) = v(0, T)EQ [{S(T) K}+] Let F(S,x) = QT {S(T) x|S(0) = S}. Show that c(K)= v(0,T){1 F(S, K)}. -