6. (Lecture Note 6) A call option is a convex function of the exercise price; that is, for X3 > X > X, c(S, X,t,T) Ac(S, X,t,T)+(1-2)c(S, X3,t,T) where = (X3-X)/(X3-X). Of three identical call options with exercise prices X3 > X > X, the value of the middle exercise price call option is never greater (i.e., ) than a weighted average of the values of the extreme exercise price call options, where the weights are = (X3-X)/(X3 X) for the first call option and (1 2) = (X X)/(X3 X) for 3 the third call option. Notice that is chosen so that X = 2X + (1 2)X3. Prove that there is a riskless arbitrage opportunity if the inequality in the above relation is violated. 6. (Lecture Note 6) A call option is a convex function of the exercise price; that is, for X3 > X > X, c(S, X,t,T) Ac(S, X,t,T)+(1-2)c(S, X3,t,T) where = (X3-X)/(X3-X). Of three identical call options with exercise prices X3 > X > X, the value of the middle exercise price call option is never greater (i.e., ) than a weighted average of the values of the extreme exercise price call options, where the weights are = (X3-X)/(X3 X) for the first call option and (1 2) = (X X)/(X3 X) for 3 the third call option. Notice that is chosen so that X = 2X + (1 2)X3. Prove that there is a riskless arbitrage opportunity if the inequality in the above relation is violated