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Problem 4. (5 Points) Prove the following statement about American option: The Ameri- can put option price is a convex function of strike price X,

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Problem 4. (5 Points) Prove the following statement about American option: The Ameri- can put option price is a convex function of strike price X, i.e., for any X1, X2 > 0 and any a (0,1], PA(aX1 + (1 - a)X2) 0 and any a (0,1], PA(aX1 + (1 - a)X2)

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