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Consider a family of European call options on a non-dividend-paying stock, each option being identical except for its strike price. The value of the call

Consider a family of European call options on a non-dividend-paying stock, each option being identical except for its strike price. The value of the call with strike price K is denoted by C(K). Prove 1 the following two general relations using arbitrage arguments:

(a). If K2 > K1, then C(K1) C(K2). (Hint: You may argue this by contradiction. Assume that C(K1) < C(K2) and construct an arbitrage portfolio to obtain positive arbitrage profit. Then, that implies the conclusion must be true in an efficient market.)

(b) If K2 > K1, then K2 K1 C(K1) C(K2).

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