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Exercise I.A.4. Prove that the call price Ct(E,T) satisfies 1E2E1C(E2)C(E1)0. (You may assume that r=0.) Prove that, if C is differentiable with respect to E,
Exercise I.A.4. Prove that the call price Ct(E,T) satisfies 1E2E1C(E2)C(E1)0. (You may assume that r=0.) Prove that, if C is differentiable with respect to E, then this is equivalent to 1EC0. Hints: For the first part you may (a) see Exercise I.A.2 and use P-C parity or (b) use the Portfolio Lemma, see Exercise I.A.7. For the second part, let E2=E1+E1 and take the limit E10 to get from (I.A.1) to (I.A.2). To go from (I.A.2) to (I.A.1), use Mean Value Theorem
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