# Option Pricing Proof:C2 is <= 0.5(C1+C3)

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Suppose that c1, c2 and c3 are the prices of European call options with strike prices X1, X2 and X3, respectively, where X3>X2>X1 and X3-X2=X2-X1. All options have the same maturity.

Show that C2 is less than or equal to 0.5(C1+C3)

(Hint: Consider a portfolio that is long one option with strike price X1, long one option with strike price X3, and short two options with strike price X2).

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##### Solution Summary

Solution provides proof for C2 is <= 0.5(C1+C3) given that C1, C2 and C3 are the prices of European call options with strike prices X1, X2 and X3, respectively, where X3>X2>X1 and X3-X2=X2-X1 and all options have the same maturity.

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