Can someone please explain why when X1

Why is it not just greater than?

Proof: Consider portfolio A, containing two call options with strike X2, and portfolio B, containing one call option with strike X and one call option with strike X3. Assuming the portfolios are held to expiration, Exhibit 5 illustrates the profits. Exhibit 5 Strike Price Relationships for Call Options St SX1 X1 X3 0 A: 2C (X2) 0 B: Co(X1) + Co(X3) 0 (ST-X1) 2(Sr - X2) (ST-X1) 2(ST - X2) (ST-X1) +(ST - X3) VA(T) VA(O). Hence C + C3 > 2C2, from which the result follows. If C2> C + C3)/2, then an investor would sell portfolio A and buy portfolio B. The initial amount of money received would be 2C2-C - Cz. If held to expiration, additional arbitrage profits might become available. If, however, the X, options were exercised prior to expiration, when the stock was at S*, the amount owed could be obtained by exercising both the X1, and X3 calls. Hence, regardless of what price occurs in the future, riskless arbitrage strategies become available unless the middle strike call is valued less than the average of its neighboring strikes. A similar result holds for put options