Question

(a) Consider three European put options which have identical maturity T and underlying security. The options have strike prices K1, K2 and K3, where K1 < K3 and K2 = (1/2) (K1 + K3). Denote the prices by P(K1), P(K2) and P(K3), respectively. Show that P(K2) ≤ 1/2 (P(K1) + P(K3)). Hint: You can show this by drawing a graph with the cash-flows of the portfolios at maturity.

Hint: You can show this by drawing a graph with the cash-flows of the portfolios at maturity.

Answer 1

Let us take the strike prices as:

• K1 = 100
• K2 = 200
• K3 = 300

These fulfill the condition of K1 < K3 and K2 = (1/2) (K1 + K3).

Following will be the result at the expiry:

The following is its chart:

Hence, it is proved that, P(K2) ≤ 1/2 (P(K1) + P(K3)).