Question

There are two call options for the same underlying asset and same maturity. One call option C1 has exercise price of $120 and the other call option C2 has exercise price of $150. Also, one call sells for $8 and the other sells for $10. Select the prices of C1 and C2 from the given two values. Explain the reason/s for your price selection reflecting on the payoff and profit diagrams of the call options.

Answer 1

C1 with exercise price of 120 should sell for 10 & C2 with exercise price of 150 should sell for 8.

Explanation

Call option with a higher strike price has lower probability of landing in the money and therefore it commands lower premium

Let us consider the following stock price on expiry and analyse the payoff and profit from both the call options

Stock Price	Payoff Call C1	Premium Paid	Profit Call C1	Payoff Call C2	Premium paid	Profit Call C2
100	0	10	-10	0	8	-8
110	0	10	-10	0	8	-8
120	0	10	-10	0	8	-8
130	10	10	0	0	8	-8
140	20	10	10	0	8	-8
150	30	10	20	0	8	-8
160	40	10	30	10	8	2
170	50	10	40	20	8	12
180	60	10	50	30	8	22
190	70	10	60	40	8	32
200	80	10	70	50	8	42

Payoff and profit diagram

It is clear form the above graph, C1 starts giving positive payoff as soon as stock price is above 120 (shown in red), C2 starts giving payoff when the stock price is above 150. Therefore C1 should command a higher premium to C2

Hence price of C1 call option is 10 and price of C2 call option is 8