Consider two call options written on different stocks. Both call options have a strike price of $15 and expire one year from today. The first option is written on HearFour, Inc., whose current stock price is $16. One year from now, shares of HearFour will either rise to $18 or fall to $14. The second option is written on EsoOne, Inc., whose current stock price is also $16. One year from now shares of EsoOne Inc. will either rise to $22, or fall to $0. The risk-free interest rate is 0 percent. Which call option is worth more?

Question

Quizplus · Accepted Answer

To determine which option is worth more, we must calculate the payoff of each option in both of the possible scenarios. For the first option, if HearFour's stock price rises to $18, the option payoff will be $3 ($18 - $15); if HearFour's stock price falls to $14, the option payoff will be $0 (since the option is out of the money). For the second option, if EsoOne's stock price rises to $22, the option payoff will be $7 ($22 - $15); if EsoOne's stock price falls to $0, the option payoff will be $0 (since the option is worthless). Therefore, the expected payoff for the first option is $1.50 ($3 x 0.5), and the expected payoff for the second option is $3.50 ($7 x 0.5). Thus, the call option on EsoOne is worth more.

Consider Two Call Options Written on Different Stocks