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. In one year, 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 call option is worth more, we need to calculate the payoffs of each option at expiration and discount them back to the present using the risk-free interest rate.

For the first option on HearFour, if the stock price rises to $18, the option payoff is $3 ($18 - $15) and if the stock price falls to $14, the option payoff is $0. Therefore, the expected payoff is ($3 + $0) / 2 = $1.50. 
Discounting this back to the present with a 0 percent risk-free interest rate gives us a present value of $1.50.

For the second option on EsoOne, if the stock price rises to $22, the option payoff is $7 ($22 - $15) and if the stock price falls to $0, the option payoff is $0. Therefore, the expected payoff is ($7 + $0) / 2 = $3.50. 
Discounting this back to the present with a 0 percent risk-free interest rate gives us a present value of $3.50.

Therefore, the second option on EsoOne is worth more.

Consider Two Call Options Written on Different Stocks