Assume we have a stock currently worth $100. We also assume the interest rate is zero, and we can buy options for this stock with a strike price of $100. If the stock can rise or fall by $20 with equal probability over the option period, and the option cannot be exercised until the expiration date, what is the time value of the option?
A) $20
B) $0
C) $10
D) $100

Question

Quizplus · Accepted Answer

The time value of an option is the difference between the option's premium and its intrinsic value. In this case, the option has no intrinsic value because the stock is currently trading at the strike price of $100. However, there is still time left until expiration, and there is a chance that the stock will rise or fall by $20. Therefore, the option has some value based on the probability of the stock moving in one direction or the other.

To calculate the time value, we can use the binomial model, which considers the potential outcomes of the stock's movement. If the stock goes up to $120, the option will have an intrinsic value of $20 ($120 - $100). If the stock goes down to $80, the option will have no intrinsic value. Therefore, the expected value of the option is 0.5*$20 + 0.5*$0 = $10.

This $10 represents the time value of the option, which is the premium paid for the chance to profit from the potential movement of the stock.

Assume We Have a Stock Currently Worth $100