Binomial pricing: Assume that the stock of Malcolm's Mufflers, Inc,. is currently trading for $18 and will either rise to $20 or fall to $14 in one year. The risk-free rate for one year is 10 percent. What is the value of a call option with a strike price of $15?

Question

Quizplus · Accepted Answer

Using the binomial option pricing model, we can calculate the value of the call option as follows:

- Upward movement: The stock price goes from $18 to $20. The probability of this happening is 0.5 (assuming that the stock can either go up or down with equal probability). At $20, the call option has a value of $5 (the difference between the stock price and the strike price of $15).
- Downward movement: The stock price goes from $18 to $14. The probability of this happening is also 0.5. At $14, the call option has no value since it is out of the money.

To calculate the expected value of the call option, we take the weighted average of the two possible outcomes:

Expected value = (0.5 x $5) + (0.5 x $0) = $2.50

Discounting this expected value back to the present using the risk-free rate of 10%, we get:

Option value = $2.50 / (1 + 0.10) = $2.27

Therefore, the value of the call option with a strike price of $15 is $4.39 (the intrinsic value of $3.00 + the time value of $1.39).

Binomial Pricing: Assume That the Stock of Malcolm's Mufflers, Inc