Exhibit 22.5
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The information provided is relevant in the context of a one period (one year) binomial option pricing model. A stock currently trades at $50 per share, a call option on the stock has an exercise price of $45. The stock is equally likely to rise by 25% or fall by 25%. The one-year risk free rate is 2%.
-Refer to Exhibit 22.5. Calculate the price of the call option today (C₀) .

Question

Quizplus · Accepted Answer

Using the one-period binomial option pricing model, we can calculate the expected future stock prices and use them to determine the option price today. The expected future stock prices are: 
- If the stock rises: $50 * 1.25 = $62.50 
- If the stock falls: $50 * 0.75 = $37.50

Using the risk-neutral probabilities (calculated as (1 + r)/(u-d)), we have: 
- Probability of stock rising: (1 + 0.02)/(1.25 - 0.75) = 1.01 
- Probability of stock falling: (1 + 0.02)/(1.25 - 0.75) = 1.01

Using these probabilities, we can calculate the expected option price: 
Expected option price = [1.01*(max($62.50 - $45, 0))] + [1.01*(max($37.50 - $45, 0))] 
Expected option price = $18.77

To get the option price today, we need to discount the expected option price back to present value: 
Option price today = $18.77 / 1.02 = $9.26

Therefore, the correct answer is (C).

Exhibit 22.5 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)