Binomial pricing: Assume that the shares of Tony's Mufflers Inc. are 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 per cent. What is the value of a call option with a strike price of $15?

Question

Quizplus · Accepted Answer

Using the binomial pricing formula, we can calculate the expected stock price at the end of the year:

u = (1 + 0.2) = 1.2
d = (1 - 0.2) = 0.8
p = (1 + r - d) / (u - d) = 0.6
q = 1 - p = 0.4

S(1) = 20p + 14q = 18

We can then use backward induction to calculate the option value at each node:

At node (2,2), where the stock price is $20, the call option value is $5.
At node (2,1), where the stock price is $14, the call option value is $0.
At node (1,2), where the stock price is $20, the call option value is $0.
At node (1,1), where the stock price is $14, the call option value is $1.

Therefore, the value of the call option is:

C(0) = (0.6*$5 + 0.4*$0) / (1+0.1) = $4.39

Thus, the best choice is A).

Binomial Pricing: Assume That the Shares of Tony's Mufflers Inc