Binomial pricing: Assume that the stock of ABC, Inc., is currently trading for $2.60 and will either rise to $10 or fall to $0 in one year. The risk-free rate for one year is 1 percent. What is the value of a put option with a strike price of $5?

Question

Quizplus · Accepted Answer

Using the binomial pricing model, we can calculate the expected value of the stock in one year:
(0.5 x $10) + (0.5 x $0) = $5
Using this information and the risk-free rate, we can calculate the probability of the stock price going up and down in one year:
u = e^(σ√T) = e^(0.822 √1) = 2.28
d = 1/u = 1/2.28 = 0.438
p = (e^(rT) - d) / (u - d) = (e^(0.01 x 1) - 0.438) / (2.28 - 0.438) = 0.325
q = 1 - p = 0.675
Using the formula for the value of a put option in the model, we can calculate the value of the put option with a strike price of $5:
Put option value = (p x max(K - S, 0)) + (q x max(K - S, 0))
Put option value = (0.325 x max($5 - $5, 0)) + (0.675 x max($5 - $2.60, 0))
Put option value = $3.65
Therefore, the best choice is C, with a put option value of $3.65.

Binomial Pricing: Assume That the Stock of ABC, Inc