Assume that the stock of Phoneeffect, Inc., is currently trading for $16 and will either rise to $23.50 or fall to $9 in one year. The risk-free rate for one year is 3 percent. What is the value of a put option with a strike price of $18 that expires in three months? (Do not round intermediate computations. Round final answer to two decimal places.)

Question

Quizplus · Accepted Answer

First, we need to calculate the expected future stock price:
Expected future stock price = (0.5 x $23.50) + (0.5 x $9) = $16.25
Next, we can calculate the value of the put option using the Black-Scholes model:
d1 = [ln($16/$18) + (0.03 + (0.5 x 0.3^2) x 0.25] / (0.3 x sqrt(0.25)) = -0.56
d2 = d1 - (0.3 x sqrt(0.25)) = -0.86
N(-d2) = 0.8051
N(-d1) = 0.29
Value of put option = $18 x e^(-0.03 x 0.25) x N(-d2) - $16.25 x N(-d1) = $4.23
Therefore, the answer is C.

Assume That the Stock of Phoneeffect, Inc