analyst wants to use the Black-Scholes model to value call options on the stock of Ledbetter Inc.based on the following data: • The price of the stock is $40.
• The strike price of the option is $40.
• The option matures in 3 months (t = 0.25)• The standard deviation of the stock's returns is 0.40, and the variance is 0.16.
• The risk-free rate is 6%.
Given this information, the analyst then calculated the following necessary components of the Black-Scholes model:
• d1 = 0.175
• d2 = -0.025
• N(d1)• N(d2)N(d1) and N(d2) represent areas under a standard normal distribution function.Using the Black-Scholes model, what is the value of the call option?
A)$2.81
B)$3.12
C)$3.47
D)$3.82
E)$4.20

Question

Quizplus · Accepted Answer

According to the Black-Scholes model, the value of the call option can be calculated using the formula:

C = S*N(d1) - X*e^(-r*t)*N(d2)

where C is the option price, S is the stock price, X is the strike price, r is the risk-free rate, t is the time to maturity, and N() represents the cumulative normal distribution function.

Substituting the given values, we get:

C = 40*N(0.175) - 40*e^(-0.06*0.25)*N(-0.025)

Using a calculator or a standard normal distribution table, we can find N(0.175) = 0.5714 and N(-0.025) = 0.4901.

Therefore,

C = 40*0.5714 - 40*e^(-0.06*0.25)*0.4901 = $3.47

Therefore, the best choice is (C) with the explanation that it is the value calculated using the Black-Scholes formula with the given inputs.

Analyst Wants to Use the Black-Scholes Model to Value Call