An 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?

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula, we can calculate the value of the call option as:
Call Option Value = S*N(d1) - X*e^(-r*t)*N(d2)
Where:
S = Stock Price = $40
N(d1) = N(0.175) = 0.5704 (using standard normal distribution table)
X = Strike Price = $40
r = Risk-free rate = 6% = 0.06
t = Time to maturity = 3 months = 0.25 (in years)
N(d2) = N(-0.025) = 0.4901 (using standard normal distribution table)
Plugging in the values, we get:
Call Option Value = $40*0.5704 - $40*e^(-0.06*0.25)*0.4901
= $22.82 - $19.35
= $3.47
Therefore, the value of the call option is $3.47. The correct answer is option C.

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