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) = 0.56946∙ N(d₂) = 0.49003N(d₁) and N(d₂) represent areas under a standard normal distribution function.What is the value of the call option? A)$2.81 B)$3.12 C)$3.47 D)$3.82

Question

Quizplus · Accepted Answer

Using the Black-Scholes model, the value of the call option can be calculated as 
C = S*N(d1) - X*e^(-r*t)*N(d2)
where 
S = 40 (stock price)
X = 40 (strike price)
r = 6% (risk-free rate)
t = 0.25 (time to maturity)
sigma = 0.4 (standard deviation)

Using the given data, we can calculate d1 and d2 as

d1 = [ln(S/X) + (r + sigma^2/2)*t] / (sigma*sqrt(t)) 
= [ln(40/40) + (0.06 + 0.4^2/2)*0.25] / (0.4*sqrt(0.25))
= 0.175

d2 = d1 - sigma*sqrt(t) 
= 0.175 - 0.4*sqrt(0.25)
= -0.025

Using the values of d1 and d2, we can find the values of N(d1) and N(d2) from the standard normal distribution table.

N(d1) = 0.56946 
N(d2) = 0.49003

Now, substituting these values in the call option formula, we get

C = 40*0.56946 - 40*e^(-0.06*0.25)*0.49003 
= $3.47

Therefore, the value of the call option is $3.47, which is option C.

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