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) = 0.49003
N(d₁) and N(d₂) represent areas under a standard normal distribution function. What is the value of the call option?

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula, we have:
C = S * N(d1) - Ke^(-rt) * N(d2)
where
d1 = (ln(S/K) + (r + σ^2/2)t) / (σ * sqrt(t)) = 0.175
d2 = d1 - σ * sqrt(t) = -0.025
N(d1) = 0.56946
N(d2) = 0.49003
Plugging in the values, we get:
C = 40 * 0.56946 - 40e^(-0.06*0.25) * 0.49003
= 22.7784 - 19.3102
= 3.4682
Therefore, the value of the call option is $3.47, which is closest to option C.

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