Use the Black-Scholes model to value call options on the stock of Ledbetter Inc.

ID: 2740035 • Letter: U

Question

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. Using the Black-Scholes model, what is the value of the call option?

Price of Stock = $40.00

N(d1) = 0.56946

Strike price: $40.00

N(d2) = 0.49003

Option maturity: 0.25

Variance of stock returns: 0.16

Risk-free rate: 6.0%

The Black-Scholes model calculate the value of the call option as :

V = P[N(d1)] - Xe-rt[N(d2)]

= $40(0.56946) - $40e-rt(0.49003)

= $22.78 - $19.31

= $3.47

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.