# Black-Scholes Option Pricing Model

An analyst is interested in using the Black-Scholes model to value call options on the stock of Ledbetter Inc. The analyst has accumulated the following information:

The price of the stock is $33.

The strike price is $33

The option matures in 6 months (t=0.50)

The standard deviation of the stock's returns is 0.30 and the variance is 0.09.

The risk-free rate is 10 percent.

Given this information, the analyst is then able to calculate some other necessary components of the Black-Scholes model:

d1=0.34177

d2=0.12964

N(d1)=0.63369

N(d2)=0.55155

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?

The course text book provides the solution, but I have a question???

The solution is stated as follows:

V=P(N(d1)) -Xe(-krft) (N(d2)

V=(33.00(0.63369) - (33(0.95123)(0.55155)

V=20.91-17.31

V=$3.60

My question is how to calculate the figure (0.95123) Please explain. Thanks.

https://brainmass.com/business/black-scholes-model/black-scholes-option-pricing-model-45313

#### Solution Preview

e^(-krft) = e^(-10%*0.5) = e^(-0.05) = 0.95123

The first term is P(N(d1)=33*0.63369= $20.91

The second term is Xe^(-krft) (N(d2))=

This is X(strike price) multiplied by e raised to the power (-krf *t) multiplied by ...

#### Solution Summary

Black-Scholes Option Pricing Model has been used for valuing option on Ledbetter Inc.