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# Black-Scholes Option Pricing Model

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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.

#### 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.

\$2.49