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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.

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    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

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