It is beyond the scope of this document to get into the theoretical details behind the Black Scholes pricing model. The interested reader should refer to Black and Scholes (1973) for the details. However, we will briefly discuss some of the mechanics of the key formulas involved in the model.

In our model, we compute the option's value in two key steps. First, we compute the variable Z as follows:

Z = (( I + YVAR/2) *

   T + @LOG( S/ K))/( YSD * T^.5);

where,

I        =        the yearly interest rate,

YVAR        =        variance of the stock's price,

T        =        time until expiration in years,

S        =        current share price,

K        =        exercise price, and

YSD        =        standard deviation on stock's price.

We then use the value of Z in the following formula to determine the expected value of the option:

VALUE = S *@PSN( Z) - K *@EXP( - I * T) *

   @PSN( Z - YSD *T^.5);

where,

@PSN( Z)  returns the cumulative standard normal probability, and

@EXP( X)  returns e raised to the power of x.