```MODEL: ! Computing the value of an option using the Black Scholes formula (see "The Pricing of Options and Corporate Liabilities", Journal of Political Economy, May-June, 1973); ! Keywords: Black/Scholes, option pricing, derivative/financial; SETS: ! We have 27 weeks of prices P( t), LOGP( t) is log of prices; WEEK/1..27/: P, LOGP; ENDSETS DATA: ! Weekly prices of National Semiconductor; P = 26.375, 27.125, 28.875, 29.625, 32.250, 35.000, 36.000, 38.625, 38.250, 40.250, 36.250, 41.500, 38.250, 41.125, 42.250, 41.500, 39.250, 37.500, 37.750, 42.000, 44.000, 49.750, 42.750, 42.000, 38.625, 41.000, 40.750; ! The current share price; S = 40.75; ! Time until expiration of the option, expressed in years; T = .3644; ! The exercise price at expiration; K = 40; ! The yearly interest rate; I = .163; ENDDATA SETS: ! We will have one less week of differences; WEEK1( WEEK)| &1 #LT# @SIZE( WEEK): LDIF; ENDSETS ! Take log of each week's price; @FOR( WEEK: LOGP = @LOG( P)); ! and the differences in the logs; @FOR( WEEK1( J): LDIF( J) = LOGP( J + 1) - LOGP( J); ! LDIF may take on negative values; @FREE( LDIF(J)); ); ! Compute the mean of the differences; MEAN = @SUM( WEEK1: LDIF)/ @SIZE( WEEK1); ! and the variance; WVAR = @SUM( WEEK1: ( LDIF - MEAN)^2)/ ( @SIZE( WEEK1) - 1); ! Get the yearly variance and standard deviation; YVAR = 52 * WVAR; YSD = YVAR^.5; ! Here is the Black-Scholes option pricing formula; @FREE(Z); Z = (( I + YVAR/2) * T + @LOG( S/ K))/( YSD * T^.5); ! where VALUE is the expected value of the option; VALUE = S *@PSN( Z) - K *@EXP( - I * T) * @PSN( Z - YSD *T^.5); ! The price quoted in the Wall Street Journal for this option when there were 133 days left was \$6.625; ```