A new challenge in the HP19BII solver for the MOHPC community!!

[Aconzio]

Dear MOHPC-Community!

Here I am again to bother you!-
Last week I couldn’t believe my eyes; I submitted to your attention a code for programming a call formula out of a finance book and Bill and Gerson discovered an error in the edited book in less than an hour!! - AMAZING..
I have already written to the publisher to notify the error and hopefully the 3rd edition will come out correctly…

Now I have a similar and related problem on HP19BII

Wanting to calculate the Black-Scholes version of the formulas for calls and Puts

C=SxN(d1)-XxEXP(-RxT)xN(d2) with

d1=((LN((SxX^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))
d2=((LN((SxX^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5)) -oxT^.5

P=XxEXP(-RxT)xN(-d2)-SxN(-d1)

and using an approximation of the Normal distribution according to Zelen and Severo (1964) as follows:

Ν=1-(((2xPΙ)^-.5xEXP((-Y^2)÷2))x((.4361836x(1+.33267xΥ)^-1+(-.1201676)x(1+.33267xΥ)^-2
+.9372980x(1+.33267xΥ)^-3)))

substituting one gets these results for call and put:

CALL=Sx(1-(((2xPI)^-.5)xEXP(-((LN((Sx(X^-
1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5)))^2÷2))x(.4361836x((1+(.33267x(LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))))^-1)+(-.1201676)x((1+(.33267x(LN((Sx(X^-
1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))))^-2)+.9372980x((1+(.33267x(LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))))^-3)))-
XxEXP(-RxT)x
(1-(((2xPI)^-.5)xEXP(-((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)^2÷2))x
(.4361836x((1+(.33267x((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)))^-1)
+(-.1201676)x((1+(.33267x((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5 )+(.5xoxT^.5))-oxT^.5)))^-2)
+.9372980x((1+(.33267x((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)))^-3)))

********************************************************************************​*****************************

PUT=XxEXP(-RxT)x((1-(((2xPI)^-.5)xEXP(-((LN((Sx(X^-
1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)^2÷2))x(.4361836x((1+(.33267x((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)))^-1)+(-.1201676)x((1+(.33267x((LN((Sx(X^-
1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)))^-2)+.9372980x((1+(.33267x((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))-oxT^.5)))^-3))))-
Sx(1-(1-(((2xPI)^-.5)xEXP(-((LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5)))^2÷2))x
(.4361836x((1+(.33267x(LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))))^-1)
+(-.1201676)x((1+(.33267x(LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5 )+(.5xoxT^.5))))^-2)
+.9372980x((1+(.33267x(LN((Sx(X^-1xEXP(RxT))))÷(oxT^.5)+(.5xoxT^.5))))^-3))))

Where S=Spot price, X=Strike, R=interest rate, T=Time to maturity, o=Standard deviation

These formulas used to work well in the past …now after a battery change where all the solver’s content got lost ;-)) I re-inputted both both they deliver fully uncorrected results…My HPBii seems still to work…What happened? Did I do some input mistake with the brackets? Maybe other formulas in the solver with similar variables “contaminate“ those for Black and Scholes?...What do you thinK?...Regards!!