Black-Scholes on HP 17BII, 19BII



#6

I would appreciate anyone interested in option pricing on the 17BII and 19BII to try this modification of HP's program. It's a little more accurate, and is a bit smaller.

Modified Black-Scholes:
http://home.comcast.net/wsb-cgi-bin/ssi.cgi?PWPTool=HTMLView&State=False&wsbID=409909&GroupID=372953&Owner=bobwang&SiteID=1372814

HP's original version:
http://h20015.www2.hp.com/en/document.jhtml?lc=en&docName=bpia5179

Thanks,
Bob Wang


#7

Excellent work Bob! In DataFile V22N3 pp13-21 I did a B-S article about the 12C but included this version for the 17bii which uses a simplified form of the approximation you use:

=========snippet from DataFile =================
This equation is 15% shorter than the one on the HP page and
produces answers 20 times more accurate:

{BLK.SCHLS|if(S(PUTV):-PS+PE*EXP(-RF%*T/100)+0*S+CALLV-PUTV:
0*L(D5:(LN(PS/PE)+(RF%/100+S^2/2)*T)/S/SQRT(T))
*L(D6:G(D5)-S*SQRT(T))
*L(D1:1/(1+ABS(G(D5)/3.006)))
*L(D2:1/(1+ABS(G(D6)/3.006)))
+PS*ABS(IF(G(D5)<0;0;-1)+
EXP(-G(D5)^2/2)*G(D1)*(((187*G(D1))-24)*G(D1)+87)/500)
-PE*EXP(-RF%*T/100)*ABS(IF(G(D6)<0:0:-1)+
EXP(-G(D6)^2/2)*G(D2)*(((187*G(D2))-24)*G(D2)+87)/500)
-CALLV)}
==============================

There is another version for the 17bii as well that enables resolving for the any of the 5 inputs, including the implied volatility. This one above could even be shortened again but accuracy suffers a little.

For DataFile, see www.hpcc.org


#8

ive always been peeved that neither the 17bii nor 19bii have UTPN (normal distribution). it would make this a lot easier.

#9

Thanks for the HPCC link. I'll have to get the CD with your articles. I do like the compactness of your approximation, I have to say that I'm impressed that Black-Scholes can fit on a 12C.

#10

Tony:

I tried your version for the upper tail and got very inaccurate results. Would you mind checking the routines N(d1) and N(d2)?
Thanks,

Bob


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