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### Very simple dispersion option pricer

Posted: **July 15th, 2008, 1:01 pm**

by **Siberian**

How bad an approximation is the following procedure:1) assume log-normal for each underlying stock2) get terminal value as S(t)=exp[(mu-q-1/2vol^2)*YrsTM]+vol*YrsTM*e, where e is drawn from multivariate normal with assumed correlation bwn the stocks in the basket, mu is the risk-free rate and q is the div yield3) get the basket return and the centroid4) get the dispersion5) repeat 2-4 N times and get the "average" payoff6) discount back to today using the risk free rate muGreatly appreciate any criticism.Rgs,Ev Name Edited

### Very simple dispersion option pricer

Posted: **August 11th, 2008, 7:38 am**

by **BLOBY**

What do you call "centroid" ?

### Very simple dispersion option pricer

Posted: **August 11th, 2008, 12:00 pm**

by **gjlipman**

You'll get a much better value if you simulate byS(t)=exp[(mu-q-1/2vol^2)*YrsTM+vol*sqrt(YrsTM)*e](this being the process assumed by lognormal multivariate)Not entirely certain what you mean by steps 3-5, and am not too familiar with dispersion options.

### Very simple dispersion option pricer

Posted: **August 14th, 2008, 12:16 pm**

by **Siberian**

oops, silly typo, it is of course sqrt(YrsTM)...centroid is just a mean return, dispersion in this case is the MAD (mean absolute deviation)the rest is just simulating the return N times, averaging out and discounting.thanksEv