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Siberian
Topic Author
Posts: 298
Joined: June 25th, 2003, 8:56 pm

### Very simple dispersion option pricer

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
Last edited by Siberian on July 14th, 2008, 10:00 pm, edited 1 time in total.

BLOBY
Posts: 113
Joined: May 17th, 2004, 5:07 am

### Very simple dispersion option pricer

What do you call "centroid" ?

gjlipman
Posts: 1102
Joined: May 20th, 2002, 9:13 pm

### Very simple dispersion option pricer

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.

Siberian
Topic Author
Posts: 298
Joined: June 25th, 2003, 8:56 pm

### Very simple dispersion option pricer

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

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