leptokurtic returns

diffusion2000 · August 31st, 2006, 6:59 pm

Have anyone tryied to model a stochastic process for stock returns using a t-student distribution? My stochastic calculus isn't that good so i don't even know if it's possible.Any help? Thanks

twofish · September 1st, 2006, 2:28 am

In principle it is possible, but I'm not sure what it will get you. The difference between a t-student and a Gaussian doesn't seem to be big enough to create a significant volatility smile. Also, its not clear to me why one would want a t-student distribution.

cosmologist · September 1st, 2006, 4:27 am

QuoteOriginally posted by: diffusion2000Have anyone tryied to model a stochastic process for stock returns using a t-student distribution? My stochastic calculus isn't that good so i don't even know if it's possible.Any help? ThanksWhat is so spectacular about it?Just put the t-student pdf in place of lognormal. Integrate it. Numerically otherwise.You must try on your own. It gives you a sense of satisfaction. always,try on your own these small stuff. Excel spreadsheets with VBA codes for numerical integration is available on net.cheers Cosmic Intervention

TooNeat · September 1st, 2006, 7:06 am

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diffusion2000 · September 1st, 2006, 8:01 pm

I have a feeling that a t-student with 2/3 df would provide a better fit than gaussian.

Gmike2000 · September 1st, 2006, 11:05 pm

Like cosmologist said, just do it and see what you get. It is a good idea, after all the smile exists to correct for the nonnormal underlying distribution. When you back out the implied distribution from the smile, you will see that it is in fact non normal. Any other distribution with fatter tails will do the job of fitting the data better, the student t distribution is just one of them.

PointerLover · September 18th, 2006, 5:01 pm

I'm currently working on a similar topic: flattening the implied volatility smile using non-normal yield distributions..The distributions that I tried to fit to different market smiles are: student-t, edgeworth and lambda..The edgeworth distribution gives pretty good results. The student-t gives - as Gmike200 just said - a smile that is flatter than the B/S-smile but also far away from the fit quality the edgeworth provides.What other distribution classes can propose to try for this project?Thanks for your help!

spigeols · September 19th, 2006, 5:44 am

What do you mean by "a flatter smile than the BS smile"? In (1), they provide a better flexibility than Edgeworth (a bigger positivity domain). Perhaps to try.(1): In 'PARAMETRIC PROPERTIES OF SEMI-NONPARAMETRIC DISTRIBUTIONS, WITH APPLICATIONS TO OPTION VALUATION'(Ángel León, Javier Mencía and Enrique Sentana)

Rez · September 19th, 2006, 10:19 am

You can also try the Pearson family or -in a more parametric setting- the VG/CGMY density.Do you want to model the smile for a given maturity? or simultaneously extract some dynamics that fit all maturities?Kyriakos

PointerLover · September 20th, 2006, 7:44 am

Thanks Rez and spigeols.. I'll have a look at that!spigeols:By "flattening" I meant the search for a yield distribution whose implied volatilities calculated from the market prices don't form a smile but (in the optimal case) a flat line. The BS existis because yields are not normally distributed in reality -> if you manage to fit the expected distribution than the smile disappears..Rez:I'm trying both - on the one hand I'm doing the fitting for every maturity of a surface itself and on the other I try to find out how the distribution parameters behave over time..