How to include the skew and kurtosis to Monte Carlo simulation?

rock31 · July 20th, 2006, 12:28 pm

Normally, the Monte Carlo simulation is assumed to be normal distributed. But in real world, there exist the skew and kurtosis in the return distribution. I wonder, how should I include this into my simulation. Any reference are welcomed. Thanks.

chromo · July 20th, 2006, 12:35 pm

Histogram of historic log returns is easy.

rock31 · July 20th, 2006, 12:49 pm

thanks for reply. I guess my question was not clear enough. What I want to is not the value of skew and kurtosis for a given distribution. WHAT I DO NEED is given the value of skew and kurtosis, how to generate the random series whose distribute is consistent with the given skew and kurtosis values. Thanks alot.

DavidF · July 20th, 2006, 2:11 pm

You can use any kind of parametric law in which the skewness and kurtosis are known explicitely function of the parameters.

rock31 · July 20th, 2006, 3:16 pm

Thank you davidF. Can you recommend some articles or books?

DavidF · July 21st, 2006, 8:26 am

QuoteOriginally posted by: rock31Thank you davidF. Can you recommend some articles or books?I have no article in mind but a simple google research on "normal inverse gaussian" (for example) should do the thing.

rock31 · July 21st, 2006, 10:30 am

DavidF, thanks.

fab10ab · August 7th, 2006, 12:41 pm

You can also try an Edgeworth or Gram-Charlier expansion. The Gram-Charlier is handy because it uses values of the normal CDF, which are already built-in with most software.

rock31 · August 7th, 2006, 1:04 pm

Dear Fab, Thanks. That is a great help. R.