Risk using Student T

Discussion on Value-at-Risk Models
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FelixTanudjaja
Posts: 2
Joined: Mon May 03, 2010 7:42 am

Re: Risk using Student T

Postby FelixTanudjaja » Tue May 04, 2010 2:18 am

hi,
i want to ask about cornish fisher expansion in jorion 2007
he only considering the skewness of distribution, which is

Z-adjusted = z+1/6 * {z^2 - 1}*M3
Variables,
Z : Confidence level value of normal distribution
M3 : Skewness

can u explain more about this??

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Risk using Student T

Postby coalexander » Tue May 04, 2010 9:32 am

Hi Felix

This CF approximation is only based on a first order expansion, the second order expansion inlcudes a kurtosis and a squared skewness term. In most cases (like Edgeworth expnasions), the higher the order of the expansion, the better the approximation. However, the CF does not have this property. So, a second order expansion can sometimes (in fact, very often) give you worse results than a first order one.

As you can see from my strongly critical remarks following the comparative study of semi-parameteric VaR ethods, I am no fan of CF expansions. I find Johnson distributions and Edgeworth expansions to be much, much better.

Carol


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