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Brian,<br>
<br>
John Hull's text Options, Futures and other derivatives has a nice
appendix for Cornish Fisher on pagers 370-371. This example only
requires linear algebra to approximate the moments. The appendix
does not define z<small>q</small> but it is u<small>p</small>*sigma<small>p</small>
* alphahat where alphahat is the require percentile of a standard
normal distribution (1%) in the appendix's example.<br>
<br>
Good Luck<br>
Joe W. Byers<br>
Professor of Finance<br>
The University of Tulsa<br>
<br>
<br>
<blockquote type="cite">
<pre wrap="">The limitations of VaR in modeling of risk for non-normal distributions
have been known for quite some time, and this approach seems to hold some
value over other approaches already implemented in RMetrics like
Conditional VaR.
I'm trying to replicate the calculation as laid out in:
Favre, Laurent, and Jose-Antonio Galeano. ?Mean-Modified
Value at Risk Optimization with Hedge Funds.? The Journal
of Alternative Investments, 5 (2002), pp. 21-25.
and presented in a different form in an earlier paper:
Fallon, William. "Calculating Value-at-Risk"
Working Paper, Wharton, 1996.
Both of these papers rely on calculating traditional VaR (as is done with
fPortfolio.VaR() from the RMetrics package) and then using a
Cornish-Fisher Expansion for skew (both papers) or skew and kurtosis
(Favre 2002) (as is done using the fBasics.skewness() and
fBasics.kurtosis() functions from RMetrics)
I'm wondering if anyone has already replicated this work in R, and could
provide a pointer, or alternately if some of the more experienced people
on this list could render an opinion on which of the Cornish-Fisher
functions in the core R stats package might be appropriate for this kind
of analysis.
I would like to implement and share a function for Modified Cornish-Fisher
VaR, so any assistance would be greatly appreciated.
Regards,
- Brian
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