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In sample Value at Risk and backtesting with the Pearson type IV distribution

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company name:
Stavros Stavroyiannis
license: Free
minimum requirements: MATLAB 7.11 (2010b)
functional limitations:
In sample Value at Risk and backtesting with the Pearson type IV distribution description
There are two issues with the Pearson type IV distribution: (I) the complex gamma function entering the normalization constant in the probability density function (pdf) and (II) the complex Gauss hypergeometric function entering the cumulative distribution function (cdf). For the complex gamma function we transcribe in Matlab code the C++ code by Heinrich. Since for several reasons the hypergeom function for complex arguments in Matlab is slow and accessible only in the last versions, for better dissemination we calculate the constants at the confidence integrals by numerical integration and inversion of the pdf. The Value at Risk backtesting criteria for now, are the same with the previous varin.m file. In our humble opinion this distribution is better than the skewed Student distribution used and it is only the first member of the Extended Pearson system of distributions. The user can change the Garch model at will. The code takes about 45 seconds to execute and we hope experienced programmers will optimize the file. The results will be presented at the Business & Economics Society International conference at Split, Croatia, July 6 - 9, 2011.
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