Density approximations and VaR computation for compound Poisson-lognormal distributions |
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Authors: | M Bee |
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Institution: | Department of Economics and Management, University of Trento, Trento, Italy |
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Abstract: | Parametric approximations of the compound Poisson-lognormal distribution are developed and used to compute Value-at-Risk (VaR). As guidelines for finding an approximation, the skewness–kurtosis space and the tail behavior are considered. The Generalized Beta distribution of the second kind (GB2) and a mixture of lognormals are found to provide a good fit. In certain cases, the GB2 can be estimated by moment-matching, thus providing a simulation-free procedure for VaR computation. For confidence levels larger than 99%, extreme value theory approaches are developed. According to extensive Monte Carlo evidence, the proposed approximations are more efficient than crude Monte Carlo. |
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Keywords: | Extreme value theory Generalized beta distribution Lognormal mixture Probability-weighted moments Random sum |
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