Density approximations and VaR computation for compound Poisson-lognormal distributions. Issue 3 (16th March 2017)

• Record Type: Journal Article
• Authors: Bee, M.
• Is Part Of: Communications in statistics. Volume 46:Issue 3(2017)
• Page Start: 1825
• Page End: 1841
• Publication Date: 2017-03-16
• Subjects: Extreme value theory -- Generalized beta distribution -- Lognormal mixture -- Probability-weighted moments -- Random sum; 62E17 -- 62P05; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2015.1016237
• Languages: English
• ISSNs: 0361-0918

Abstract

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.