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Financial Data Analysis with Two Symmetric Distributions

Published online by Cambridge University Press:  29 August 2014

Werner Hürlimann
Werner Hürlimann*
Affiliation:
Value and Risk Management, Winterthur Life and Pensions, Postfach 300, CH-8401 Winterthur
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Abstract

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The normal inverted gamma mixture or generalized Student t and the symmetric double Weibull, as well as their logarithmic counterparts, are proposed for modeling some loss distributions in non-life insurance and daily index return distributions in financial markets. For three specific data sets, the overall goodness-offit from these models, as measured simultaneously by the negative log-likelihood, chi-square and minimum distance statistics, is found to be superior to that of various “good” competitive models including the log-normal, the Burr, and the symmetric α-stable distribution. Furthermore, the study justifies on a statistical basis different important models of financial returns like the model of Black-Scholes (1973), the log-Laplace model of Hürlimann (1995), the normal mixture by Praetz (1972), the symmetric α-stable model by Mandelbrot (1963) and Fama (1965), and the recent double Weibull as limiting geometric-multiplication stable scheme in Mittnik and Rachev (1993). As an application, the prediction of one-year index returns from daily index returns is discussed.

Keywords

Claim size datafinancial market dataindex returnnormal inverted gamma mixturegeneralized Student tsymmetric double Weibullgoodness-offit
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 187 - 211
Copyright
Copyright © International Actuarial Association 2001

References

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