Linking Tukey’s legacy to financial risk measurement

Autor: Suleyman Taspinar, Chu-Ping C. Vijverberg, Wim P.M. Vijverberg
Rok vydání: 2016
Předmět:
Zdroj: Computational Statistics & Data Analysis. 100:595-615
ISSN: 0167-9473
Popis: Financial data are often thick-tailed and exhibit skewness. The versatile Generalized Tukey Lambda (GTL) distribution is able to capture varying degrees of skewness in thin- or thick-tailed data. Such versatility makes the GTL distribution potentially useful in the area of financial risk measurement. Moreover, for GTL-distributed random variables, the familiar risk measures of Value at Risk (VaR) and Expected Shortfall (ES) may be expressed in simple analytical forms. It turns out that, both analytically and through Monte Carlo simulations, GTL's VaR and ES differ significantly from other flexible distributions. The asymptotic properties of the maximum likelihood estimator of the GTL parameters are also examined. In order to study risk in financial data, the GTL distribution is inserted into a GARCH model. This GTL-GARCH model is estimated with data on daily returns of GE stock, demonstrating that, for certain data sets, GTL may capture risk measurements better than other distributions.11Online supplementary materials consist of appendices with proofs and additional Monte Carlo results, data used in this study, an R script for fitting GTL densities by maximum likelihood, and an R script for estimation of the GTL-GARCH model (see Appendix A). We derive Value at Risk and expected shortfall for GTL-distributed random variables.GTL's VaR and ES statistics differ significantly from other flexible distributions.We derive asymptotic properties of the ML estimator of the GTL parameters.We insert GTL and other flexible distributions in a GARCH model.A GTL-GARCH model may fit real data better than GARCH with other distributions.
Databáze: OpenAIRE
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