An Extended Likelihood Framework for Modeling Discretely Observed Credit Rating Transitions - Pfeuffer, Marius; Möstel, Linda; Fischer, Matthias (Quantitative Finance, 2018)

Composite Tukey-type distributions with application to operational risk management - Möstel, Linda; Fischer, Matthias; Pfeuffer, Marius (Journal of Operational Risk, 2024)
Similarly to many other quantitative disciplines, operational risk modeling requires flexible distributions defined for non-negative values, which enable heavy-tail behavior. Because they can account for the different requirements related to “extreme” observations in the tail and “ordinary” observations in the body of such distributions, so-called composite or spliced models have gained increasing attention in recent years. The focus of this paper is on composite Tukey-type distributions. This term describes a class of distributions whose tails follow a generalized truncated Tukey-type distribution, which allows for greater flexibility than the commonly used generalized Pareto distribution. After reviewing the classical Tukey-type family, we discuss the leptokurtic properties that emerge from a general kurtosis transformation, and we study several estimation methods for the truncated Tukey-type distribution. Finally, we empirically demonstrate the flexibility of our new composite model with an operational risk data set and business interruption losses.
CRIS-Team Scopus Importer:2024-03-29
Keywords: composite distributions; kurtosis; loss data; skewness; spliced distributions; Tukey-type distributions

Parameter estimation of Tukey-type distributions: A comparative analysis - Möstel, Linda; Fischer, Matthias; Pfaelzner, Fabian; Pfeuffer, Marius (Communications in Statistics-Simulation and Computation, 2019)
Tukey-type distributions (a generalization of Tukey's gh(normal)-distribution) are attractive for a broad spectrum of applications since they can explicitly model flexible skewness and kurtosis features of practical data. However, since the likelihood function is not available in closed-form, the derivation of an accurate estimation method plays a crucial role and henceforth various procedures to overcome this issue were introduced, especially for Tukey's gh(normal)-distribution. After extending these approaches to all Tukey-type distributions, our main contribution is to provide a comprehensive simulation study to compare the methods against each other. Moreover, we illustrate the practical usage for the Nikkei225 stock index data.
CRIS-Team WoS Importer:2019-05-09