Extreme Value Theory

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 9 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 367-430 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main topics covered in this chapter are:what extreme value theory is and how it differs from classical statistics;the two pillars of extreme value theory: Fisher–Tippett–Gnedenko theorem and Pickands–Balkema–de Haan theorem;the three classes that the limit distribution of maxima will fall into: the Fréchet, Weibull, or Gumbel distribution;the generalized Pareto distribution;the maximum domain of attraction of an extreme value distribution and the concept of tail equivalence;the theory of maxima for stationary processes;extreme value theory for multivariate distributions;the role of copula in multivariate extreme value theory;the three types of copulas;three estimation methods for distributions: maximum likelihood estimation method, method of moments, and special estimators;the Hill estimator and the Pickands estimator for estimating the shape parameter of a distribution;use and limitations of the quantile plot (QQ-plot) for verifying statistical hypotheses by examining the degree of deviations of the linearity plot of a hypothesized distribution;three different approaches to compute widely-known risk measures (VaR and AVaR).

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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