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Extreme Value Theory

In: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT

Author

Listed:
  • Michele Leonardo Bianchi
  • Stoyan V Stoyanov
  • Gian Luca Tassinari
  • Frank J Fabozzi
  • Sergio M Focardi

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).

Suggested Citation

  • Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Extreme Value Theory," World Scientific Book Chapters,in: HANDBOOK OF HEAVY-TAILED DISTRIBUTIONS IN ASSET MANAGEMENT AND RISK MANAGEMENT, chapter 9, pages 367-430 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789813276208_0009
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    Keywords

    Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management;

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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