Extreme Value Theory in Finance

Brodin, Erik; Klüppelberg, Claudia

doi:10.1002/9781118445112.stat03757

Cited by 6 publications

(1 citation statement)

References 37 publications

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“…We mention the case of floods (Gumbel, 1941;Sveinsson and Boes, 2002;and Friederichs and Hense, 2007), insurance losses (Brodin andKluppelberg, 2006 andCruz, 2002); earthquakes (Sornette et al, 1996;Cornell, 1968;and Burton, 1979); meteorological and climate events (Smith, 1989;Katz and Brown, 1992;Felici et al, 2007;Vitolo et al, 2009b;and Altmann et al, 2006). An extensive review of the techniques and applications related to the EVT is presented in Ghil et al (2011).…”

Section: Introductionmentioning

confidence: 98%

Extreme value theory for singular measures

Lucarini

Faranda

Turchetti

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and Hènon maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.

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Section: Introductionmentioning

confidence: 98%

Extreme value theory for singular measures

Lucarini

Faranda

Turchetti

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

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Predicting the Tail Behavior of Financial Times Stock Exchange/Johannesburg Stock Exchange (FTSE/JSE) Closing Banking Indices: Extreme Value Theory Approach

Makatjane

Moroke

Munapo

2021

Handbook of Research on Emerging Theories, Models, and Applications of Financial Econometrics

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Extreme-value statistics of stochastic transport processes

2020

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We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. For one-dimensional biased random walks, we derive exact results which tighten bounds for entropy production extrema obtained with martingale theory and reveal a symmetry between the distribution of the maxima and minima of entropy production. Furthermore, we show that the relaxation spectrum of the full generating function, and hence of any moment, of the finite-time extrema distributions can be written in terms of the Marčenko–Pastur distribution of random-matrix theory. Using this result, we obtain efficient estimates for the extreme-value statistics of stochastic transport processes from the eigenvalue distributions of suitable Wishart and Laguerre random matrices. We confirm our results with numerical simulations of stochastic models of molecular motors.

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Extreme Value Theory in Finance

Abstract: Extreme value theory is a practical and useful tool for modeling and quantifying risk. In this article, after introducing basic concepts, we indicate how to apply it within a financial framework.

Cited by 6 publications

References 37 publications

Extreme value theory for singular measures

Extreme value theory for singular measures

Predicting the Tail Behavior of Financial Times Stock Exchange/Johannesburg Stock Exchange (FTSE/JSE) Closing Banking Indices: Extreme Value Theory Approach

Extreme-value statistics of stochastic transport processes

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