An Application of Extreme Value Theory for Measuring Risk

Manfred Gilli · Evis Këllezi

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Probability and Risk Models Financial Risk and Volatility Modeling Risk and Portfolio Optimization

Abstract

Many fields of modern science and engineering have to deal with events which are rare but have significant consequences. Extreme value theory is considered to provide the basis for the statistical modelling of such extremes. The potential of extreme value theory applied to financial problems has only been recognized recently. This paper aims at introducing the fundamentals of extreme value theory as well as practical aspects for estimating and assessing statistical models for tail-related risk measures.

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References

1994Modelling of extremal events in insurance and finance 2000Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach 1974Residual Life Time at Great Age 1996The Asymptotic Distribution of Extreme Stock Market Returns 2001Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation 2001Statistical Analysis of Extreme Values: with Applications to Insurance, Finance, Hydrology and Other Fields 2000Value-at-Risk and Extreme Returns 1998Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management

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