Estimation of Value at Risk: extreme value and and robust approaches

• Authors: Grażyna TRZPIOT , Justyna MAJEWSKA
• Languages of publication: EN

Abstracts

EN

The large portfolios of traded assets held by many financial institutions have made the measurement of market risk a necessity. In practice, VaR measures are computed for several holding periods and confidence levels. A key issue in implementing VaR and related risk measures is to obtain accurate estimates for the tails of the conditional profit and loss distribution at the relevant horizons. VaR forecasts can be heavily affected by a few influential points, especially when long forecast horizons are considered. Robustness can be enhanced by fitting a generalized Pareto distribution to the tails of the distribution of the residual and sampling tail residuals from this density. However, to ensure a sufficiently large breakdown point for the estimator of the generalized Pareto tails, robust estimation is needed (see Dell’Aquila, Ronnchetti, 2006). The aim of the paper is to compare selected approaches to computing Value at Risk. We consider classical and robust conditional (GARCH) and unconditional (EVT) semi-nonparametric models where tail events are modeled using the generalized Pareto distribution. We wish to answer the question of whether the robust semi-nonparametric procedure generates more accurate VaRs than the classical approach does.

Keywords

EN

extreme value theory; Value at Risk; semi-nonparametric method; robust methods of estimation

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2010
• Volume: 20
• Issue: 1
• Pages: 132-143

Contributors

author

Grażyna TRZPIOT

• Department of Demography and Business Statistics, Karol Adamiecki University of Economics, ul. Bogucicka 14, 40-226 Katowice, Poland

author

Justyna MAJEWSKA

• Department of Demography and Business Statistics, Karol Adamiecki University of Economics, ul. Bogucicka 14, 40-226 Katowice, Poland

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