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Estimation of Value at Risk: extreme value and robust approaches

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  • Grażyna Trzpiot
  • Justyna Majewska

Abstract

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.

Suggested Citation

  • Grażyna Trzpiot & Justyna Majewska, 2010. "Estimation of Value at Risk: extreme value and robust approaches," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 20(1), pages 131-143.
  • Handle: RePEc:wut:journl:v:1:y:2010:p:131-143
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    References listed on IDEAS

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    1. Rosario Dell’Aquila & Paul Embrechts, 2006. "Extremes and Robustness: A Contradiction?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(1), pages 103-118, April.
    2. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
    3. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 281-313, Spring.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, vol. 76(1), pages 83-108, January.
    6. Hsieh, David A., 1993. "Implications of Nonlinear Dynamics for Financial Risk Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 41-64, March.
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    Cited by:

    1. Trzpiot Grażyna, 2012. "Selected Robust Methods for Camp Model Estimation," Folia Oeconomica Stetinensia, Sciendo, vol. 12(2), pages 58-71, December.
    2. Wang, Zongrun & Wang, Wuchao & Chen, Xiaohong & Jin, Yanbo & Zhou, Yanju, 2012. "Using BS-PSD-LDA approach to measure operational risk of Chinese commercial banks," Economic Modelling, Elsevier, vol. 29(6), pages 2095-2103.
    3. Kellner, Ralf & Rösch, Daniel, 2016. "Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk," Journal of Economic Dynamics and Control, Elsevier, vol. 68(C), pages 45-63.

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