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Estimating and backtesting risk under heavy tails

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  • Marcin Pitera
  • Thorsten Schmidt

Abstract

While the {estimation} of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and negatively impacts backtesting results, especially in small sample cases. In this article we show that the link between estimation bias and backtesting can be traced back to the dual relationship between risk measures and the corresponding performance measures, and discuss this in reference to value-at-risk, expected shortfall and expectile value-at-risk. Motivated by the consistent underestimation of risk by plug-in procedures, we propose a new algorithm for bias correction and show how to apply it for generalized Pareto distributions to the i.i.d. setting and to a GARCH(1,1) time series. In particular, we show that the application of our algorithm leads to gain in efficiency when heavy tails or heteroscedasticity exists in the data.

Suggested Citation

  • Marcin Pitera & Thorsten Schmidt, 2020. "Estimating and backtesting risk under heavy tails," Papers 2010.09937, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2010.09937
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    References listed on IDEAS

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    1. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, May.
    2. Tobias Fissler & Johanna F. Ziegel & Tilmann Gneiting, 2015. "Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting," Papers 1507.00244, arXiv.org, revised Jul 2015.
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    Cited by:

    1. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    2. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    3. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).

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