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Estimating and backtesting risk under heavy tails

Author

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  • Pitera, Marcin
  • Schmidt, Thorsten

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.

Suggested Citation

  • Pitera, Marcin & Schmidt, Thorsten, 2022. "Estimating and backtesting risk under heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 1-14.
    • Handle: RePEc:eee:insuma:v:104:y:2022:i:c:p:1-14
    DOI: 10.1016/j.insmatheco.2022.01.006
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    Citations

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    Cited by:

    1. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    2. 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).
    3. 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.

    More about this item

    Keywords

    Value-at-risk; Expected shortfall; Estimation of risk capital; Bias; Risk estimation; Backtesting; Unbiased estimation of risk measures; Generalized Pareto distribution;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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