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Risk Analysis via Generalized Pareto Distributions

Author

Listed:
  • Yi He
  • Liang Peng
  • Dabao Zhang
  • Zifeng Zhao

Abstract

We compute the value-at-risk of financial losses by fitting a generalized Pareto distribution to exceedances over a threshold. Following the common practice of setting the threshold as high sample quantiles, we show that, for both independent observations and time-series data, the asymptotic variance for the maximum likelihood estimation depends on the choice of threshold, unlike the existing study of using a divergent threshold. We also propose a random weighted bootstrap method for the interval estimation of VaR, with critical values computed by the empirical distribution of the absolute differences between the bootstrapped estimators and the maximum likelihood estimator. While our asymptotic results unify the inference with nondivergent and divergent thresholds, the finite sample studies via simulation and application to real data show that the derived confidence intervals well cover the true VaR in insurance and finance.

Suggested Citation

  • Yi He & Liang Peng & Dabao Zhang & Zifeng Zhao, 2022. "Risk Analysis via Generalized Pareto Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 852-867, April.
  • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:2:p:852-867
    DOI: 10.1080/07350015.2021.1874390
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    Cited by:

    1. Parvin Malekzadeh & Zissis Poulos & Jacky Chen & Zeyu Wang & Konstantinos N. Plataniotis, 2024. "EX-DRL: Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning," Papers 2408.12446, arXiv.org, revised Aug 2024.
    2. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    3. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks," Papers 2304.06950, arXiv.org.

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