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On the estimation of Value-at-Risk and Expected Shortfall at extreme levels

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  • Lazar, Emese
  • Pan, Jingqi
  • Wang, Shixuan

Abstract

The estimation of risk at extreme levels (such as 0.1%) can be crucial to capture the losses during market downturns, such as the global financial crisis and the COVID-19 market crash. For many existing models, it is challenging to estimate risk at extreme levels. In order to improve such estimation, we develop a framework to estimate Value-at-Risk and Expected Shortfall at an extreme level by extending the one-factor GAS model and the hybrid GAS/GARCH model to estimate Value-at-Risk and Expected Shortfall for two levels simultaneously, namely for an extreme level and for a more common level (such as 10%). Our simulation results indicate that the proposed models outperform the GAS model benchmarks in terms of in-sample and out-of-sample loss values, as well as backtest rejection rates. We apply the proposed models to oil futures (WTI, Brent, gas oil and heating oil) and compare them with a range of parametric, nonparametric, and semiparametric alternatives. The results show that our proposed models are generally superior to the alternatives.

Suggested Citation

  • Lazar, Emese & Pan, Jingqi & Wang, Shixuan, 2024. "On the estimation of Value-at-Risk and Expected Shortfall at extreme levels," Journal of Commodity Markets, Elsevier, vol. 34(C).
    • Handle: RePEc:eee:jocoma:v:34:y:2024:i:c:s2405851324000102
    DOI: 10.1016/j.jcomm.2024.100391
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    More about this item

    Keywords

    Risk models; Value-at-Risk; Expected Shortfall; Semiparametric model; Oil futures;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • Q02 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Commodity Market

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