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Using the Extremal Index for Value-at-Risk Backtesting

Author

Listed:
  • Axel Bücher
  • Peter N Posch
  • Philipp Schmidtke

Abstract

We introduce a set of new Value-at-Risk independence backtests by establishing a connection between the independence property of Value-at-Risk forecasts and the extremal index, a general measure of extremal clustering of stationary sequences. For this purpose, we introduce a sequence of relative excess returns whose extremal index is to be estimated. We compare our backtest to both popular and recent competitors using Monte Carlo simulations and find considerable power in many scenarios. In an applied section, we perform realistic out-of-sample forecasts with common forecasting models and discuss advantages and pitfalls of our approach.

Suggested Citation

  • Axel Bücher & Peter N Posch & Philipp Schmidtke, 2020. "Using the Extremal Index for Value-at-Risk Backtesting," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 556-584.
    • Handle: RePEc:oup:jfinec:v:18:y:2020:i:3:p:556-584.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbaa011
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    More about this item

    Keywords

    VaR backtesting; extremal index; independence; risk measures;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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