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Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling

Author

Listed:
  • Lennart Hoogerheide

    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    (Erasmus University Rotterdam)

Abstract
This discussion paper resulted in a publication in the International Journal of Forecasting , 2010, 26(2), 231-247. An efficient and accurate approach is proposed for forecasting Value at Risk [VaR] and Expected Shortfall [ES] measures in a Bayesian framework. This consists of a new adaptive importance sampling method for Quantile Estimation via Rapid Mixture of t approximations [QERMit]. As a first step the optimal importance density is approximated, after which multi-step `high loss' scenarios are efficiently generated. Numerical standard errors are compared in simple illustrations and in an empirical GARCH model with Student- t errors for daily S&P 500 returns. The results indicate that the proposed QERMit approach outperforms several alternative approaches in the sense of more accurate VaR and ES estimates given the same amount of computing time, or equivalently requiring less computing time for the same numerical accuracy.

Suggested Citation

  • Lennart Hoogerheide & Herman K. van Dijk, 2008. "Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling," Tinbergen Institute Discussion Papers 08-092/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20080092
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Value at Risk; Expected Shortfall; numerical accuracy; numerical standard error; importance sampling; mixture of Student-t distributions; variance reduction technique;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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