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

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  • Lennart Hoogerheide

    ()
    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    ()
    (Erasmus University Rotterdam)

Abstract

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-092/4.

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Date of creation: 02 Oct 2008
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Handle: RePEc:dgr:uvatin:20080092

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Web page: http://www.tinbergen.nl

Related research

Keywords: Value at Risk; Expected Shortfall; numerical accuracy; numerical standard error; importance sampling; mixture of Student-t distributions; variance reduction technique;

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References

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  10. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  11. Hoogerheide, L.F. & van Dijk, H.K. & van Oest, R.D., 2007. "Simulation based bayesian econometric inference: principles and some recent computational advances," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 2007-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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Cited by:
  1. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: the R package AdMit," DQE Working Papers, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland 9, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  2. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3498-3516.
  3. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, 2008. "Adaptive Mixture of Student-t distributions as a Flexible Candidate Distribution for Efficient Simulation," Tinbergen Institute Discussion Papers, Tinbergen Institute 08-062/4, Tinbergen Institute, revised 15 Dec 2008.
  4. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2011. "A Class of Adaptive EM-based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-004/4, Tinbergen Institute.
  5. Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  6. Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, University of Manchester, vol. 82(1), pages 71-102, 01.
  7. Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2012. "A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation," Journal of Econometrics, Elsevier, Elsevier, vol. 171(2), pages 101-120.
  8. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2012. "A Class of Adaptive Importance Sampling Weighted EM Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-026/4, Tinbergen Institute.
  9. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2011. "A Class of Adaptive EM-based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-004/4, Tinbergen Institute.
  10. Lennart F. Hoogerheide & Francesco Ravazzolo & Herman K. van Dijk, 2011. "Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-131/4, Tinbergen Institute.
  11. Lennart F. Hoogerheide & Francesco Ravazzolo & Herman K. van Dijk, 2011. "Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-131/4, Tinbergen Institute.
  12. Ardia, David & Lennart, Hoogerheide & Nienke, Corré, 2011. "Stock index returns’ density prediction using GARCH models: Frequentist or Bayesian estimation?," MPRA Paper 28259, University Library of Munich, Germany.
  13. Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  14. David Ardia & Lennart Hoogerheide, 2013. "GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-047/III, Tinbergen Institute.
  15. Hoogerheide, Lennart F. & Ardia, David & Corré, Nienke, 2012. "Density prediction of stock index returns using GARCH models: Frequentist or Bayesian estimation?," Economics Letters, Elsevier, Elsevier, vol. 116(3), pages 322-325.
  16. Franc Klaassen, 2011. "Identifying the Weights in Exchange Market Pressure," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-020/2, Tinbergen Institute.

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