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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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  1. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  2. HOOGERHEIDE, Lennart F. & VAN DIJK, Herman K. & VAN OEST, Rutger D., 2007. "Simulation based Bayesian econometric inference: principles and some recent computational advances," CORE Discussion Papers 2007015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  4. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  5. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
  6. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  7. van Dijk, H. K. & Kloek, T., 1980. "Further experience in Bayesian analysis using Monte Carlo integration," Journal of Econometrics, Elsevier, vol. 14(3), pages 307-328, December.
  8. Bauwens, L. & Lubrano, M., . "Bayesian inference on GARCH models using the Gibbs sampler," CORE Discussion Papers RP -1307, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  10. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  11. Nakatsuma, Teruo, 2000. "Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach," Journal of Econometrics, Elsevier, vol. 95(1), pages 57-69, March.
  12. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
  13. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  14. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  16. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
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Citations

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Cited by:
  1. 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, vol. 56(11), pages 3498-3516.
  2. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, . "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, American Statistical Association, vol. 29(i03).
  3. 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 11-004/4, Tinbergen Institute.
  4. 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 11-131/4, 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 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  6. 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.
  7. Franc Klaassen, 2011. "Identifying the Weights in Exchange Market Pressure," Tinbergen Institute Discussion Papers 11-020/2, Tinbergen Institute.
  8. Hoogerheide, Lennart F. & Ardia, David & Corré, Nienke, 2012. "Density prediction of stock index returns using GARCH models: Frequentist or Bayesian estimation?," Economics Letters, Elsevier, vol. 116(3), pages 322-325.
  9. 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 13-047/III, Tinbergen Institute.
  10. 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 12-026/4, Tinbergen Institute.
  11. 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, vol. 82(1), pages 71-102, 01.
  12. 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 08-062/4, Tinbergen Institute, revised 15 Dec 2008.
  13. 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 11-131/4, Tinbergen Institute.
  14. 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 12-026/4, Tinbergen Institute.
  15. 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 11-004/4, Tinbergen Institute.
  16. 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 13-060/III, Tinbergen Institute, revised 06 Mar 2014.

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