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Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets

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Author Info

  • Gerlach, Richard H.
  • Chen, Cathy W. S.
  • Chan, Nancy Y. C.

Abstract

Recently, Bayesian solutions to the quantile regression problem, via the likelihood of a Skewed-Laplace distribution, have been proposed. These approaches are extended and applied to a family of dynamic conditional autoregressive quantile models. Popular Value at Risk models, used for risk management in finance, are extended to this fully nonlinear family. An adaptive Markov chain Monte Carlo sampling scheme is adapted for estimation and inference. Simulation studies illustrate favourable performance, compared to the standard numerical optimization of the usual nonparametric quantile criterion function, in finite samples. An empirical study generating Value at Risk forecasts for ten major financial stock indices finds significant nonlinearity in dynamic quantiles and evidence favoring the proposed model family, for lower level quantiles, compared to a range of standard parametric volatility models, a semi-parametric smoothly mixing regression and some nonparametric risk measures, in the literature.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 29 (2011)
Issue (Month): 4 ()
Pages: 481-492

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Handle: RePEc:bes:jnlbes:v:29:i:4:y:2011:p:481-492

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Cited by:
  1. Richard Gerlach & Zudi Lu & Hai Huang, 2013. "Exponentially Smoothing the Skewed Laplace Distribution for Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 534-550, 09.
  2. Chen, C.W.S. & Gerlach, R. & Hwang, B.B.K. & McAleer, M.J., 2011. "Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intraday Range," Econometric Institute Research Papers EI 2011-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Huarng, Kun-Huang & Yu, Tiffany Hui-Kuang, 2014. "A new quantile regression forecasting model," Journal of Business Research, Elsevier, vol. 67(5), pages 779-784.
  4. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
  5. Liu, Xiaochun, 2013. "Markov-Switching Quantile Autoregression," MPRA Paper 55800, University Library of Munich, Germany.
  6. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
  7. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
  8. Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.

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