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Employing Bayesian Forecasting of Value-at-Risk to Determine an Appropriate Model for Risk Management

Listed author(s):
  • CHEN, Cathy W.S.
  • WENG, Monica M.C.
  • WATANABE, Toshiaki

To allow for a higher degree of flexibility in model parameters, we propose a general and time-varying nonlinear smooth transition (ST) heteroskedastic model with a second-order logistic function of varying speed in the mean and variance. This paper evaluates the performance of Value-at-Risk (VaR) measures in a class of risk models, specially focusing on three distinct ST functions with GARCH structures: first- and second-order logistic functions, and the exponential function. The likelihood function is non-differentiable in terms of the threshold values and delay parameter. We employ Bayesian Markov chain Monte Carlo sampling methods to update the estimates and quantile forecasts. The proposed methods are illustrated using simulated data and an empirical study. We estimate VaR forecasts for the proposed models alongside some competing asymmetric models with skew and fat-tailed error probability distributions, including realized volatility models. To evaluate the accuracy of VaR estimates, we implement two loss functions and three backtests. The results show that the ST model with a second-order logistic function and skew Student’s t error is a worthy choice at the 1% level, when compared to a range of existing alternatives.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/27665/3/070_hiasDP-E-16.pdf
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Paper provided by Hitotsubashi Institute for Advanced Study, Hitotsubashi University in its series Discussion paper series with number HIAS-E-16.

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Length: 35 p.
Date of creation: 08 Dec 2015
Handle: RePEc:hit:hiasdp:hias-e-16
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  1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  2. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
  3. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
  4. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
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  6. 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.
  7. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  8. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
  9. Jansen, Eilev S. & Teräsvirta, Timo, 1995. "Testing Parameter Constancy and super Exogeneity in Econometric Equations," SSE/EFI Working Paper Series in Economics and Finance 53, Stockholm School of Economics.
  10. 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.
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  12. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, 09.
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  15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  16. Richard H. Gerlach & Cathy W. S. Chen & Nancy Y. C. Chan, 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 481-492, October.
  17. Masato Ubukata & Toshiaki Watanabe, 2014. "Pricing Nikkei 225 Options Using Realized Volatility," The Japanese Economic Review, Japanese Economic Association, vol. 65(4), pages 431-467, December.
  18. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  19. Chen, Cathy W. S. & Chiang, Thomas C. & So, Mike K. P., 2003. "Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model," Journal of Economics and Business, Elsevier, vol. 55(5-6), pages 487-502.
  20. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
  21. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  22. Lin, Edward M.H. & Chen, Cathy W.S. & Gerlach, Richard, 2012. "Forecasting volatility with asymmetric smooth transition dynamic range models," International Journal of Forecasting, Elsevier, vol. 28(2), pages 384-399.
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