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A Switching ARCH Model for the German DAX Index

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Author Info
Sylvia Kaufmann (Oesterreichische Nationalbank)
Martin Scheicher (European Central Bank)

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Abstract

This paper estimates a switching autoregressive conditional heteroskedastic time series model for returns on the daily German stock market index. Volatility clustering is captured by persistent periods of different volatility levels and by the dependence on past innovations. We introduce a leverage term to model the asymmetric response of volatility to shocks. Model specification and estimation is performed within a Bayesian framework using Markov Chain Monte Carlo simulation methods. Model diagnostics document a good fit of the switching ARCH model. The persistence of shocks in volatility coming from the autoregressive conditional part of the variance is considerably lower than that obtained using a GARCH(1,1) model. Our volatility estimate closely follows market implied volatility. When we compare the forecasting performance, switching ARCH turns out to be an unbiased estimator of realized volatility. Nevertheless, over all forecast horizons, model-based volatility forecasts do not add information about future volatility. Up to a 7-day horizon, market implied volatility already contains nearly all information.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 10 (2006)
Issue (Month): 4 ()
Pages: 1290-1290
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Handle: RePEc:bep:sndecm:10:2006:4:1290-1290

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Related research
Keywords: Bayesian model diagnostics forecast evaluation Markov chain Monte Carlo methods switching ARCH

References listed on IDEAS
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  1. Stapf, Jelena & Werner, Thomas, 2003. "How wacky is the DAX? The changing structure of German stock market volatility," Discussion Paper Series 1: Economic Studies 2003,18, Deutsche Bundesbank, Research Centre. [Downloadable!]
  2. Craig, Ben R & Glatzer, Ernst & Keller, Joachim & Scheicher, Martin, 2003. "The Forecasting Performance of German Stock Option Densities," Discussion Paper Series 1: Economic Studies 2003,17, Deutsche Bundesbank, Research Centre. [Downloadable!]
  3. Kalimipalli, Madhu & Susmel, Raul, 2004. "Regime-switching stochastic volatility and short-term interest rates," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 309-329, June. [Downloadable!] (restricted)
  4. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May. [Downloadable!] (restricted)
  5. Ser-Huang Poon & Clive W. J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  7. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November. [Downloadable!] (restricted)
  8. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, 06. [Downloadable!] (restricted)
  9. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  10. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November. [Downloadable!] (restricted)
  11. Ben Craig & Ernst Glatzer & Joachim Keller & Martin Scheicher, 2003. "The forecasting performance of German stock option densities," Working Paper 0312, Federal Reserve Bank of Cleveland. [Downloadable!]
  12. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
    Other versions:
  13. 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. [Downloadable!] (restricted)
  14. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(2), pages 1211-1211. [Downloadable!] (restricted)
    Other versions:
  15. Sylvia Fruhwirth-Schnattaer & Sylvia Kaufmann, 2000. "Bayesian Analysis of Switching ARCH Models," Econometric Society World Congress 2000 Contributed Papers 1381, Econometric Society. [Downloadable!]
  16. Maheu, John M & McCurdy, Thomas H, 2000. "Identifying Bull and Bear Markets in Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 100-112, January.
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