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Keywords:

  • EGARCH model;
  • generalized error distribution;
  • Markov chain Monte Carlo method;
  • value-at-risk;
  • skewed Student-t;
  • market risk charge;
  • global financial crisis

ABSTRACT

Value-at-risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student-t, skewed-t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1-day horizon, models with skewed-t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti-conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.