摘要：This paper extends the threshold stochastic volatility (THSV) model specification proposed in So et al. (2002) and Chen et al. (2008) by incorporating thick-tails in the mean equation innovation using the scale mixture of normal distributions (SMN). A Bayesian Markov Chain Monte Carlo algorithm is developed to estimate all the parameters and latent variables. Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting via a computational Bayesian framework are considered. The MCMC-based method exploits a mixture representation of the SMN distributions. The proposed methodology is applied to daily returns of indexes from BM&F BOVESPA (BOVESPA), Buenos Aires Stock Exchange (MERVAL), Mexican Stock Exchange (MXX) and the Standar & Poors 500 (SP500). Bayesian model selection criteria reveals that there is a significant improvement in model fit for the returns of the data considered here, by using the THSV model with slash distribution over the usual normal and Student-t models. Empirical results show that the skewness can improve VaR and ES forecasting in comparison with the normal and Student-t models.
其他摘要：This paper extends the threshold stochastic volatility (THSV) model specification proposed in So et al. (2002) and Chen et al. (2008) by incorporating thick-tails in the mean equation innovation using the scale mixture of normal distributions (SMN). A Bayesian Markov Chain Monte Carlo algorithm is developed to estimate all the parameters and latent variables. Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting via a computational Bayesian framework are considered. The MCMC-based method exploits a mixture representation of the SMN distributions. The proposed methodology is applied to daily returns of indexes from BM&F BOVESPA (BOVESPA), Buenos Aires Stock Exchange (MERVAL), Mexican Stock Exchange (MXX) and the Standar & Poors 500 (SP500). Bayesian model selection criteria reveals that there is a significant improvement in model fit for the returns of the data considered here, by using the THSV model with slash distribution over the usual normal and Student-t models. Empirical results show that the skewness can improve VaR and ES forecasting in comparison with the normal and Student-t models.
关键词：Expected shortfall; Markov chain Monte Carlo; Non linear state space models; Scale mixtures
of normal distributions; Stochastic volatility; Threshold; Value-at-Risk.
其他关键词：MMarkov chain Monte Carlo;Non linear state space models;Scale mixtures of normal distributions;Stochastic volatility;Threshold;Value-at-Risk;Expected shortfall
