Abstract
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.
Highlights
A large literature in financial econometrics has documented many stylized facts for financial asset returns
1, we plot the absolute returns, the posterior smoothed mean of e ht 2 obtained from the MCMC output for the SV-N model and the threshold stochastic volatility (THSV)-S model, which are the worst and the best model fit according to the WAIC criterion, for BOVESPA, MERVAL, Mexican Stock Exchange (MXX) and Standar & Poors 500 (SP500) returns
We have proposed the threshold stochastic volatility model with scale mixture of normal distributions (THSV-SMN) errors as an alternative to the normal assumption in the conditional distribution of the returns
Summary
A large literature in financial econometrics has documented many stylized facts for financial asset returns. We extend the setup of So et al (2002), Chen et al (2008) and Abanto et al (2010), in order to take account simultaneously for heavy-tails of the returns and volatility asymmetries, by considering the THSV model with SMN distributions. We refer to this generalization as THSV-SMN distributions. In Appendices A and B, we show some derivations for sampling from the full conditionals of parameters and states, respectively
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