Threshold Stochastic Volatility Models with Heavy Tails: A Bayesian Approach - Abanto-Valle, Carlos A.; Garrafa-Aragón, Hernán B. (Pontificia Universidad Católica del Perú. Fondo Editorial, 2019)
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.
Keywords: MMarkov chain Monte Carlo; Non linear state space models; Scale mixtures of normal distributions; Stochastic volatility; Threshold; Value-at-Risk; Expected shortfall; Modelos de volatilidad; https://purl.org/pe-repo/ocde/ford#5.02.01