Threshold Stochastic Volatility Models with Heavy Tails: A Bayesian Approach

  • Carlos A. Abanto-Valle Universidad de Rio de Janeiro

    Department of Statistics, Federal University of Rio de Janeiro, Caixa Postal 68530, CEP: 21945-970, Rio de Janeiro, Brazil.

  • Hernán B. Garrafa-Aragón Universidad Nacional de Ingeniería

    Escuela de Ingeniería Estadística de la Universidad Nacional de Ingenieria, Lima, Perú.

Keywords: MMarkov chain Monte Carlo, Non linear state space models, Scale mixtures of normal distributions, Stochastic volatility, Threshold, Value-at-Risk, Expected shortfall


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.


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How to Cite
Abanto-Valle, C. A., & Garrafa-Aragón, H. B. (2019). Threshold Stochastic Volatility Models with Heavy Tails: A Bayesian Approach. Economia, 42(83), 32-53.