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Threshold Stochastic Volatility Models with Heavy Tails:A Bayesian Approach

Author

Listed:
  • Carlos A. Abanto-Valle

    (Department of Statistics, Federal University of Rio de Janeiro)

  • Hernán B. Garrafa-Aragón

    (Escuela de Ingeniería Estadística de la Universidad Nacional de Ingeniería, Lima, Perú)

Abstract

This paper extends the threshold stochastic volatility (THSV) model specification proposed in Soet 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) andExpected Shortfall (ES) forecasting via a computational Bayesian framework are considered. TheMCMC-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), BuenosAires 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 improveVaR and ES forecasting in comparison with the normal and Student-t models.

Suggested Citation

  • Carlos A. Abanto-Valle & Hernán B. Garrafa-Aragón, 2019. "Threshold Stochastic Volatility Models with Heavy Tails:A Bayesian Approach," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 42(83), pages 32-53.
    • Handle: RePEc:pcp:pucrev:y:2019:i:83:p:32-53
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    References listed on IDEAS

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    More about this item

    Keywords

    Expected shortfall; Markov chain Monte Carlo; Non linear state space models; Scale mixtures of normal distributions; Stochastic volatility; Threshold; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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