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MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model

Author

Listed:
  • Cappuccio Nunzio

    () (University of Padova)

  • Lubian Diego

    () (University of Verona, Italy)

  • Raggi Davide

    () (Università degli Studi di Verona)

Abstract

In this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails.

Suggested Citation

  • Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
  • Handle: RePEc:bpj:sndecm:v:8:y:2004:i:2:n:6
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    References listed on IDEAS

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    1. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    3. Neil Shephard & Siddhartha Chib, 1998. "Markov Chain Monte Carlo methods for Generalized Stochastic Volatility Models," Economics Series Working Papers 1998-W21, University of Oxford, Department of Economics.
    4. C.S. Forbes & G.M. Martin & J. Wright, 2002. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices," Monash Econometrics and Business Statistics Working Papers 2/02, Monash University, Department of Econometrics and Business Statistics.
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    Citations

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    Cited by:

    1. Kaufmann Sylvia & Scheicher Martin, 2006. "A Switching ARCH Model for the German DAX Index," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-37, December.
    2. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2014. "Score driven asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws142618, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Genya Kobayashi, 2016. "Skew exponential power stochastic volatility model for analysis of skewness, non-normal tails, quantiles and expectiles," Computational Statistics, Springer, vol. 31(1), pages 49-88, March.
    5. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    6. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science, revised Aug 2014.
    7. Ehlers, Ricardo S., 2012. "Computational tools for comparing asymmetric GARCH models via Bayes factors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 858-867.
    8. Patricia Lengua & Cristian Bayes & Gabriel Rodríguez, 2015. " A Stochastic Volatility Model with GH Skew Student’s t-Distribution: Application to Latin-American Stock Returns," Documentos de Trabajo / Working Papers 2015-405, Departamento de Economía - Pontificia Universidad Católica del Perú.
    9. Tsiotas, Georgios, 2012. "On generalised asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 151-172, January.
    10. Rydlewski, Jerzy P. & Snarska, Małgorzata, 2014. "On geometric ergodicity of skewed—SVCHARME models," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 192-197.

    More about this item

    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
    • G1 - Financial Economics - - General Financial Markets

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