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Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution

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  • Jouchi Nakajima
  • Yasuhiro Omori

Abstract

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailness as well as leverage effects. An efficient Markov chain Monte Carlo estimation method is described exploiting a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as a mixing distribution. The proposed method is illustrated using simulated data, daily TOPIX and S&P500 stock returns. The model comparison for stock returns is conducted based on the marginal likelihood in the empirical study. The strong evidence of the leverage and asymmetric heavy-tailness is found in the stock returns. Further, the prior sensitivity analysis is conducted to investigate whether obtained results are robust with respect to the choice of the priors.

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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd09-124.pdf
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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd09-124.

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Date of creation: Mar 2010
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Handle: RePEc:hst:ghsdps:gd09-124

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Keywords: generalized hyperbolic skew Student's t-distribution; Markov chain Monte Carlo; Mixing distribution; State space model; Stochastic volatility; Stock returns;

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References

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  1. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2009. "Estimating stochastic volatility models using daily returns and realized volatility simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2404-2426, April.
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  4. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors," CIRJE F-Series CIRJE-F-700, CIRJE, Faculty of Economics, University of Tokyo.
  5. Jouchi Nakajima & Yasuhiro Omori, 2007. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," CIRJE F-Series CIRJE-F-514, CIRJE, Faculty of Economics, University of Tokyo.
  6. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
  7. Raggi, Davide & Bordignon, Silvano, 2006. "Comparing stochastic volatility models through Monte Carlo simulations," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1678-1699, April.
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  12. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
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Citations

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Cited by:
  1. Tsunehiro Ishihara & Yasuhiro Omori, 2010. "Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors," CARF F-Series CARF-F-221, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
  3. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2013. "News impact curve for stochastic volatility models," Economics Letters, Elsevier, vol. 120(1), pages 130-134.
  4. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
  5. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
  6. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  7. Cabral, Celso Rômulo Barbosa & da-Silva, Cibele Queiroz & Migon, Helio S., 2014. "A dynamic linear model with extended skew-normal for the initial distribution of the state parameter," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 64-80.

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