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Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models

  • Jouchi Nakajima

    (Department of Statistical Science, Duke University)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

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-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf738.pdf
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-738.

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Length: 33pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:tky:fseres:2010cf738
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  1. Chris M Strickland & Gael Martin & Catherine S Forbes, 2006. "Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models," Monash Econometrics and Business Statistics Working Papers 22/06, Monash University, Department of Econometrics and Business Statistics.
  2. 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.
  3. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  4. Jun Yu, 2004. "On leverage in a stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 497, Econometric Society.
  5. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
  6. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
  7. Makoto Takahashi & Yasuhiro Omori & Toshiaki Watanabe, 2007. "Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously," CIRJE F-Series CIRJE-F-515, CIRJE, Faculty of Economics, University of Tokyo.
  8. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  9. 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.
  10. Yasuhiro Omori & Toshiaki Watanabe, 2007. "Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models," CIRJE F-Series CIRJE-F-507, CIRJE, Faculty of Economics, University of Tokyo.
  11. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the "t"-distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174.
  12. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201.
  13. Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 44-54, January.
  14. 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.
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