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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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Author Info

  • Jouchi Nakajima

    (Department of Statistical Science, Duke University)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

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-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.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/224.pdf
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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-215.

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Length: 33 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:cfi:fseres:cf215

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References

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  1. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic volatility with leverage: fast likelihood inference," Economics Papers 2004-W19, Economics Group, Nuffield College, University of Oxford.
  2. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  3. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  4. 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.
  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. 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. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
  8. 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.
  9. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  10. 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.
  11. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201.
  12. 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.
  13. 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.
  14. 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.
  15. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
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Cited by:
  1. Joshua C C Chan, 2012. "Moving Average Stochastic Volatility Models with Application to Inflation Forecast," ANU Working Papers in Economics and Econometrics 2012-591, Australian National University, College of Business and Economics, School of Economics.

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