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Leverage, heavy-tails and correlated jumps in stochastic volatility models

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  • Jouchi Nakajima

    (Bank of Japan)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract

This paper proposes the efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps. We illustrate our method using simulated data and analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2007/2007cf514.pdf
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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-514.

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Length: 34 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:tky:fseres:2007cf514

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References

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  1. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
  2. 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.
  3. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  4. Bartolucci, F. & De Luca, G., 2003. "Likelihood-based inference for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 445-449, March.
  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 & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  7. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-89, July.
  8. Siddhartha Chib & Ivan Jeliazkov, 2005. "Accept-reject Metropolis-Hastings sampling and marginal likelihood estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 30-44.
  9. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, 04.
  10. 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.
  11. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  12. 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.
  13. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
  14. 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.
  15. Masahito Kobayashi, 2005. "Testing for Volatility Jumps in the Stochastic Volatility Process," Asia-Pacific Financial Markets, Springer, vol. 12(2), pages 143-157, June.
  16. 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.
  17. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
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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," CIRJE F-Series CIRJE-F-746, CIRJE, Faculty of Economics, University of Tokyo.
  2. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
  3. Jouchi Nakajima & Yasuhiro Omori, 2009. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student's t-distribution," CARF F-Series CARF-F-199, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  4. Luc Bauwens & Jeroen V.K. Rombouts, 2009. "On Marginal Likelihood Computation in Change-point Models," Cahiers de recherche 0942, CIRPEE.
  5. 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.
  6. António Alberto Santos & João Andrade, 2014. "Stochastic Volatility Estimation with GPU Computing," GEMF Working Papers 2014-10, GEMF - Faculdade de Economia, Universidade de Coimbra.
  7. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models," CIRJE F-Series CIRJE-F-738, CIRJE, Faculty of Economics, University of Tokyo.
  8. Shinichiro Shirota & Takayuki Hizu & Yasuhiro Omori, 2013. "Realized Stochastic Volatility with Leverage and Long Memory," CIRJE F-Series CIRJE-F-880, CIRJE, Faculty of Economics, University of Tokyo.
  9. 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.

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