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Stochastic volatility with leverage: fast likelihood inference

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Author Info

  • Yasuhiro Omori

    (University of Tokyo)

  • Siddhartha Chib

    (Washington University)

  • Neil Shephard

    ()
    (Nuffield College, University of Oxford, UK)

  • Jouchi Nakajima

    (University of Tokyo)

Abstract

Kim, Shephard and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a very fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which limited its scope for applications. Despite this, their basic method has been extensively used in financial economics literature and more recently in macroeconometrics. In this paper we show how to overcome the limitation of this analysis so that the essence of the Kim, Shephard and Chib (1998) can be used to deal with the leverage effect, greatly extending the applicability of this method. Several illustrative examples are provided.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2004/w19/mixture28.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2004-W19.

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Length: 23 pages
Date of creation: 22 Aug 2004
Date of revision:
Handle: RePEc:nuf:econwp:0419

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: Leverage effect; Markov chain Monte Carlo; Mixture sampler; Stochastic volatility; Stock returns.;

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References

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  1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers, Toulouse - GREMAQ 95.400, Toulouse - GREMAQ.
  2. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers, Singapore Management University, School of Economics 13-2004, Singapore Management University, School of Economics.
  3. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(3), pages 603-616, August.
  4. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers, Economics Group, Nuffield College, University of Oxford 146, Economics Group, Nuffield College, University of Oxford.
  5. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/1392, Paris Dauphine University.
  6. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  7. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  8. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  9. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers, Duke University, Department of Economics 02-03, Duke University, Department of Economics.
  10. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, Elsevier, vol. 71(1), pages 113-141, January.
  11. Mahieu, R.J. & Schotman, P.C., 1998. "An empirical application of stochastic volatility models," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-3131739, Tilburg University.
  12. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 217-252.
  13. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 2(1), pages 107-160.
  14. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  15. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  16. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 281-316, June.
  17. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  18. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(4), pages 429-34, October.
  19. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 63(2), pages 167-241.
  20. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
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Citations

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Cited by:
  1. Fulvia Focker & Umberto Triacca, 2006. "A new proxy of the average volatility of a basket of returns: A Monte Carlo study," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-14.
  2. Hans J. Skaug & Jun Yu, 2009. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers, Singapore Management University, School of Economics 15-2009, Singapore Management University, School of Economics.
  3. Tsunehiro Ishihara & Yasuhiro Omori & Manabu Asai, 2013. "Matrix Exponential Stochastic Volatility with Cross Leverage," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-904, CIRJE, Faculty of Economics, University of Tokyo.
  4. Yuriy Kitsul & Jonathan H. Wright, 2012. "The Economics of Options-Implied Inflation Probability Density Functions," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 600, The Johns Hopkins University,Department of Economics.
  5. Toshitaka Sekine, 2006. "Time-varying exchange rate pass-through: experiences of some industrial countries," BIS Working Papers 202, Bank for International Settlements.
  6. Fruhwirth-Schnatter, Sylvia & Fruhwirth, Rudolf, 2007. "Auxiliary mixture sampling with applications to logistic models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 51(7), pages 3509-3528, April.

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