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Stochastic volatility with leverage: fast likelihood inference

  • Yasuhiro Omori

    (University of Tokyo)

  • Siddhartha Chib

    (Washington University)

  • Neil Shephard

    ()

    (Nuffield College, University of Oxford, UK)

  • Jouchi Nakajima

    (University of Tokyo)

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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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
Contact details of provider: Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  2. 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, vol. 2(1), pages 107-160.
  3. Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series 2000mf02, Oxford Financial Research Centre.
  4. 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.
  5. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  6. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
  7. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Series Working Papers 2003-W12, University of Oxford, Department of Economics.
  8. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
  9. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
  11. 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.
  12. 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, vol. 39(4), pages 863-83, November.
  13. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  14. Ronald J. Mahieu & Peter C. Schotman, 1998. "An empirical application of stochastic volatility models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 333-360.
  15. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
  16. 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.
  17. 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.
  18. 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.
  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, vol. 63(2), pages 167-241.
  20. 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.
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