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Stochastic Volatility with Leverage: Fast Likelihood Inference

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Author Info
Yasuhiro Omori (Faculty of Economics, University of Tokyo)
Siddhartha Chib (Olin School of Business, Washington University)
Neil Shephard (Nuffield College, Oxford)
Jouchi Nakajima (Faculty of Economics, University of Tokyo)

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Abstract

Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which is known to be important in applications. Despite this, their basic method has been extensively used in the financial economics literature and more recently in macroeconometrics. In this paper we show how the basic approach can be extended in a novel way to stochastic volatility models with leverage without altering the essence of the original approach. Several illustrative examples are provided.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-297.

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Length: 24 pages
Date of creation: Aug 2004
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Handle: RePEc:tky:fseres:2004cf297

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  1. 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.
  2. 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. [Downloadable!]
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  3. Stroud J.R. & Muller P. & Polson N.G., 2003. "Nonlinear State-Space Models With State-Dependent Variances," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 377-386, January. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. 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.
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  7. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Econometric Society 2004 Far Eastern Meetings 506, Econometric Society.
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  8. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Papers 2003-W12, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  9. 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. [Downloadable!] (restricted)
  10. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  11. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
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  12. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January. [Downloadable!] (restricted)
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  13. 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.
  14. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Oxford University Press for Biometrika Trust, vol. 89(3), pages 603-616, August.
  15. 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. [Downloadable!]
  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Malik, Sheheryar & Pitt, Michael K, 2009. "Modelling Stochastic Volatility with Leverage and Jumps : A Simulated Maximum Likelihood Approach via Particle Filtering," The Warwick Economics Research Paper Series (TWERPS) 897, University of Warwick, Department of Economics. [Downloadable!]
  2. Jouchi Nakajima & Munehisa Kasuya & Toshiaki Watanabe, 2009. "Bayesian Analysis of Time-Varying Parameter Vector Autoregressive Model for the Japanese Economy and Monetary Policy," IMES Discussion Paper Series 09-E-13, Institute for Monetary and Economic Studies, Bank of Japan. [Downloadable!]
  3. Jouchi Nakajima, 2008. "EGARCH and Stochastic Volatility: Modeling Jumps and Heavy-tails for Stock Returns," IMES Discussion Paper Series 08-E-23, Institute for Monetary and Economic Studies, Bank of Japan. [Downloadable!]
  4. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Fulvia Focker & Umberto Triacca, 2006. "A new proxy of the average volatility of a basket of returns: A Monte Carlo study," Economics Bulletin, Economics Bulletin, vol. 3(15), pages 1-14. [Downloadable!]
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