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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 17, Issue 5

Issues

Stochastic volatility model with regime-switching skewness in heavy-tailed errors for exchange rate returns

Jouchi Nakajima
  • Corresponding author
  • Department of Statistical Science (currently, Monetary Affairs Department, Bank of Japan), Duke University
  • Email
  • Other articles by this author:
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Published Online: 2013-07-13 | DOI: https://doi.org/10.1515/snde-2012-0021

Abstract

A Bayesian analysis of the stochastic volatility model with regime-switching skewness in heavy-tailed errors is proposed using a generalized hyperbolic (GH) skew Student’s t-distribution. The skewness parameter is allowed to shift according to a first-order Markov switching process. We summarize Bayesian methods for model fitting and discuss analyses of exchange rate return time series. Empirical results show that interpretable regime-switching skewness can improve model fit and Value-at-Risk performance in a comparison against several other SV models with constant skewness or jump diffusions.

This article offers supplementary material which is provided at the end of the article.

Keywords: exchange rate return; generalized hyperbolic skew Student’s t-distribution; regime-switching skewness; stochastic volatility; Value-at-Risk

References

  • Aas, K., and I. H. Haff. 2006. “The Generalized Hyperbolic Skew Student’s t-Distribution.” Journal of Financial Econometrics 4: 275–309.CrossrefGoogle Scholar

  • Andersson, J. 2001. “On The Normal Inverse Gaussian Stochastic Volatility Model.” Journal of Business and Economic Statistics, 19: 44–54.Google Scholar

  • Andersen, T., L. Benzoni, and J. Lund. 2002. “An Empirical Investigation of Continuous-time Models for Equity Returns.” Journal of Finance 57: 1239–1284.CrossrefGoogle Scholar

  • Bakshi, G., C. Cao, and Z. Chen. 1997. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance 52: 2003–2049.CrossrefGoogle Scholar

  • Barndorff-Nielsen, O. E. 1977. “Exponentially Decreasing Distributions for the Logarithm of Particle Size.” Proceedings of the Royal Society of London, Series A 353: 401–419.Google Scholar

  • Barndorff-Nielsen, O. E. 1997. “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling.” Scandinavian Journal of Statistics 24: 1–13.CrossrefGoogle Scholar

  • Berg, A., R. Meyer, and J. Yu. 2004. “DIC as a Model Comparison Criterion for Stochastic Volatility Models.” Journal of Business and Economic Statistics 22: 107–120.Google Scholar

  • Black, F. 1976. “Studies of Stock Market Volatility Changes.” in Proceedings of the American Statistical Association, Business and Economic Statistics Section 177–181.Google Scholar

  • Carter, C. K., and R. Kohn. 1994. “On Gibbs Sampling for State Space Models.” Biometrika 81: 541–553.CrossrefGoogle Scholar

  • Chen, C. W. S., F. C. Liu, and M. K. P. So. 2008. “Heavy-tailed-Distributed Threshold Stochastic Volatility Models in Financial Time Series.” Australian and New Zealand Journal of Statistics 50: 29–51.Google Scholar

  • Chernov, M., A. R. Gallant, E. Ghysels, and G. Tauchen. 2003. “Alternative Models for Stock Price Dynamics.” Journal of Econometrics 116: 225–257.CrossrefGoogle Scholar

  • Chib, S. 1995. “Marginal Likelihood from the Gibbs Output.” Journal of the American Statistical Association 90: 1313–1321.Google Scholar

  • Chib, S. 1996. “Calculating Posterior Distributions and Modal Estimates in Markov Mixture Models.” Journal of Econometrics 75: 79–97.CrossrefGoogle Scholar

  • Chib, S. 1998. “Estimation and Comparison of Multiple Change-Point Models.” Journal of Econometrics 86: 221–241.CrossrefGoogle Scholar

  • Chib, S. 2001. “Markov chain Monte Carlo Methods: Computation and Inference.” In Handbook of Econometrics, edited by J. J. Heckman and E. Leamer. vol. 5, 3569–3649. Amsterdam: North-Holland.Google Scholar

  • Chib, S., and I. Jeliazkov. 2001. “Marginal Likelihood from the Metropolis-Hastings Output.” Journal of the American Statistical Association 96: 270–291.Google Scholar

  • Chib, S., F. Nardari, and N. Shephard. 2002. “Markov Chain Monte Carlo Methods for Stochastic Volatility Models.” Journal of Econometrics 108: 281–316.CrossrefGoogle Scholar

  • Christoffersen, P., and K. Jacobs. 2004. “Which GARCH Model for Option Valuation?” Management Science 50: 1204–1221.CrossrefGoogle Scholar

  • Das, S. R., and R. K. Sundaram. 1999. “Of Smiles and Smirks: A Term Structure Perspective.” Journal of Financial and Quantitative Analysis 34: 211–239.Google Scholar

  • Dennis, P., and S. Mayhew. 2002. “Risk-Neutral Skewness: Evidence from Stock Options.” Journal of Financial and Quantitative Analysis 37: 471–493.Google Scholar

  • de Jong, P. and N. Shephard. 1995. “The Simulation Smoother for Time series Models.” Biometrika 82: 339–350.CrossrefGoogle Scholar

  • Doornik, J. 2006. Ox: Object Oriented Matrix Programming. London: Timberlake Consultants Press.Google Scholar

  • Durbin, J., and S. J. Koopman. 2002. “Simple and Efficient Simulation Smoother for State Space Time Series Analysis.” Biometrika 89: 603–616.CrossrefGoogle Scholar

  • Durham, G. B. 2007. “SV Mixture Models with Application to S&P 500 Index Returns.” Journal of Financial Economics 85: 822–856.Google Scholar

  • Embrechts, P., R. Kaufmann, and P. Patie. 2004. “Strategic Long-term Financial Risks: Single Risk Factors.” Computational Optimization and Applications 32: 61–90.Google Scholar

  • Eraker, B. 2004. “Do Equity Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.” Journal of Finance 59: 1367–1403.CrossrefGoogle Scholar

  • Eraker, B., M. Johanners, and N. G. Polson. 2003. “The Impact of Jumps in Returns and Volatility.” Journal of Finance 53: 1269–1330.CrossrefGoogle Scholar

  • Gamerman, D., and H. F. Lopes. 2006. Markov Chain Monte Carlo. Stochastic Simulation for Bayesian Inference. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar

  • Geweke, J. 1992. “Evaluating the Accuracy of Sampling-based Approaches to the Calculation of Posterior Moments.” In Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, vol 4, 169–188. New York: Oxford University Press.Google Scholar

  • Geweke, J. 2005. Contemporary Bayesian Econometrics and Statistics. NJ: Wiley.Google Scholar

  • Ghysels, E., A. C. Harvey, and E. Renault. 2002. “Stochastic Volatility.” In Statistical Methods in Finance, edited by C. R. Rao and G. S. Maddala, 119–191. Amsterdam: North-Holland.Google Scholar

  • Hamilton, J. D. 1988. “Rational-Expectations Econometric Analysis of Changes in Regime: An Investigation of the Term Structure of Interest Rates.” Journal of Economic Dynamics and Control 12: 385–423.Google Scholar

  • Hamilton, J. D. 1989. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica 57: 357–384.CrossrefGoogle Scholar

  • Harvey, C. R., and A. Siddique. 1999. “Autoregressive Conditional Skewness.” Journal of Financial and Quantitative Analysis 34: 465–487.Google Scholar

  • Ishihara, T., and Y. Omori. 2008. “Markov Switching Asymmetric Stochastic Volatility Model with Application to TOPIX data: A Permutation Sampler Approach.” Gendai Finance 24: 75–100.Google Scholar

  • Jha, R., and M. Kalimipalli. 2010. “The Economic Significance of Conditional Skewness in Index Option Markets.” Journal of Futures Markets 30: 378–406.Google Scholar

  • Kalimipallia, M., and R. Susmel. 2004. “Regime-Switching Stochastic Volatility and Short-term Interest Rates.” Journal of Empirical Finance 65: 309–329.Google Scholar

  • Kim, C.-J., and C. Nelson. 1999. State-space models with regime switching. Cambridge, MA: MIT press.Google Scholar

  • Kim, C.-J., C. Nelson, and J. Piger. 2004. “The Less-Volatile U.S. Economy.” Journal of Business and Economic Statistics 22: 80–93.Google Scholar

  • Koop, G. 2003. Bayesian Econometrics. Chichester: Wiley.Google Scholar

  • Kupiec, P. 1995. “Techniques for Verifying the Accuracy of Risk Measurement Models.” Journal of Derivatives 2: 173–184.Google Scholar

  • Nakajima, J., and Y. Omori. 2009. “Leverage, Heavy-tails and Correlated Jumps in Stochastic Volatility Models.” Computational Statistics and Data Analysis 53: 2535–2553.Google Scholar

  • Nakajima, J., and Y. Omori. 2012. “Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed error Using GH Skew Student’s t-distribution.” Computational Statistics and Data Analysis 56: 3690–3704.Google Scholar

  • Nandi, S. 1998. “How Important is the Correlation Between Returns and Volatility in a Stochastic Volatility Model? Empirical Evidence from Pricing and hedging in the S&P 500 index options market.” Journal of Banking and Finance 5: 589–610.Google Scholar

  • Omori, Y., and T. Watanabe. 2008. “Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models.” Computational Statistics and Data Analysis 52: 2892–2910.Google Scholar

  • Omori, Y., S. Chib, N. Shephard, and J. Nakajima. 2007. “Stochastic Volatility with Leverage: Fast Likelihood Inference.” Journal of Econometrics 140: 425–449.CrossrefGoogle Scholar

  • Pastor, L., and R. Stambaugh. 2001. “The Equity Premium and Structural Breaks.” Journal of Finance 56: 1207–1239.CrossrefGoogle Scholar

  • Pitt, M., and N. Shephard. 1999. “Filtering via Simulation: Auxiliary Particle filter.” Journal of the American Statistical Association 94: 590–599.Google Scholar

  • Raggi, D., and S. Bordignon. 2006. “Comparing Stochastic Volatility Models Through Monte Carlo Simulations.” Computational Statistics and Data Analysis 50: 1678–1699.Google Scholar

  • Shephard, N. 2005. Stochastic Volatility: Selected Readings. Oxford: Oxford University Press.Google Scholar

  • Shephard, N., and M. Pitt. 1997. “Likelihood Analysis of Non-Gaussian Measurement Time Series.” Biometrika 84: 653–667.Google Scholar

  • Shibata, M., and T. Watanabe. 2005. “Bayesian Analysis of a Markov Switching Stochastic Volatility Model.” Journal of Japan Statistical Society 35: 205–219.Google Scholar

  • Silva, R. S., H. F. Lopes, and H. S. Migon. 2006. “The Extended Generalized Inverse Gaussian Distribution for Log-Linear and Stochastic Volatility Models.” Brazilian Journal of Probability and Statistics 20: 67–91.Google Scholar

  • Smith, D. R. 2002. “Markov-Switching and Stochastic Volatility Diffusion Models of Short-term Interest Rates.” Journal of Business and Economic Statistics 20: 183–197.Google Scholar

  • So, M. K. P., K. Lam, and W. K. Li. 1998. “A Stochastic Volatility Model with Markov Switching.” Journal of Business and Economic Statistics 16: 244–253.Google Scholar

  • Takahashi, M., Y. Omori, and T. Watanabe. 2009. “Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously.” Computational Statistics and Data Analysis 53: 2404–2426.Google Scholar

  • Wang, J. J. J., J. S. K. Chan, and S. T. B. Choy. 2011. “Stochastic Volatility Models with Leverage and Heavy-Tailed Distributions: A Bayesian Approach Using Scale Mixtures.” Computational Statistics and Data Analysis 55: 852–862.Google Scholar

  • Watanabe, T., and Y. Omori. 2004. “A Multi-move Sampler for Estimating Non-Gaussian Time Series Models: Comments on Shephard & Pitt (1997).” Biometrika 91: 246–248.CrossrefGoogle Scholar

  • Yu, J. 2005. “On Leverage in a Stochastic Volatility Model.” Journal of Econometrics 127: 165–178.CrossrefGoogle Scholar

About the article

Corresponding author: Jouchi Nakajima, Department of Statistical Science (currently, Monetary Affairs Department, Bank of Japan), Duke University, e-mail:


Published Online: 2013-07-13

Published in Print: 2013-12-01


Citation Information: Studies in Nonlinear Dynamics and Econometrics, Volume 17, Issue 5, Pages 499–520, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0021.

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