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Computational Economics

, Volume 53, Issue 3, pp 1153–1164 | Cite as

Bayesian Testing for Leverage Effect in Stochastic Volatility Models

  • Jin-Yu Zhang
  • Zhong-Tian Chen
  • Yong LiEmail author
Article
  • 747 Downloads

Abstract

Stochastic volatility models have been widely appreciated to model the time-varying volatility in empirical finance. In practice, whether or not there is leverage effect in asset time series is one of important stylized facts. In this paper, in the context of the stochastic volatility models, the main purpose is to develop a Bayesian approach for testing the leverage effect. The performance of the developed procedure is illustrated by the simulation studies and two empirical examples.

Keywords

Bayes factor \(\chi ^2\) test Leverage effect Markov chain Monte Carlo (MCMC) Stochastic volatility models 

JEL Classification

C11 C12 G12 

References

  1. Black, F. (1976). Studies of stock market volatility changes. In Proceedings of the American Statistical Association, business and economic statistics section (pp. 177–81).Google Scholar
  2. Christie, A. A. (1982). The stochastic behavior of common stock variances. Journal of Financial Economics, 10, 407–432.CrossRefGoogle Scholar
  3. Dempster, A., Larid, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of Royal Statistical Society. Series B. Statistical Methodology, 39, 1–38.Google Scholar
  4. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1008.CrossRefGoogle Scholar
  5. Harvey, A. C., Ruiz, E., & Shephard, N. (1994). Multivariate stochastic variance models. The Review of Economic Studies, 61(2), 247–264.CrossRefGoogle Scholar
  6. Jacquier, E., Polson, N. G., & Rossi, P. E. (1994). Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics, 12, 371–389.Google Scholar
  7. Jacquier, E., Polson, N. G., & Rossi, P. E. (2004). Bayesian analysis of stochastic variance models with fat-tails and correlated errors. Journal of Econometrics, 12, 371–389.Google Scholar
  8. Kass, R. E., & Raftery, A. E. (1995). Bayes factor. Journal of the American Statistical Association, 90, 773–795.CrossRefGoogle Scholar
  9. Kim, S., Shephard, N., & Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic studies, 65, 361–393.CrossRefGoogle Scholar
  10. Li, Y., & Yu, J. (2012). Bayesian hypothesis testing in latent variable models. Journal of Econometrics, 166, 237–246.CrossRefGoogle Scholar
  11. Li, Y., & Zhang, J. (2014). Bayesian testing for jumps in stochastic volatility models with correlated jumps. Quantitative Finance, 14, 1693–1700.CrossRefGoogle Scholar
  12. Li, Y., Liu, X. B., & Yu, J. (2015). A Bayesian Chi-squared test for hypothesis testing. Journal of Econometrics, 189(1), 54–69.CrossRefGoogle Scholar
  13. Li, Y., Zeng, T., & Yu, J. (2014). A new approach to Bayesian hypothesis testing. Journal of Econometrics, 178, 602–612.CrossRefGoogle Scholar
  14. Liu, X. B., & Li, Y. (2014). Bayesian testing volatility persistence in stochastic volatility models with jumps. Quantitative Finance, 14, 1415–1426.CrossRefGoogle Scholar
  15. Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45(1–2), 239–265.CrossRefGoogle Scholar
  16. Meyer, R., & Yu, J. (2000). BUGS for a Bayesian analysis of stochastic volatility models. Econometrics Journal, 3, 198–215.CrossRefGoogle Scholar
  17. Shephard, N. (1996). Statistical aspects of ARCH and stochastic volatility. Monographs on Statistics and Applied Probability, 65, 1–68.Google Scholar
  18. So, M. K. P., & Li, W. K. (1999). Bayesian unit-root testing in stochastic volatility models. Journal of Business and Economic Statistics, 17(4), 491–496.Google Scholar
  19. Spiegelhalter, D. J., & Best, N. G. (2003). Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling. Statist in Medicine, 22, 3687–3709.CrossRefGoogle Scholar
  20. Tanner, T. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528–550.CrossRefGoogle Scholar
  21. Yu, J. (2005). On leverage in a stochastic volatility model. Journal of Econometrics, 127, 165–178.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Software Institute, Nanjing UniversityNanjingPeople’s Republic of China
  2. 2.Department of Economics, Duke UniversityDurhamUSA
  3. 3.Hanqing Advanced Institute of Economics and FinanceRenmin University of ChinaBeijingPeople’s Republic of China

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