Advanced Search
MyIDEAS: Login to save this paper or follow this series

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Contents:

Author Info

  • Mark J Jensen
  • John M Maheu

Abstract

In this paper we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility, distribution with a infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet Process prior. This prior ensures a parsimonious, finite, posterior, mixture that bests represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-of-sample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive log-Bayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model forecasting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.economics.utoronto.ca/public/workingPapers/tecipa-453.pdf
File Function: Main Text
Download Restriction: no

Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-453.

as in new window
Length: Unknown pages
Date of creation: 20 Apr 2012
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-453

Contact details of provider:
Postal: 150 St. George Street, Toronto, Ontario
Phone: (416) 978-5283

Related research

Keywords: Bayesian nonparametrics; cumulative Bayes factor; Dirichlet process mixture; inï¬nite mixture model; leverage effect; marginal likelihood; MCMC; non-normal; stochastic volatility; volatility-return relationship;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. Mark J. Jensen, 2004. "Semiparametric Bayesian Inference of Long-Memory Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 895-922, November.
  2. Geert Bekaert & Guojun Wu, 1997. "Asymmetric Volatility and Risk in Equity Markets," NBER Working Papers 6022, National Bureau of Economic Research, Inc.
  3. Basu S. & Chib S., 2003. "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 224-235, January.
  4. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  5. Manabu Asai & Michael McAleer, 2009. "Multivariate stochastic volatility, leverage and news impact surfaces," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(2), pages 292-309, 07.
  6. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, American Economic Association, vol. 41(2), pages 478-539, June.
  7. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 69-87, January.
  8. Sanjiv R. Das & Rangarajan K. Sundaram, 1998. "Of Smiles and Smirks: A Term-Structure Perspective," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 98-024, New York University, Leonard N. Stern School of Business-.
  9. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  10. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, Elsevier, vol. 127(2), pages 165-178, August.
  11. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 425-449, October.
  12. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, Elsevier, vol. 122(1), pages 185-212, September.
  13. Mark J. Jensen & John M. Maheu, 2009. "Bayesian Semiparametric Stochastic Volatility Modeling," Working Paper Series, The Rimini Centre for Economic Analysis 23_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  14. Xilong Chen & Eric Ghysels, 2011. "News--Good or Bad--and Its Impact on Volatility Predictions over Multiple Horizons," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 24(1), pages 46-81, October.
  15. Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series, European Central Bank 0969, European Central Bank.
  16. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 3-29, September.
  17. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(4), pages 413-17, October.
  18. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  19. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  20. Geweke, John, 2001. "Bayesian econometrics and forecasting," Journal of Econometrics, Elsevier, Elsevier, vol. 100(1), pages 11-15, January.
  21. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(4), pages 407-432, December.
  22. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, Elsevier, vol. 162(2), pages 383-396, June.
  23. Geweke, John & Whiteman, Charles, 2006. "Bayesian Forecasting," Handbook of Economic Forecasting, Elsevier, Elsevier.
  24. 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.
  25. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Mark J Jensen & John M Maheu, 2012. "Bayesian semiparametric multivariate GARCH modeling," Working Papers, University of Toronto, Department of Economics tecipa-458, University of Toronto, Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:tor:tecipa:tecipa-453. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RePEc Maintainer).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.