Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture
AbstractIn 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 an 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 best 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 projecting 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.
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Bibliographic InfoPaper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2012-06.
Date of creation: 2012
Date of revision:
Other versions of this item:
- Mark J Jensen & John M Maheu, 2012. "Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture," Working Papers tecipa-453, University of Toronto, Department of Economics.
- Mark J. Jensen & John M. Maheu, 2012. "Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture," Working Paper Series 45_12, The Rimini Centre for Economic Analysis.
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
- NEP-ETS-2012-05-15 (Econometric Time Series)
- NEP-FOR-2012-05-15 (Forecasting)
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.:
- Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999.
"Of Smiles and Smirks: A Term Structure Perspective,"
Journal of Financial and Quantitative Analysis,
Cambridge University Press, vol. 34(02), pages 211-239, June.
- 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 98-024, New York University, Leonard N. Stern School of Business-.
- Hentschel, Ludger & Campbell, John, 1992.
"No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns,"
3220232, Harvard University Department of Economics.
- Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
- John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc.
- 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.
- Bekaert, Geert & Wu, Guojun, 2000.
"Asymmetric Volatility and Risk in Equity Markets,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(1), pages 1-42.
- Manabu Asai & Michael McAleer, 2009. "Multivariate stochastic volatility, leverage and news impact surfaces," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 292-309, 07.
- 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, vol. 24(1), pages 46-81, October.
- Mark J. Jensen & John M. Maheu, 2012.
"Bayesian semiparametric multivariate GARCH modeling,"
2012-09, Federal Reserve Bank of Atlanta.
- Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
- Mark J Jensen & John M Maheu, 2012. "Bayesian semiparametric multivariate GARCH modeling," Working Papers tecipa-458, University of Toronto, Department of Economics.
- Mark J. Jensen & John M. Maheu, 2012. "Bayesian Semiparametric Multivariate GARCH Modeling," Working Paper Series 48_12, The Rimini Centre for Economic Analysis.
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