Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture
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.
|Date of creation:||20 Apr 2012|
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- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 69-87, January.
- Geweke, John & Amisano, Gianni, 2010.
"Comparing and evaluating Bayesian predictive distributions of asset returns,"
International Journal of Forecasting,
Elsevier, vol. 26(2), pages 216-230, April.
- Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series 0969, European Central Bank.
- Yu, Jun, 2005.
"On leverage in a stochastic volatility model,"
Journal of Econometrics,
Elsevier, vol. 127(2), pages 165-178, August.
- Jun Yu, 2004. "On leverage in a stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 497, Econometric Society.
- Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
- Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Econometric Society 2004 Far Eastern Meetings 506, Econometric Society.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- 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.
- Geert Bekaert & Guojun Wu, 1997.
"Asymmetric Volatility and Risk in Equity Markets,"
NBER Working Papers
6022, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- 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.
- Geweke, John & Whiteman, Charles, 2006. "Bayesian Forecasting," Handbook of Economic Forecasting, Elsevier.
- Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
- 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, vol. 12(4), pages 413-17, October.
- Mark J. Jensen & John M. Maheu, 2008.
"Bayesian semiparametric stochastic volatility modeling,"
FRB Atlanta Working Paper
2008-15, Federal Reserve Bank of Atlanta.
- Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
- Mark J Jensen & John M Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Papers tecipa-314, University of Toronto, Department of Economics.
- Mark J. Jensen & John M. Maheu, 2009. "Bayesian Semiparametric Stochastic Volatility Modeling," Working Paper Series 23_09, The Rimini Centre for Economic Analysis.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- 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-.
- 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.
- 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.
- Geweke, John, 2001. "Bayesian econometrics and forecasting," Journal of Econometrics, Elsevier, vol. 100(1), pages 11-15, January.
- Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
- 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.
- French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- G. William Schwert, 1988.
"Why Does Stock Market Volatility Change Over Time?,"
NBER Working Papers
2798, National Bureau of Economic Research, Inc.
- Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
- Basu S. & Chib S., 2003. "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 224-235, January.
- Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
- 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, vol. 122(1), pages 185-212, September.
- Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
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