Abstract
Ordinal stochastic volatility (OSV) models were recently developed and fitted by Müller & Czado (2009) to account for the discreteness of financial price changes, while allowing for stochastic volatility (SV). The model allows for exogenous factors both on the mean and volatility level. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is followed to facilitate estimation in these parameter driven models. In this paper the applicability of the OSV model to financial stocks with different levels of trading activity is investigated and the influence of time between trades, volume, day time and the number of quotes between trades is determined. In a second focus we compare the performance of OSV models and SV models. The analysis shows that the OSV models which account for the discreteness of the price changes perform quite well when applied to such data sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chib, S., Nardari, F. & Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models, Journal of Econometrics 108: 281–316.
De Jong, P. & Shephard, N. (1995). The simulation smoother for time series models, Biometrika 82: 339–350.
Engle, R. F. & Russell, J. R. (1998).Autoregressive conditional duration: a newmodel for irregularly spaced transaction data, Econometrica 66: 1127–1162.
Ghysels, E., Harvey, A. C. & Renault, E. (1996). Stochastic volatility, in C. R. Rao & G. S. Maddala (eds), Statistical Methods in Finance, North-Holland, Amsterdam, pp. 119–191.
Gneiting, T. & Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation, Journal of the American Statistical Association 102: 359–378.
Harris, L. (1990). Estimation of stock variances and serial covariances from discrete observations, Journal of Financial and Quantitative Analysis 25: 291–306.
Hasbrouck, J. (1999). Security bid/ask dynamics with discreteness and clustering, Journal of Financial Markets 2: 1–28.
Hasbrouck, J. (1999a). The dynamics of discrete bid and ask quotes, Journal of Finance 54: 2109–2142.
Hasbrouck, J. (2003).Markov chain Monte Carlomethods for Bayesian estimation ofmicrostructure models (computational appendix to: Hasbrouck, J. (2004). Liquidity in the futures pits: inferring market dynamics from incomplete data, Journal of Financial and Quantitative Analysis 39: 305–326), available at http://pages.stern.nyu.edu/~jhasbrou.
Hasbrouck, J. (2004). Liquidity in the futures pits: inferring market dynamics from incomplete data, Journal of Financial and Quantitative Analysis 39: 305–326.
Hausman, J. A., Lo, A. W. & MacKinlay, A. C. (1992). An ordered probit analysis of transaction stock prices, Journal of Financial Economics 31: 319–379.
Kim, S., Shephard, N. & Chib, S. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models, Review of Economic Studies 65: 361–393.
Kitagawa, G. (1987). Non-Gaussian state space modeling of nonstationary time series, Journal of the American Statistical Association 82: 1032–1041.
Liesenfeld, R., Nolte, I. & Pohlmeier, W. (2006). Modelling financial transaction price movements: a dynamic integer count data model, Empirical Economics 30: 795–825.
Manrique, A. & Shephard, N. (1997). Likelihood analysis of a discrete bid/ask price model for a common stock quoted on the NYSE, Nuffield College Economics papers, W-15.
Müller, G. & Czado, C. (2009). Stochastic volatility models for ordinal valued time series with application to finance, Statistical Modelling 9: 69–95.
Russell, J. R. & Engle, R. F. (2005). A discrete-state continuous-time model of financial transactions prices and times: the autoregressive conditional multinomial-autoregressive conditional duration model, Journal of Business and Economic Statistics 23: 166–180.
Rydberg, T.H. & Shephard, N. (2003).Dynamics of trade-by-trade pricemovements: decomposition and models, Journal of Financial Econometrics 1: 2–25.
Shephard, N. (2006). Stochastic volatility models, in S. N. Durlauf & L. E. Blume (eds), New Palgrave Dictionary of Economics, 2nd ed., Palgrave Macmillan. doi: 10.1007/s001090000086.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P. & van der Linde, A. (2002). Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society B 64: 583–639.
Acknowledgments
Claudia Czado is supported by the Deutsche Forschungsgemeinschaft.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Czado, C., Müller, G., Nguyen, TNG. (2010). Ordinal- and Continuous-Response Stochastic Volatility Models for Price Changes: An Empirical Comparison. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2413-1_16
Published:
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2412-4
Online ISBN: 978-3-7908-2413-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)