Properties of realized variance for a pure jump process: calendar time sampling versus business time sampling
Oomen, Roel C. A. (2004) Properties of realized variance for a pure jump process: calendar time sampling versus business time sampling. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. (Working papers (Warwick Business School. Financial Econometrics Research Centre).
WRAP_oomen_wp04-01.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
In this paper we study the impact of market microstructure effects on the properties of realized variance using a pure jump process for high frequency security prices. Closed form expressions for the bias and mean squared error of realized variance are derived under alternative sampling schemes. Importantly, we show that business time sampling is generally superior to the common practice of calendar time sampling in that it leads to a reduction in mean squared error. Using IBM transaction data we estimate the model parameters and determine the optimal sampling frequency for each day in the data set. The empirical results reveal a downward trend in optimal sampling frequency over the last 4 years with considerable day-to-day variation that is closely related to changes in market liquidity.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HG Finance
H Social Sciences > HB Economic Theory
|Divisions:||Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School
|Library of Congress Subject Headings (LCSH):||International Business Machines Corporation, Time-series analysis, Sampling (Statistics), Jump processes|
|Series Name:||Working papers (Warwick Business School. Financial Econometrics Research Centre)|
|Publisher:||Warwick Business School, Financial Econometrics Research Centre|
|Place of Publication:||Coventry|
|Number of Pages:||23|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Andersen, P. K., Ø. Borgan, R. Gill, and N. Keiding, 1993, Statistical Models Based on Counting Processes. Springer-Verlag, New York. Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys, 2000, “Great Realizations,” Risk, pp. 105–108. , 2003, “Modeling and Forecasting Realized Volatility,” Econometrica, 71 (2), 579–625. An´e, T., and H. Geman, 2000, “Order Flow, Transaction Clock, and Normality of Asset Returns,” Journal of Finance, 55(5), 2259–2284. Bandi, F. M., and J. R. Russell, 2003, “Microstructure Noise, Realized Volatility, and Optimal Sampling,” manuscript GSB, The University of Chicago. Barndorff-Nielsen, O. E., and N. Shephard, 2004a, Continuous Time Approach to Financial Volatility. Cambridge University Press, forthcoming. Barndorff-Nielsen, O. E., and N. Shephard, 2004b, “Econometric Analysis of Realised Covariation: High Frequency Based Covariance, Regression and Correlation in Financial Economics,” forthcoming Econometrica, 72. Bowsher, C. G., 2002, “Modelling Security Market Events in Continuous Time: Intensity-Based, Multivariate Point Process Models,” Manuscript Nuffield College, University of Oxford. Carr, P., H. Geman, D. B. Madan, and M. Yor, 2002, “The Fine Structure of Asset Returns: An Empirical Investigation,” Journal of Business, 75 (2), 305–332. Carr, P., and L.Wu, 2003, “Time-Changed L´evy Processes and Option Pricing,” forthcoming Journal of Financial Economics. Corsi, F., G. Zumbach, U. A. Müller, and M. Dacorogna, 2001, “Consistent High-Precision Volatility from High- Frequency Data,” Olsen Group Working Paper. Cowling, A., P. Hall, and M. J. Phillips, 1996, “Bootstrap Confidence Regions for the Intensity of a Poisson Point Process,” JASA, 91 (436), 1516–1524. Cox, J. C., and S. A. Ross, 1976, “The Valuation of Options for Alternative Stochastic Processes,” Journal of Financial Economics, 3 (1/2), 145–166. Diggle, P., and J. Marron, 1988, “Equivalence of Smoothing Parameter Selectors in Density and Intensity Estimation,” JASA, 83 (403), 793–800. Geman, H., D. B. Madan, and M. Yor, 2001, “Time Changes for Levy Processes,” Mathematical Finance, 11 (1), 79–96. Hansen, P. R., and A. Lunde, 2004a, “An Unbiased Measure of Realized Variance,” manuscript Department of Economics, Brown University. , 2004b, “Realized Variance and IID Market Microstructure Noise,” manuscript Brown University. Karlin, S., and H. M. Taylor, 1981, A Second Course in Stochastic Processes. Academic Press, New York. Maheu, J. M., and T. H. McCurdy, 2003, “Modeling Foreign Exchange Rates with Jumps,” manuscript University of Toronto. , 2004, “News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns,” Journal of Finance, 59 (2). Meddahi, N., 2002, “A Theorical Comparison Between Integrated and Realized Volatility,” Journal of Applied Econometrics, 17, 479–508. Mürmann, A., 2001, “Pricing Catastrophe Insurance Derivatives,” Manuscript Insurance and Risk Management Department, The Wharton School. Press, S. J., 1967, “A Compound Events Model for Security Prices,” Journal of Business, 40(3), 317–335. , 1968, “A Modified Compound Poisson Process with Normal Compounding,” Journal of the American Statistical Association, 63, 607–613. Rogers, L., and O. Zane, 1998, “Designing and Estimating Models of High-Frequency Data,” Manuscript University of Bath. Rydberg, T. H., and N. Shephard, 2003, “Dynamics of Trade-by-Trade Price Movements: Decomposition and Models,” Journal of Financial Econometrics, 1 (1), 2–25. Zhang, L., P. A. Mykland, and Y. Ait-Sahalia, 2003, “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data,” manuscript Princeton University.|
Actions (login required)