A partially observed model for micromovement of asset prices with Bayes estimation via filtering

Mathematical Finance

Volumn 13, Issue 3, 2003, Pages 411-444

  Zeng, Yong ^a  

^a UNIVERSITY OF MISSOURI KANSAS CITY   (United States)

Author keywords

Bayes estimation; Conditional distribution; Counting process; Filtering; High frequency data; Markov chain approximation; Price clustering; Price discreteness

Indexed keywords

EID: 1842451116     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9965.t01-1-00022     Document Type: Article

References (53)

1. AÏT-SAHALIA, Y. (2002): Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach, Econometrica 70, 223-262.
2. AMIHUD, Y., and H. MENDELSON (1987): Trading Mechanisms and Stock Returns: An Empirical Investigation, J. Finance 42, 533-553.
3. BAGEHOT, W. (1971): The Only Game in Town, Financial Anal. J. 27, 12-14, 22.
4. BALL, C. (1988): Estimation Bias Induced by Discrete Security Prices, J. Finance 43, 841-865.
5. BARCLAY, M., W. CHRISTIE, J. HARRIS, E. KANDEL, and P. H. SCHULTZ (1999): The Effects of Market Reform on the Trading Costs and Depths of NASDAQ Stocks, J. Finance 54 (1), 1-34.
6. BERTSIMAS, D., L. KOGAN, and A. LO (2000): When Is Time Continuous?, J. Financial Econ. 55, 173-204.
7. BLACK, F. (1986): Noise, J. Finance 41, 529-543.
8. BREMAUD, P., (1981): Point Processes and Queues: Martingale Dynamics. New York: Springer-Verlag.
9. CHAN, L. K. C., and J. LAKONISHOK (1993): Institutional Trades and Intraday Stock Price Behavior, J. Financial Econ. 33, 173-199.
10. CHO, D., and E. W. FREES (1988): Estimating the Volatility of Discrete Stock Prices, J. Finance 43, 451-466.
11. CHRISTIE, W., and P. H. SCHULTZ (1994): Why Do NASDAQ Market Makers Avoid Odd-Eighth Quotes?, J. Finance 49, 1813-1840.
12. COHEN, K., G. HAWAWINI, S. MAIER, R. SCHWARTZ, and D. WHITCOMB (1980): Implications of Microstructure Theory for Empirical Research on Stock Price Behavior, J. Finance 35, 249-257.
13. DUFFIE, D., J. PAN, and K. SINGLETON (2000): Transform Analysis and Asset Pricing for Affine Jump-Diffusions, Econometrica 68, 1343-1376.
14. EASLEY, D., and M. O'HARA (1992): Time and the Process of Security Price Adjustment, J. Finance 47, 577-605.
15. ELLIOTT, R. J., A. LAKHDAR, and J. B. MOORE (1995): Hidden Markov Models: Estimation and Control. New York: Springer-Verlag.
16. ENGLE, R. (2000): The Econometrics of Ultra-High-Frequency Data, Econometrica 68, 1-22.
17. ENGLE, R., and J. RUSSELL (1998): Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data, Econometrica 66, 1127-1162.
18. ETHIER, S., and T. KURTZ (1986): Markov Processes: Characterization and Convergence. New York: Wiley.
19. FORSTER, M., and T. GEORGE (1995): Trading Hours, Information Flow and International Cross-Listing, Inter. Rev. Financial Anal. 4, 19-34.
20. GEORGE, T., and C. HWANG (1998): Information Flow and Pricing Errors: A Unified Approach to Estimation and Testing. Working paper, University of Iowa.
21. GHOSAL, S., J. K. GHOSH, and T. SAMANTA (1995): On Convergence of Posterior Distributions, Ann. Statistics 23, 2145-2152.
22. GODEK, P. (1996): Why NASDAQ Market Makers Avoid Odd-Eighth Quotes, J. Financial Econ. 41, 465-474.
23. GOGGIN, E. (1994): Convergence in Distribution of Conditional Expectations, Ann. Probab. 22, 1097-1114.
24. GOTTLIEB, G., and A. KALAY (1985): Implications of the Discreteness of Observed Stock Prices, J. Finance 40, 135-153.
25. GROSSMAN, S., M. MILLER, K. CONE, D. FISCHEL, and D. ROSS (1997): Clustering and Competition in Asset Markets, J. Law & Econ. 40, 23-60.
26. HARRIS, L. (1990): Estimation of Stock Price Variances and Serial Covariances from Discrete Observations, J. Financial Quant. Anal. 25, 291-306.
27. HARRIS, L. (1991): Stock Price Clustering and Discreteness, Rev. Financial Stud. 4, 389-415.
28. HASBROUCK, J. (1988): Trades, Quotes, Inventories and Information, J. Financial Econ. 42, 229-252.
29. HASBROUCK, J. (1993): Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement, Rev. Financial Stud. 6, 191-212.
30. HASBROUCK, J. (1996): Modeling Market Microstructure Time Series; in Handbook of Statistics, Vol. 14, eds. G. Maddala and C. Rao. Amsterdam: North-Holland, pp. 647-692.
31. HASBROUCK, J. (1999): Security Bid/Ask Dynamics with Discreteness and Clustering: Simple Strategies for Modeling and Estimation, J. Financial Markets 2, 1-28.
32. HAUSMAN, J., A. LO, and C. MACKINLAY (1992): An Ordered Probit Analysis of Stock Transaction Prices, J. Financial Econ. 31, 319-379.
33. KALLIANPUR, G. (1980): Stochastic Filtering Theory. New York: Springer-Verlag.
34. KASS, R. E., and A. E. RAFTERY (1995): Bayes Factors and Model Uncertainty, J. Am. Stat. Assoc. 90, 773-795.
35. KITAGAWA, G. (1987): Non-Gaussian State-Space Modeling of Nonstationary Time Series, J. Am. Stat. Assoc. 82, 1032-1041.
36. KLIEMANN, W., G. KOCH, and F. MARCHETTI (1990): On the Unnormalized Solution of the Filtering Problem with Counting Process Observations, IEEE Trans. Info. Theory 36, 1415-1425.
37. KURTZ, T., and D. OCONE (1988): Unique Characterization of Conditional Distributions in Nonlinear Filtering, Ann. Probab. 16, 80-107.
38. KURTZ, T., and P. PROTTER (1991): Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations, Ann. Probab. 19, 1035-1070.
39. KUSHNER, H., and P. DUPUIS (1994): Numerical Methods for Stochastic Control Problems in Continuous Time. New York: Springer-Verlag.
40. MENDELSON, H. (1982): Market Behavior in a Clearing House, Econometrica 50, 1505-1524.
41. MERTON, R. (1976): Option Pricing When Underlying Stock Returns Are Discontinuous, J. Financial Econ. 3, 125-144.
42. NELSON, D. B. (1990): ARCH Models as Diffusion Approximations, J. Econometrics 45, 7-39.
43. NIEDERHOFFER, V. (1965): Clustering of Stock Prices, Oper. Res. 13, 258-265.
44. NIEDERHOFFER, V. (1966): A New Look at Clustering of Stock Prices, J. Business 39, 309-313.
45. O'HARA, M. (1995): Market Microstructure Theory. Oxford: Blackwell.
46. OSBORNE, M. (1962): Periodic Structure in the Brownian Motion of Stock Prices, Oper. Res. 10, 345-379.
47. PROTTER, P. (1992): Stochastic Integration and Differential Equations. New York: Springer-Verlag.
48. ROGERS, L. and O. ZANE (1998): Designing and Estimating Models of High-Frequency Data, Working paper, University of Bath.
49. RUSSELL, J., and R. ENGLE (1998): Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model. Discussion paper 98-10, University of California, San Diego, Department of Economics.
50. RYDBERG, T. H., and N. SHEPHARD (1988): Dynamics of Trade-by-Trade Price Movements: Decomposition and Models. Working paper, Nuffield College, Oxford.
51. SERFLING, R. J. (1980): Approximation Theorems of Mathesmatical Statistics. New York: Wiley.
52. ZENG, Y. (1999): A Class of Partially-Observed Models with Discrete, Clustering and Non-Clustering Noises: Application to Micro-movement of Stock Prices. Unpublished doctoral dissertation, The University of Wisconsin-Madison, Statistics Department.
53. ZHANG, M. Y., J. R. RUSSELL, and R. S. TSAY (2000): A Nonlinear Autoregressive Conditional Duration Model with Application to Financial Transaction Data. Working paper, Graduate School of Business, University of Chicago.