A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering

Author: Zeng Y.

Source: Mathematical Finance, Volume 13, Number 3, July 2003 , pp. 411-444(34)

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Abstract:

A general micromovement model that describes transactional price behavior is proposed. The model ties the sample characteristics of micromovement and macromovement in a consistent manner. An important feature of the model is that it can be transformed to a filtering problem with counting process observations. Consequently, the complete information of price and trading time is captured and then utilized in Bayes estimation via filtering for the parameters. The filtering equations are derived. A theorem on the convergence of conditional expectation of the model is proved. A consistent recursive algorithm is constructed via the Markov chain approximation method to compute the approximate posterior and then the Bayes estimates. A simplified model and its recursive algorithm are presented in detail. Simulations show that the computed Bayes estimates converge to their true values. The algorithm is applied to one month of intraday transaction prices for Microsoft and the Bayes estimates are obtained.

Keywords: high-frequency data; filtering; Bayes estimation; counting process; conditional distribution; Markov chain approximation; price discreteness; price clustering

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9965.t01-1-00022

Affiliations: 1: Department of Mathematics and Statistics, University of Missouri at Kansas City

Publication date: 2003-07-01