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A partially observed model for micromovement of asset prices with Bayes estimation via filtering. (English) Zbl 1130.91346
Summary: 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.
This paper is a revision of the author’s doctoral dissertation (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 Unpublished doctoral dissertation, The University of Wisconsin-Madison, Statistics Department at Madison, completed under the supervision of Thomas G. Kurtz.

##### MSC:
 91G70 Statistical methods; risk measures 62F15 Bayesian inference 62P05 Applications of statistics to actuarial sciences and financial mathematics
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