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

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  • Yong Zeng

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.

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  • Yong Zeng, 2003. "A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 411-444, July.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:3:p:411-444
    DOI: 10.1111/1467-9965.t01-1-00022
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    Cited by:

    1. Wu, Zhengxiao, 2012. "On the intraday periodicity duration adjustment of high-frequency data," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 282-291.
    2. Field, Jonathan & Large, Jeremy, 2008. "Pro-rata matching and one-tick futures markets," CFS Working Paper Series 2008/40, Center for Financial Studies (CFS).
    3. Large, Jeremy, 2011. "Estimating quadratic variation when quoted prices change by a constant increment," Journal of Econometrics, Elsevier, vol. 160(1), pages 2-11, January.
    4. Liu Xiangdong & Li Xianglong & Zheng Shaozhi & Qian Hangyong, 2020. "PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps," Journal of Systems Science and Information, De Gruyter, vol. 8(2), pages 159-169, April.
    5. Christoph Kuhn & Matthias Riedel, 2012. "Price-Setting of Market Makers: A Filtering Problem with an Endogenous Filtration," Papers 1210.4000, arXiv.org.
    6. Jeremy Large, 2005. "Estimating quadratic variation when quoted prices jump by a constant increment," OFRC Working Papers Series 2005fe05, Oxford Financial Research Centre.
    7. Giesecke, Kay & Schwenkler, Gustavo, 2018. "Filtered likelihood for point processes," Journal of Econometrics, Elsevier, vol. 204(1), pages 33-53.
    8. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    9. Iacus, Stefano Maria & Uchida, Masayuki & Yoshida, Nakahiro, 2009. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1580-1600, May.
    10. Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.

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