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Dynamic Density Estimation of Market Microstructure Variables
via Auxiliary Particle Filtering

Daniel Nehren, David Fellah, Jesus Ruiz-Mata and Yichen Qin
The Journal of Trading Fall 2012, 7 (4) 55-64; DOI: https://doi.org/10.3905/jot.2012.7.4.055
Daniel Nehren
is the global head of the Equity Quantitative Solutions groups at J.P. Morgan in New York, NY.
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David Fellah
runs the Americas Quantitative Solutions’ Algorithmic Trading group at J.P. Morgan in New York, NY.
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Jesus Ruiz-Mata
runs the Quantitative Solutions’ Portfolio Analytics group at J.P. Morgan in New York, NY.
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Yichen Qin
is a Ph.D. student at the Department of Applied Math and Statistics, Johns Hopkins University in Baltimore, Maryland.
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Abstract

In this article, we introduce a new density estimation approach to sequentially model the distribution of market microstructure variables on a continuous basis. We employ a nonlinear state space model as our basic framework, where the market microstructure variables follow a distribution with unknown parameters that are identified as the states in the model. Instead of specifying a parametric family for the posterior distribution of the states given the observed microstructure variables, we use a discrete approximation approach. Combining an (auxiliary) particle filtering approach with an efficient change point detection methodology, we efficiently update the posterior distribution of the “states” with newly arrived observations of the relevant microstructure variables, which are detected to indicate a departure from the previous distributional regime. The methodology offers a potential solution to the challenge of updating the distribution of market variables of interest using only relevant data arriving at high frequencies while filtering out noise that is unlikely to indicate departures from previously estimated regimes. The method is validated using simulated data and real bid–ask spread data, and excellent performance is found.

TOPICS: Statistical methods, exchanges/markets/clearinghouses

  • © 2012 Pageant Media Ltd
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The Journal of Trading: 7 (4)
The Journal of Trading
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Fall 2012
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Dynamic Density Estimation of Market Microstructure Variables
via Auxiliary Particle Filtering
Daniel Nehren, David Fellah, Jesus Ruiz-Mata, Yichen Qin
The Journal of Trading Sep 2012, 7 (4) 55-64; DOI: 10.3905/jot.2012.7.4.055

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Dynamic Density Estimation of Market Microstructure Variables
via Auxiliary Particle Filtering
Daniel Nehren, David Fellah, Jesus Ruiz-Mata, Yichen Qin
The Journal of Trading Sep 2012, 7 (4) 55-64; DOI: 10.3905/jot.2012.7.4.055
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  • Article
    • Abstract
    • GOAL AND BACKGROUND
    • STATE SPACE MODELING
    • PARTICLE FILTERING
    • ESTIMATION OF TIME VARYING HYPER PARAMETERS IN STATE SPACE MODEL
    • RESULTS AND VALIDATION
    • CONCLUSION
    • REFERENCES
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