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2013

A Fokker-Planck description for the queue dynamics of large tick stocks

Gareche, A., Disdier, G., Kockelkoren, J. et al.

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Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e.

the fact that the drift and diffusion depends on the volume present on both sides of the spread.
"Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation.
All quantities involved in the equation can be calibrated using high-frequency data on best quotes.

A Fokker-Planck description for the queue dynamics of large tick stocks · Around

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P. Weber, B. Rosenow, Order Book Approach to Price Impact
2005
Earlier work this paper cites.
J.-P. Bouchaud, J. Kockelkoren, M. Potters, Random walks, liquidity molasses and critical response in financial markets
2006
Earlier work this paper cites.
I. Rosu, A dynamic model of the limit order book
2009
Earlier work this paper cites.
V. Alfi, G. Parisi, L. Pietronero, Conference Registration: How people react to a deadline
2009
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