Informatics and Applications
2018, Volume 12, Issue 2, pp 29-34
A PROBABILITY MODEL OF THE INFLUENCE OF THE ORDER BOOK ON THE PRICE PROCESS
- L. V. Nazarov
- V. V. Lavrentyev
- E. V. Bykovets
Abstract
The Limit Order Book model is considered, with buy and sell orders arriving as two independent Cox
processes. It includes the price impact model built on the basis of a physical model of perfectly elastic collision.
Price is treated as a particle of some mass, moving along a straight line without friction. The incoming buy orders
and outgoing sell orders hit the price giving it additional momentum in one direction, while incoming sell orders
and outgoing buy orders do the same in the opposite direction. A functional limit theorem for the price process is
obtained at a high intensity of incoming order flow, which allows approximation by some Levy process
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[+] About this article
Title
A PROBABILITY MODEL OF THE INFLUENCE OF THE ORDER BOOK ON THE PRICE PROCESS
Journal
Informatics and Applications
2018, Volume 12, Issue 2, pp 29-34
Cover Date
2018-05-30
DOI
10.14357/19922264180205
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
limit orders; perfectly elastic collision; limit order book model; price process; Cox process; functional limit theorem
Authors
L. V. Nazarov  , V. V. Lavrentyev , and E. V. Bykovets
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
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