Order book dynamics with liquidity fluctuations: limit theorems and large deviations

21 Pages Posted: 28 Apr 2020 Last revised: 6 Jan 2021

See all articles by Helder Rojas

Helder Rojas

University of São Paulo (USP); Santander Bank, Brazil

Artem Logachov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Russia

Anatoly Yambartsev

Federal University of Sao Paulo

Date Written: April 3, 2020

Abstract

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Keywords: Limit order book, Liquidity fluctuations, Markov chains, Limit theorems, Large Deviations, Flash crash.

JEL Classification: C, G.

Suggested Citation

Rojas, Helder and Logachov, Artem and Yambartsev, Anatoly, Order book dynamics with liquidity fluctuations: limit theorems and large deviations (April 3, 2020). Available at SSRN: https://ssrn.com/abstract=3567718 or http://dx.doi.org/10.2139/ssrn.3567718

Helder Rojas (Contact Author)

University of São Paulo (USP)

Sao Paulo, Sao Paulo
Brazil

Santander Bank, Brazil ( email )

Sao Paulo
Brazil

Artem Logachov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Russia ( email )

630090 Novosibirsk
United States

Anatoly Yambartsev

Federal University of Sao Paulo ( email )

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