Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations

Version 1 : Received: 16 June 2021 / Approved: 18 June 2021 / Online: 18 June 2021 (12:35:04 CEST)

How to cite: Rojas, H.; Yambartsev, A.; Logachov, A. Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations. Preprints 2021, 2021060478 (doi: 10.20944/preprints202106.0478.v1). Rojas, H.; Yambartsev, A.; Logachov, A. Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations. Preprints 2021, 2021060478 (doi: 10.20944/preprints202106.0478.v1).

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

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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