Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime | Sciact - Система учета научной деятельности ИМ СО РАН

Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime Научная публикация

Журнал

Mathematics
, E-ISSN: 2227-7390

Вых. Данные

Год: 2023, Том: 2023, Номер: 11, Номер статьи : 4235, Страниц : 24 DOI: 10.3390/math11204235

Ключевые слова

limit order book; liquidity fluctuations; Markov process; large deviations; flash crash

Авторы

Rojas H ¹ , Logachov A ^2,3,4 , Yambartsev A ⁵

Организации

1	National Engineering University
2	Sobolev Institute of Mathematics
3	Department of Computer Science in Economics, Novosibirsk State Technical University (NSTU)
4	Department of Higher Mathematics, Siberian State University of Geosystems and Technologies (SSUGT)
5	Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo (USP)

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0010

We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations.

Rojas H. , Logachov A. , Yambartsev A.
Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime
Mathematics. 2023. V.2023. N11. 4235 :1-24. DOI: 10.3390/math11204235 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	5 окт. 2023 г.
Принята к публикации:	8 окт. 2023 г.
Опубликована в печати:	10 окт. 2023 г.
Опубликована online:	10 окт. 2023 г.

Web of science:	WOS:001093512100001
Scopus:	2-s2.0-85175087424
РИНЦ:	63498965
OpenAlex:	W4387494375

БД	Цитирований
OpenAlex	1
Scopus	1
Web of science	1