Bid-ask spread dynamics: large upward jump with geometric catastrophes

¹ Econometric Modelling and Data Science Research Group, National University of Engineering, Av. Tupac Amaru, 210, Lima, Perú
² Laboratory of Probability Theory and Mathematical Statistics, Koptyuga str. 4, Novosibirsk 630090, Russian Federation
³ Department of Statistics, Institute of Mathematics and Statistics, University of Sãao Paulo, Sãao Paulo, Brazil
⁴ Department of Statistics, Institute of Mathematics and Statistics, University of Sãao Paulo, Sãao Paulo, Brazil

^* Corresponding author: jcerdah@uni.edu.pe

Received: 19 September 2023
Accepted: 10 February 2024

Abstract

We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by [D. Farmer, L. Gillemot, F. Lillo, S. Mike and A. Sen, Quant. Finance 4 (2004) 383–397.], we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model’s properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.