Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes

TL;DR

This paper introduces a micro-scale model for limit order book dynamics using two-sided risk processes to analyze order flow imbalance, providing a detailed view of market microstructure beyond price changes.

Contribution

It develops a novel stochastic model for order flow imbalance based on doubly stochastic Poisson processes and two-sided risk processes, capturing high-frequency market dynamics.

Findings

Order flow imbalance (OFI) effectively tracks market microstructure changes.

OFI process changes faster than prices, providing detailed market insights.

Two-sided risk processes model the stochastic nature of order flows.

Abstract

A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid and ask orders that determine the price discovery mechanism in financial markets. The process of {\it order flow imbalance} (OFI) is studied. This process is a sensitive indicator of the current state of the limit order book since time intervals between events in a limit order book are usually so short that price changes are relatively infrequent events. Therefore price changes provide a very coarse and limited description of market dynamics at time micro-scales. The OFI process tracks best bid and ask queues and change much faster than prices. It incorporates information about build-ups and depletions of order queues so that it can be used to interpolate market dynamics between price changes and to track the toxicity of order flows. The {\it two-sided risk processes} are suggested as mathematical models of the OFI process.