On binomial order avalanches

TL;DR

This paper models a discrete limit order book with two trading mechanisms and analyzes the distribution of order avalanche lengths, providing insights into the dynamics of order executions and price movements.

Contribution

It introduces a novel discrete limit order book model with specific trading mechanisms and studies the distribution of order avalanche lengths.

Findings

Distribution of order avalanche lengths characterized

Two types of trades defined and analyzed

Insights into price movement dynamics obtained

Abstract

This paper introduces a discrete limit order book model where new orders are placed with a fixed displacement from the mid-price. Further, the trade event occurs whenever the mid-price hits the price level on which there is some volume. Therefore, the dynamics of the limit order book model leads to two trading mechanisms, namely Type I trade and Type II trade. A Type I trade takes place whenever the price maximum increases, while a Type II trade occurs if the price drops by $\mu$ or more and then increases by $\mu$ again. Our focus is mainly on the distribution of order avalanches length, and by an avalanche length we consider a series of order executions where the length of periods with no trade event cannot exceed $\varepsilon$.