Coupling limit order books and branching random walks

TL;DR

This paper introduces a novel coupling between a limit order book model and a branching random walk, enabling analysis of long-term price behavior and proposing a versatile approach for complex financial models.

Contribution

It presents a new coupling method linking limit order books with branching random walks, enhancing understanding of price dynamics.

Findings

Coupling provides insights into the long-term behavior of prices.

Enrichment of state-space via filiation is a promising technique.

Potential applicability to broader classes of financial models.

Abstract

We consider a model for a one-sided limit order book proposed by Lakner et al. We show that it can be coupled with a branching random walk and use this coupling to answer a non-trivial question about the long-term behavior of the price. The coupling relies on a classical idea of enriching the state-space by artificially creating a filiation, in this context between orders of the book, that we believe has the potential of being useful for a broader class of models.