Modelling Universal Order Book Dynamics in Bitcoin Market

TL;DR

This paper develops a universal field theory model based on KPZ-like stochastic equations that accurately describes Bitcoin market order book dynamics across different countries, revealing underlying universal market behaviors.

Contribution

It introduces a novel effective field theory model for order book dynamics that captures universal features across diverse Bitcoin markets, bridging empirical data and theoretical physics.

Findings

The model accurately predicts empirical order book dynamics.

Universality class of market dynamics is consistent across markets.

Model aligns with stochastic volatility models at large scales.

Abstract

Understanding the emergence of universal features such as the stylized facts in markets is a long-standing challenge that has drawn much attention from economists and physicists. Most existing models, such as stochastic volatility models, focus mainly on price changes, neglecting the complex trading dynamics. Recently, there are increasing studies on order books, thanks to the availability of large-scale trading datasets, aiming to understand the underlying mechanisms governing the market dynamics. In this paper, we collect order-book datasets of Bitcoin platforms across three countries over millions of users and billions of daily turnovers. We find a 1+1D field theory, govern by a set of KPZ-like stochastic equations, predicts precisely the order book dynamics observed in empirical data. Despite the microscopic difference of markets, we argue the proposed effective field theory captures the correct universality class of market dynamics. We also show that the model agrees with the existing stochastic volatility models at the long-wavelength limit.