Equilibrium Pricing in an Order Book Environment: Case Study for a Spin Model

TL;DR

This paper investigates whether equilibrium pricing models can replicate real market behaviors within an order book environment by embedding a spin model into a realistic agent-based order book simulation.

Contribution

It introduces a novel integration of the Bornholdt-Kaizoji-Fujiwara spin model into an agent-based order book framework, challenging the necessity of equilibrium pricing assumptions.

Findings

Realistic stylized facts are observed in the model.

Equilibrium pricing assumptions may be unnecessary.

Order book dynamics can produce market features without fundamental prices.

Abstract

When modelling stock market dynamics, the price formation is often based on an equilbrium mechanism. In real stock exchanges, however, the price formation is goverend by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more generally, are compatible with the order book environment. We tackle this issue in the framework of a case study by embedding the Bornholdt-Kaizoji-Fujiwara spin model into the order book dynamics. To this end, we use a recently developed agent based model that realistically incorporates the order book. We find realistic stylized facts. We conclude for the studied case that equilibrium pricing is not needed and that the corresponding assumption of a "fundamental" price may be abandoned.