Equilibrium pricing in an order book environment: Case study for a spin model

• Microscopic models for financial markets entail decision making and price formation.
• We embed the Bornholdt–Kaizoji–Fujiwara spin model into the order book dynamics.
• We conclude that the artificial assumption of a fundamental price can be abandoned.

When modeling stock market dynamics, the price formation is often based on an equilibrium mechanism. In real stock exchanges, however, the price formation is governed 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.