Modelling Financial Market Imperfection Using Open Quantum Systems

TL;DR

This paper proposes using open quantum systems to model financial markets, highlighting how classical and non-classical dynamics influence market states and incorporating factors like illiquidity and trading imperfections.

Contribution

It introduces a novel quantum-inspired framework for financial market modeling, distinguishing classical and non-classical evolution modes and their effects on market states.

Findings

Classical and non-classical modes converge to maximum entropy states at different rates.

Non-classical modes can model illiquid trades and trading imperfections.

Classical systems reach equilibrium faster than non-classical ones.

Abstract

We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time evolution, and look at the development of the reduced density matrix, that represents the state of the market, over long time frames. In particular we distinguish between classical and non-classical modes of time evolution. We show that whilst both tend to the same set of maximum entropy states, this occurs faster in classical systems, with a knock on effect on the resulting probability distributions. We demonstrate how non-classical modes of time-evolution can be used to incorporate factors such as illiquid trades and imperfect trading mechanisms, and distinguish between different mechanisms of non-classical time evolution.