Modelling the market dynamics of the exchange rate through Maxwell electrodynamic system

We analyze the dynamics of the foreign exchange market (FOREX) within the framework of gauge theory, providing an interdisciplinary point of view that builds bridges among physics, mathematics and economics. We model the actual currency exchanges of euro-dollar-Mexican peso during the period of January to June 2023 through a one-dimensional electrodynamic system derived from Maxwell’s equations. Findings of this study reveal that it is possible to describe out-of-equilibrium features and arbitrage conditions consistent with the FOREX dynamics. A natural outcome calls for the extension of the model including more currencies and real-time fluctuations to obtain a broader description of the market. The framework developed here provides a structural perspective to understand complex financial phenomena from theoretical physics arguments. An original feature of the present study is to translate the principles of electrodynamics into financial analysis, and thus, it offers a strong foundation to explore exchange rate dynamics and paves the way for further interdisciplinary research.