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

Abstract

This study explores the application of gauge theory in the description of the foreign exchange market (FOREX), a global platform for currency trading. By modelling market dynamics through a one-dimensional electrodynamic system, the research examines arbitrage behaviour from the perspective of gauge symmetry. This approach offers an alternative perspective to traditional econometric models. The article discusses the connections between physics, mathematics, and economics, focusing on how gauge theory contributes to financial modelling. It is based on the theoretical framework developed by Igor Ilinsky, in which asset prices are influenced by “gauge connections”, and develops a simplified model of an electrodynamic system. This model captures the interactions between traders and external economic factors within the FOREX market, known for its liquidity and high daily trading volumes. Using an idealised model, the study analyses currency exchanges involving the euro, the US dollar, and the Mexican peso, focusing on the relationship between profits and market dynamics. The findings indicate that, although the model is an approximation, it captures behaviours observed in financial markets out of equilibrium.