Physics of Finance

TL;DR

This paper applies gauge theory concepts to finance, interpreting market variables as geometric connections and curvature, providing a novel geometric framework for understanding arbitrage, interest rates, and asset prices.

Contribution

It introduces a geometric gauge theory framework for finance, mapping capital markets onto lattice QED and offering new insights into arbitrage and asset dynamics.

Findings

Interest rates and prices as connection components

Market arbitrage represented by curvature tensor

Quantum gauge theory relates to log-normal asset walks

Abstract

We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. This allows us to map the theory of capital market onto the theory of quantized gauge field interacted with a money flow field. The gauge transformations of the matter field correspond to a dilatation of security units which effect is eliminated by a gauge transformation of the connection. The curvature tensor for the connection consists of the excess returns to the risk-free interest rate for the local arbitrage operation. Free quantum gauge theory is equivalent to the assumption about the log-normal walks of assets prices. In general case the consideration maps the capital market onto lattice QED.