An application of symmetry approach to finance: Gauge symmetry in finance

Abstract

The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of the pricing equation can keep invariant under all the local nuḿeraire transformations, this symmetry behind the pricing equation of derivatives is revealed. In addition a corresponding relationship between the curvature of the fiber bundle and the arbitrage in finance arises. © 2010 by the authors; licensee MDPI, Basel, Switzerland.