Next Article in Journal
A Direct Road to Majorana Fields
Next Article in Special Issue
A Hypothesis for Self-Organization and Symmetry Reduction in the Synchronization of Organ-Level Contractions in the Human Uterus during Labor
Previous Article in Journal
Polyanionic Hexagons: X6n(X = Si, Ge)
Previous Article in Special Issue
Will Science and Consciousness Ever Meat? Complexity, Symmetry and Qualia
Article Menu

Article Versions

Export Article

Open AccessArticle
Symmetry 2010, 2(4), 1763-1775;

An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance

Business School, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China
Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
Author to whom correspondence should be addressed.
Received: 19 September 2010 / Accepted: 17 October 2010 / Published: 21 October 2010
(This article belongs to the Special Issue Complexity and Symmetry)
PDF [266 KB, uploaded 21 October 2010]


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 num´eraire 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.
Keywords: options pricing equation; gauge symmetry; fiber bundle options pricing equation; gauge symmetry; fiber bundle
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Zhou, S.; Xiao, L. An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance. Symmetry 2010, 2, 1763-1775.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top