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Symmetry 2010, 2(4), 1763-1775; doi:10.3390/sym2041763

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

1,*  and 2
1 Business School, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China 2 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)
Download 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).

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

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