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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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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