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

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

1,* email and 2email
Received: 19 September 2010; Accepted: 17 October 2010 / Published: 21 October 2010
(This article belongs to the Special Issue Complexity and Symmetry)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 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
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MDPI and ACS Style

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

AMA Style

Zhou S, Xiao L. An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance. Symmetry. 2010; 2(4):1763-1775.

Chicago/Turabian Style

Zhou, Shipeng; Xiao, Liuqing. 2010. "An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance." Symmetry 2, no. 4: 1763-1775.

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