Application of gauge theory to finance: a systematic literature review - Rodrigues, Nelson Deus (2020)
In this dissertation, a systematic literature review was undertaken, exploring the application of gauge theory, an important formalism in physics literature, to finance. A set of keywords pertaining both gauge theory and finance were established and used as a search string in the database Web of Science. After exclusion and inclusion principles were applied to the set of articles generated, 14 papers were obtained. By systematically reviewing them, three major approaches to a financial gauge theory were found: Beliefs-Preferences Gauge Symmetry, Local Num´eraire Gauge Symmetry, and Deflator-Term Structure Gauge Symmetry. These can be essentially differentiated by the kind of gauge symmetry explored. Changing pairs of beliefs and preferences, local num´eraires and pairs of deflator and term structure is argued to be of no consequence to the dynamics of the financial market under consideration. A differential geometric treatment of financial markets as fibre bundles was shown to be necessary for an understanding of the gauge theory application, and proved itself to be successful in rethinking certain concepts, such as gains from arbitrage opportunities, being equivalent to the curvature of the said fibre bundle, an invariant under gauge transformations. The local num´eraire gauge symmetry turned out to be the most investigated one, leading to the execution of various numerical simulations, each with different added variations. Amongst them, the idea of using path integrals, a formalism from quantum mechanics, as a way of simulating the log price probability distributions of a market is used. This works by assuming that the market is characterized by the minimization of arbitrage opportunities. It was found good agreement with historical data, which substantiates the existence of gauge symmetry in financial markets, at least to some extent.