Gauge Theory of Finance?

Didier Sornette ()
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Didier Sornette: Department of Earth and Space Science and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA;

International Journal of Modern Physics C (IJMPC), 1998, vol. 09, issue 03, 505-508

Abstract: The recent stimulating proposal of a "Gauge Theory of Finance" by Ilinskyet al. is connected here with traditional approaches. First, the derivation of the log-normal distribution is shown to be equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Samuelson. Similarly, the re-derivation of Black–Scholes equation is shown equivalent to the standard one because the limit of no uncertainty is equivalent to the standard risk-free replication argument. Both re-derivations of the log-normality and Black–Scholes result do not provide a test of the theory because it is not uniquely specified in the limits where these results apply. Third, the choice of the exponential forma laBoltzmann, of the weight of a given market configuration, is a key postulate that requires justification. In addition, the "Gauge Theory of Finance" seems to lead to "virtual" arbitrage opportunities for a pure Markov random walk market when there should be none. These remarks are offered in the hope to improve the formulation of the "Gauge Theory of Finance" into a coherent and useful framework.

Keywords: Finance; Black–Scholes; Random Walks; Boltzmann; Gauge Theory; Arbitrage; Log-Normal Distribution (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S0129183198000406

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