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Gauge Theory of Finance?

Author

Listed:
  • Didier Sornette

    (Department of Earth and Space Science and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR6622, Université des Sciences, B.P. 70, Parc Valrose, 06108 Nice Cedex 2, France)

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.

Suggested Citation

  • Didier Sornette, 1998. "Gauge Theory of Finance?," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 505-508.
    • Handle: RePEc:wsi:ijmpcx:v:09:y:1998:i:03:n:s0129183198000406
    DOI: 10.1142/S0129183198000406
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