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Article overview
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Gauge theory of Finance? | | D. Sornette
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4 Apr 1998 | | Journal: | Int. J. Mod. Phys. 9 (3), 505-508 (1998) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance’’ by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown 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 degenerate in the limits where these results apply. Third, the choice of the exponential form a la Boltzmann, 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 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. | | Source: | arXiv, cond-mat/9804045 | | Services: | Forum | Review | PDF | Favorites | |
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