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arXiv · 2008.06184

No-Arbitrage Symmetries

I. L. Degano·S. E. Ferrando·A. L. Gonzalez
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Abstract

The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of (idealized) markets. The paper addresses the following basic question: can one characterize the class of transformations that leave the law of no-arbitrage invariant? We provide a geometric formalization of this question in a non probabilistic setting of discrete time, the so-called trajectorial models. The paper then characterizes, in a local sense, the no-arbitrage symmetries and illustrates their meaning in a detailed example. Our context makes the result available to the stochastic setting as a special case

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I. L. Degano, S. E. Ferrando, A. L. Gonzalez. 2020-08-14. No-Arbitrage Symmetries. https://arxiv.org/abs/2008.06184

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