No-Arbitrage Symmetries

TL;DR

This paper explores the transformations that preserve the no-arbitrage condition in financial markets, providing a geometric framework in discrete time and illustrating the concept with detailed examples.

Contribution

It offers a geometric characterization of no-arbitrage symmetries in a non probabilistic discrete-time setting, extending to stochastic models.

Findings

Identifies local no-arbitrage symmetries in trajectorial models

Provides a geometric formalization of no-arbitrage invariance

Illustrates the concepts with detailed examples

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