Universal approximation on non-geometric rough paths and applications to financial derivatives pricing

TL;DR

This paper extends the universal approximation theorem to non-geometric rough paths using polynomial-based methods, with applications in financial derivatives pricing under no-arbitrage conditions, enabling better analysis of signature payoffs.

Contribution

It introduces a polynomial approximation class for rough path functionals and extends universal approximation to non-geometric rough paths, addressing key financial modeling challenges.

Findings

Addresses universal approximation for non-geometric rough paths

Provides a new polynomial-based approximation framework

Facilitates analysis of signature payoffs in finance

Abstract

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate It\^o integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}.