Cubature on Wiener space: pathwise convergence

TL;DR

This paper introduces a pathwise convergence analysis for cubature on Wiener space, enhancing the understanding of its application to path-dependent option pricing using rough path theory.

Contribution

It provides a novel pathwise convergence framework for cubature methods on Wiener space, extending their applicability to path-dependent options via rough path analysis.

Findings

Establishes weak convergence for path-dependent option prices

Provides a new interpretation of cubature as a random walk

Extends cubature methods to more general functionals

Abstract

Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the Ninomiya--Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.