Gamma Hedging without Rough Paths

TL;DR

This paper presents a novel approach to gamma and delta hedging that avoids rough-path theory by using p-th variation and Taylor's theorem, simplifying proofs and extending to barrier and Asian options.

Contribution

It introduces a method that bypasses rough-path theory for hedging analysis, providing simpler proofs and broader applicability to complex options.

Findings

Gamma hedging robustness explained without rough paths

Classical delta-hedging results proved without stochastic integrals

Applicable to barrier and Asian options

Abstract

We show how the robustness of gamma hedging can be understood without using rough-path theory. Instead, we use the concepts of $p^{th}$ variation along a partition sequence and Taylor's theorem directly, rather than defining an integral and proving a version of It\^o's lemma. The same approach allows classical results on delta-hedging to be proved without defining an integral and without the need to define the concept of self-financing in continuous time. We show that the approach can also be applied to barrier options and Asian options