Model-free trading and hedging with continuous price paths

TL;DR

This paper develops a model-independent framework for dynamic hedging of derivatives with continuous price paths, using PDEs to characterize replication strategies across various market settings.

Contribution

It introduces a general PDE-based approach to model-independent hedging, extending existing identities and enabling new derivations in different market scenarios.

Findings

Characterizes model-independent replication strategies via coupled PDEs

Applies framework to markets with no traded claims, convex claims, and co-maturing options

Provides a unified methodology for deriving new identities in derivative pricing

Abstract

In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via solutions of coupled PDEs. We provide a general framework and then apply it to a market with no traded claims, a market with an underlying asset and a convex claim and a market with an underlying asset and a set of co-maturing call options. The results encompass known examples of model-independent identities and provide a methodology for deriving new identities.