Model-independent bounds for Asian options: a dynamic programming approach

TL;DR

This paper introduces a dynamic programming approach to determine model-independent bounds for Asian options, leveraging PDE formulation without requiring specific payoff constraints, thus broadening the scope of pricing methods.

Contribution

It presents a novel dynamic programming framework for Asian option bounds that uses PDEs and does not depend on payoff convexity constraints.

Findings

Provides a PDE-based method for model-independent pricing.

Applicable to a wide range of payoff functions.

Offers a generalization over existing approaches.

Abstract

We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we consider the problem as a dynamic programming problem, where the controlled process is the conditional distribution of the asset at the maturity date. By formulating the problem in this manner, we are able to determine the model-independent price through a PDE formulation. Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to generalise to many related problems.