A New Approach to Model Free Option Pricing

TL;DR

This paper presents a novel model-free approach for path-dependent option pricing using a duality framework, which does not require marginal distributions and can be extended to multi-asset scenarios.

Contribution

It introduces a new duality-based method for model-free option pricing that simplifies computation and broadens applicability without needing marginal distributions.

Findings

The approach effectively prices path-dependent options using market data.

The model does not require marginal distributions of stock prices.

It is easily extendable to multi-asset frameworks.

Abstract

In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of model-free option pricing can be formulated in the new framework. We then introduce a model to solve the problem numerically when the only information provided is the market data of vanilla call or put option prices. Compared to the common approaches in the literature, e.g. [4], the model does not require the marginal distributions of the stock price for different maturities. Though the experiments are carried out for simple path-dependent options on a single stock, the model is easy to generalise for multi-asset framework.