Mathematics of Differential Machine Learning in Derivative Pricing and Hedging

TL;DR

This paper develops a rigorous mathematical framework for differential machine learning algorithms in derivative pricing and hedging, highlighting their theoretical foundations and optimality in financial models.

Contribution

It introduces a novel mathematical approach to differential machine learning in finance, emphasizing the impact of model assumptions and providing a unified theoretical basis.

Findings

Differential machine learning shows optimality in derivative valuation.

Theoretical assumptions significantly influence algorithm construction.

Experimental results support the proposed method's effectiveness.

Abstract

This article introduces the groundbreaking concept of the financial differential machine learning algorithm through a rigorous mathematical framework. Diverging from existing literature on financial machine learning, the work highlights the profound implications of theoretical assumptions within financial models on the construction of machine learning algorithms. This endeavour is particularly timely as the finance landscape witnesses a surge in interest towards data-driven models for the valuation and hedging of derivative products. Notably, the predictive capabilities of neural networks have garnered substantial attention in both academic research and practical financial applications. The approach offers a unified theoretical foundation that facilitates comprehensive comparisons, both at a theoretical level and in experimental outcomes. Importantly, this theoretical grounding lends substantial weight to the experimental results, affirming the differential machine learning method's optimality within the prevailing context. By anchoring the insights in rigorous mathematics, the article bridges the gap between abstract financial concepts and practical algorithmic implementations.