Mathematics of Differential Machine Learning in Derivative Pricing and Hedging
This provides a foundational approach for finance professionals and researchers to improve data-driven models in derivative markets, though it appears incremental in integrating theory with existing methods.
The paper tackles the problem of derivative pricing and hedging by introducing a differential machine learning algorithm with a rigorous mathematical framework, establishing its optimality in this context.
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.