Differential ML with a Difference

TL;DR

This paper enhances Differential ML for derivatives pricing by introducing alternative sensitivity estimation methods, including likelihood ratio and hybrid approaches, to improve accuracy for discontinuous payoffs.

Contribution

It proposes new sensitivity estimation techniques that extend Differential ML to handle discontinuous payoffs effectively, reducing errors.

Findings

Likelihood ratio method reduces test errors for discontinuous payoffs.

Hybrid approach with gamma estimates further improves regularization.

Differential ML can be effectively applied to digital and barrier options.

Abstract

Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through pathwise adjoint differentiation to reduce pricing and hedging errors. However, for options with discontinuous payoffs, such as digital or barrier options, the pathwise sensitivities are biased, and incorporating them into the loss function can magnify errors. We consider alternative methods for estimating sensitivities and find that they can substantially reduce test errors in prices and in their sensitivities. Using differential labels calculated through the likelihood ratio method expands the scope of Differential ML to discontinuous payoffs. A hybrid method incorporates gamma estimates as well as delta estimates, providing further regularization.