KrigHedge: Gaussian Process Surrogates for Delta Hedging

TL;DR

This paper presents a Gaussian process-based machine learning method for efficiently approximating option Greeks, enabling better hedging strategies in complex models by providing accurate sensitivities with quantified uncertainty.

Contribution

It introduces a novel GP surrogate approach for Greeks approximation, including analysis of kernel choices, simulation design, and application to Delta hedging with new theoretical insights.

Findings

Matern kernels outperform other choices

Including virtual points improves boundary accuracy

Training on stock-path data reduces fidelity

Abstract

We investigate a machine learning approach to option Greeks approximation based on Gaussian process (GP) surrogates. The method takes in noisily observed option prices, fits a nonparametric input-output map and then analytically differentiates the latter to obtain the various price sensitivities. Our motivation is to compute Greeks in cases where direct computation is expensive, such as in local volatility models, or can only ever be done approximately. We provide a detailed analysis of numerous aspects of GP surrogates, including choice of kernel family, simulation design, choice of trend function and impact of noise. We further discuss the application to Delta hedging, including a new Lemma that relates quality of the Delta approximation to discrete-time hedging loss. Results are illustrated with two extensive case studies that consider estimation of Delta, Theta and Gamma and benchmark approximation quality and uncertainty quantification using a variety of statistical metrics. Among our key take-aways are the recommendation to use Matern kernels, the benefit of including virtual training points to capture boundary conditions, and the significant loss of fidelity when training on stock-path-based datasets.