KrigHedge: Gaussian Process Surrogates for Delta Hedging

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