KrigHedge: Gaussian Process Surrogates for Delta Hedging
- URL: http://arxiv.org/abs/2010.08407v4
- Date: Fri, 14 Jan 2022 05:14:22 GMT
- Title: KrigHedge: Gaussian Process Surrogates for Delta Hedging
- Authors: Mike Ludkovski and Yuri Saporito
- Abstract summary: We investigate a machine learning approach to option Greeks approximation based on Gaussian process (GP) surrogates.
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 discuss the application to Delta hedging, including a new Lemma that relates quality of the Delta approximation to discrete-time hedging loss.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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