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KrigHedge: Gaussian Process Surrogates for Delta Hedging

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 to implement Delta hedging in cases where direct computation is expensive, such as in local volatility models, or can only ever be done approximately. The proposed method takes in noisily observed option prices, fits a non-parametric input-output map and then analytically differentiates the latter to obtain the various price sensitivities. Thus, a single surrogate yields multiple self-consistent Greeks. 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 moreover connect the quality of the Delta approximation to the resulting 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 Matérn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

KrigHedge: Gaussian Process Surrogates for Delta Hedging

Ludkovski, Mike; Saporito, Yuri
Applied Mathematical Finance , Volume 28 (4): 31 – Jul 4, 2021
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KrigHedge: Gaussian Process Surrogates for Delta Hedging

Abstract

We investigate a machine learning approach to option Greeks approximation based on Gaussian Process (GP) surrogates. Our motivation is to implement Delta hedging in cases where direct computation is expensive, such as in local volatility models, or can only ever be done approximately. The proposed method takes in noisily observed option prices, fits a non-parametric input-output map and then analytically differentiates the latter to obtain the various price sensitivities. Thus, a single...
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Publisher
Taylor & Francis
Copyright
© 2022 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2022.2039250
Publisher site
See Article on Publisher Site

Abstract

We investigate a machine learning approach to option Greeks approximation based on Gaussian Process (GP) surrogates. Our motivation is to implement Delta hedging in cases where direct computation is expensive, such as in local volatility models, or can only ever be done approximately. The proposed method takes in noisily observed option prices, fits a non-parametric input-output map and then analytically differentiates the latter to obtain the various price sensitivities. Thus, a single surrogate yields multiple self-consistent Greeks. 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 moreover connect the quality of the Delta approximation to the resulting 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 Matérn 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.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Jul 4, 2021

Keywords: Gaussian process; hedging; Greeks; data-driven; local volatility; machine learning

References

  • Stochastic Kriging for Simulation Metamodeling
  • Practical Heteroskedastic Gaussian Process Modeling for Large Simulation Experiments
  • AAD and Least-square Monte Carlo: Fast Bermudan-style Options and XVA Greeks
  • Enhancing Stochastic Kriging Metamodels with Gradient Estimators
  • Machine Learning for Quantitative Finance: Fast Derivative Pricing, Hedging and Fitting
  • Estimating Multiple Option Greeks Simultaneously Using Random Parameter Regression
  • Chebyshev Interpolation for Parametric Option Pricing
  • Improved Error Bound for Multivariate Chebyshev Polynomial Interpolation
  • The Chebyshev Method for the Implied Volatility
  • Machine Learning for Pricing American Options in High-dimensional Markovian and Non-Markovian Models
  • The Stochastic Grid Bundling Method: Efficient Pricing of Bermudan Options and Their Greeks
  • Functional Itô Calculus, Path-dependence and the Computation of Greeks
  • Dicekriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-based Metamodeling and Optimization
  • Neural Networks for Option Pricing and Hedging: A Literature Review
  • Hedging with Linear Regressions and Neural Networks
  • An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs