The deep parametric PDE method and applications to option pricing

作者：

Highlights：

• Efficient numerical solution to high-dimensional parametric PDEs by neural networks.

• Unsupervised approach without the need for sample solutions or simulations.

• Real-time evaluation of solution and sensitivities for a range of parameter values.

• Accurate results for option pricing problems in the multivariate Black–Scholes model.

• Numerical results of up to 25 dimensions confirm effectiveness of the approach.

摘要

•Efficient numerical solution to high-dimensional parametric PDEs by neural networks.•Unsupervised approach without the need for sample solutions or simulations.•Real-time evaluation of solution and sensitivities for a range of parameter values.•Accurate results for option pricing problems in the multivariate Black–Scholes model.•Numerical results of up to 25 dimensions confirm effectiveness of the approach.

论文关键词：Basket options,Deep neural networks,High-dimensional problems,Greeks for multi-asset options,Parametric option pricing,Parametric partial differential equations

论文评审过程：Received 7 July 2021, Revised 2 March 2022, Accepted 23 June 2022, Available online 2 July 2022, Version of Record 2 July 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127355