Sparse grid method for highly efficient computation of exposures for xVA

作者：

Highlights：

• Application of the sparse grid method significantly reduces the computational time for calculating exposures.

• The stochastic collocation method significantly reduces the number of portfolio evaluations, even when dealing with many risk factors.

• The proposed model can be easily applied to any portfolio and size, even for a portfolio comprising linear and non-linear derivatives.

• The article gives illustrative examples and examines the method with realistic multi-currency portfolios consisting of interest rate swaps and swaptions.

摘要

•Application of the sparse grid method significantly reduces the computational time for calculating exposures.•The stochastic collocation method significantly reduces the number of portfolio evaluations, even when dealing with many risk factors.•The proposed model can be easily applied to any portfolio and size, even for a portfolio comprising linear and non-linear derivatives.•The article gives illustrative examples and examines the method with realistic multi-currency portfolios consisting of interest rate swaps and swaptions.

论文关键词：Stochastic collocation,SC,xVA,Valuation adjustment,Expected exposures,Smolyak’s sparse grids,Chebyshev polynomials,Clenshaw–Curtis

论文评审过程：Received 29 April 2021, Revised 23 May 2022, Accepted 24 July 2022, Available online 10 August 2022, Version of Record 10 August 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127446