Accelerated Computations of Sensitivities for xVA

TL;DR

This paper introduces polynomial approximation methods to efficiently compute sensitivities in xVA calculations, significantly reducing computational costs while maintaining high accuracy, and extends the approach to complex models like CVA with wrong-way risk.

Contribution

It presents a novel polynomial approximation technique for sensitivities in xVA, including a new approach based on approximating the difference between shocked and unshocked valuations.

Findings

High accuracy in sensitivity approximations demonstrated

Significant reduction in computational costs achieved

Method extended to complex xVA models like CVA with wrong-way risk

Abstract

Exposure simulations are fundamental to many xVA calculations and are a nested expectation problem where repeated portfolio valuations create a significant computational expense. Sensitivity calculations which require shocked and unshocked valuations in bump-and-revalue schemes exacerbate the computational load. A known reduction of the portfolio valuation cost is understood to be found in polynomial approximations, which we apply in this article to interest rate sensitivities of expected exposures. We consider a method based on the approximation of the shocked and unshocked valuation functions, as well as a novel approach in which the difference between these functions is approximated. Convergence results are shown, and we study the choice of interpolation nodes. Numerical experiments with interest rate derivatives are conducted to demonstrate the high accuracy and remarkable computational cost reduction. We further illustrate how the method can be extended to more general xVA models using the example of CVA with wrong-way risk.