  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.
