This paper presents a deep learning approach to compute Credit Valuation Adjustment (CVA) and Debit Valuation Adjustment (DVA) by modeling future portfolio values using neural networks. The key idea is to parameterize the derivatives of the discounted future value with respect to risk factors (deltas) as neural networks at each time step. These networks are trained via backward stochastic differential equations (BSDE) and optimization (Adam) to satisfy boundary conditions (e.g., zero at maturity). The method avoids the need for hand-picked basis functions used in traditional American Monte Carlo (AMC) methods.

The authors apply the framework to two products: a Bermudan swaption under a Hull-White one-factor model and a Mark-to-Market cross-currency swap under a multi-factor model with interest rate and FX risk. For the swaption, the neural network learns a future value function that resembles a Bachelier option price, with EPE decreasing over time and vanishing after exercise. For the cross-currency swap, the method reproduces expected exposures that agree with proxy methods and captures the impact of volatility parameters. The results demonstrate that neural networks can effectively approximate high-dimensional, nonlinear future value functions, offering a flexible and accurate tool for XVA calculations.