  A new challenge to quantitative finance after the recent financial crisis is
the study of credit valuation adjustment (CVA), which requires modeling of the
future values of a portfolio. In this paper, following recent work in [Weinan
E(2017), Han(2017)], we apply deep learning to attack this problem. The future
values are parameterized by neural networks, and the parameters are then
determined through optimization. Two concrete products are studied: Bermudan
swaption and Mark-to-Market cross-currency swap. We obtain their expected
positive/negative exposures, and further study the resulting functional form of
future values. Such an approach represents a new framework for modeling XVA,
and it also sheds new lights on other methods like American Monte Carlo.
