Pathwise CVA regressions with oversimulated defaults
提出一种分层模拟方案，通过为每个外生路径模拟多条内生路径来降低方差，并基于GPU实现神经网络回归，用于计算条件期望等统计量，在CVA案例中验证了该方法的有效性。
Abstract We consider the computation by simulation and neural net regression of conditional expectations, or more general elicitable statistics, of functionals of processes . Here an exogenous component Y (Markov by itself) is time‐consuming to simulate, while the endogenous component X (jointly Markov with Y ) is quick to simulate given Y , but is responsible for most of the variance of the simulated payoff. To address the related variance issue, we introduce a conditionally independent, hierarchical simulation scheme, where several paths of X are simulated for each simulated path of Y . We analyze the statistical convergence of the regression learning scheme based on such block‐dependent data. We derive heuristics on the number of paths of Y and, for each of them, of X , that should be simulated. The resulting algorithm is implemented on a graphics processing unit (GPU) combining Python/CUDA and learning with PyTorch. A CVA case study with a nested Monte Carlo benchmark shows that the hierarchical simulation technique is key to the success of the learning approach.