Nonlinear Monte Carlo schemes for counterparty risk on credit derivatives.

Summary Two nonlinear Monte Carlo schemes, namely, the linear Monte Carlo expansion with randomization of Fujii and Takahashi (2012a,2012b) and the marked branching diffusion scheme of Henry-Labordère (2012), are compared in terms of applicability and numerical behavior regarding counterparty risk computations on credit derivatives. This is done in two dynamic copula models of portfolio credit risk: the dynamic Gaussian copula model and the model in which default dependence stems from joint defaults. For such high-dimensional and nonlinear pricing problems, more standard deterministic or simulation/regression schemes are ruled out by Bellman's " curse of dimensionality " and only purely forward Monte Carlo schemes can be used.