Efficient Calibration for CVA Using Multi-Level Monte Carlo

The evaluation of credit value adjustments (CVA) usually intensive computations basing on Monte Carlo simulations. In practice, often the CVA itself is not the quantity we are looking for, but a parameter which gives a certain CVA level or a worst-case CVA. Concrete examples are the translation of an upfront CVA payment into running spread (RS) payments or worst-case bounds for wrong-way risk (WWR) effects. We introduce Multi-Level Monte Carlo (MLMC) in the context of CVA. In particular, we demonstrate how to apply parametric integration using MLMC to significantly reduce computation time in for CVA calibration, such as RS and worst-case bounds for WWR.