Efficient Calibration for CVA Using Multi-Level Monte Carlo

Abstract

The evaluation of credit valuation adjustments (CVA) usually involves 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 a running spread (RS) payments or a worst-case bounds for wrong-way risk (WWR) effects. In this article 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 the computational time for CVA calibration, such as needed for RS and for computing worst-case bounds for WWR.

Keywords: Multi-level Monte Carlo, Credit Value Adjustments (CVA), XVA, running CVA spread, worst-case bounds, wrong way risk