XVA Greeks via Likelihood Ratio Method

Credit Value Adjustment sensitivities represent the quantitative basis for the full spectrum of steering activities of CVA desks: hedging, control, explanation and forecasting. In realistic applications, typically involving large numbers of market risk-factors, calculation of CVA Greeks poses significant computational challenges. Different approaches have been explored in literature. In this paper we present an alternative technique, the Likelihood Ratio Method (LRM), originally introduced in the framework of derivatives' pricing. With respect to most common practices, LRM does not require the explicit differentiation of involved payoffs. The aim of this paper is to frame the theoretical formalism in a realistic banking industry's CVA model, focusing on the financial interpretation of the results and the practical issues potentially affecting the reliability thereof. To this purpose, a proof of concept is presented to provide a concrete test of the features of the proposed approach