Fast and Stable Credit Gamma of CVA

Abstract

Credit Valuation Adjustment is a balance sheet item which is nowadays subject to active risk management by specialized traders. However, one of the most important risk factors, which is the vector of default intensities of the counterparty, affects in a non-differentiable way the most general Monte Carlo estimator of the adjustment, through simulation of default times. Thus the computation of first and second order (pure and mixed) sensitivities involving these inputs cannot rely on direct path-wise differentiation, while any approach involving finite differences shows very high statistical noise. We present ad hoc analytical estimators which overcome these issues while offering very low runtime overheads over the baseline computation of the price adjustment. We also discuss the conversion of the so-obtained sensitivities to model parameters (e.g. default intensities) into sensitivities to market quotes (e.g. Credit Default Swap spreads).