  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).
