Estimating the sensitivities of portfolio credit risk with respect to the underlying model parameters is an important problem for credit risk management. In this paper, we consider performance measures that may be expressed as an expectation of a performance function of the portfolio credit loss and derive closed-form expressions of its sensitivities to the underlying parameters. Our results are applicable to both idiosyncratic and macroeconomic parameters and to performance functions that may or may not be continuous. Based on the closed-form expressions, we first develop an estimator for sensitivities, in a general framework, that relies on the kernel method for estimation. The unified estimator allows us to further derive two general forms of the estimators by using conditioning techniques on either idiosyncratic or macroeconomic factors. We then specialize our results to develop faster estimators for three popular classes of models used for portfolio credit risk: latent variable models, Bernoulli mixture models, and doubly stochastic models.