Empirical literature increasingly supports that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort from the theoretical literature to develop credit risk models that would include this possibility. The goals of this paper are, first, to develop the theoretical, reduced-form framework needed to handle stochastic correlation of recovery and intensity, proposing a new class of models; second, to understand under what conditions would our class of models reflect empirically observed features; and, finally, to use a concrete model from our class to study the impact of this correlation on credit risk term structures. We show that, in our class of models, it is possible to model directly empirically observed features. For instance, we can define default intensity and losses given default to be higher during economic depression periods – the well-known credit risk business cycle effect. Using the concrete model, we show that in reduced-form models different assumptions (concerning default intensities, distribution of losses given default and specifically their correlation) have a significant impact on the shape of credit spread term structures and consequently on pricing of credit products as well as credit risk assessment in general. Finally, we propose a way to calibrate this class of models to market data and illustrate the technique using our concrete example using US market data on corporate yields.