A multivariate credit risk model is presented that introduces dependence to individual default events via a stochastic time change. To demonstrate its practical value, this model is applied to the pricing of kth-to-default swaps. Despite the freedom in specifying the term structures of individual default probabilities, it is still possible to present closed-form solutions for the resulting portfolio loss distribution. Hence, the model can be used to simultaneously explain spreads of individual credit default and kth-to-default swaps. Moreover, the stochastic time change introduces a dynamic component that allows for the consistent pricing of credit derivatives across all maturities. Qualitative and quantitative results on the dependence structure include the induced copula of the default times, the pairwise default correlation, the lower-extremal dependence coefficient and the distribution of the kth default time.