We consider a classical term structure model framework, ie, a Heath–Jarrow–Morton framework, on a time-discrete tenor, such as the London Interbank Offered Rate market model, using a sequence of tenor discretizations, where the tenors are valid for a specific simulation time interval. At time t_j, when a possible change of the tenor time discretization from T^{j–1};T^j occurs, the models fulfill a consistency condition such that the curve simulation is arbitrage-free for all times t. The setup then allows us to model dynamic refinements of the tenor structure and, as a special case, a quasi-time-homogeneous tenor structure. Our numerical results show that the time-homogeneous modeling approach improves other model aspects, eg, forward correlation and forward volatility. We discuss these aspects in the context of (valuation adjustment) exposure simulations.