Interest rate models with both continuous and discrete uncertainties are studied. The researchers use a Poisson random measure to model event-driven noise. They price interest rate derivatives under real-world probabilities using a growth optimal portfolio as a benchmark. The forward rates' real-world dynamics are determined, and for certain volatility structures, finite Markovian representations are found. Additionally, they identify a class of tractable affine term structures that do not require an equivalent risk-neutral probability measure.