We introduce a tractable class of non-affine price processes with multifrequency stochastic volatility and jumps. The specications require few xed parameters and deliver fast option pricing. One key ingredient is a tight link between jumps and volatility regimes, as asset pricing theory suggests. Empirically, the model matches implied volatility surfaces and their dynamics without requiring parameter recalibration. A variety of metrics show improvements over traditional benchmarks in- and out-of-sample.