It exist strong consensus in the academic literature that if we want to describe the random behaviour of equity products, as e.g. the S&P 500 index, we need to understand two main structures: stochastic volatility and jumps. Our paper compares the performance of a large number of state of the art continuous-time models. The model specifications are either purely driven by a stochastic volatility model component or combine a stochastic volatility model component with a jump component. Our finding shows first of all, that recently developed more flexibel stochastic volatility specifications outperform stochastic volatility specifications used commonly in the finance literature. Even more strikingly, we find that adding a jump component to a model will lead to the fact that any pure stochastic volatility component, even the most flexibel once, will be strictly outperformed as can be seen in the following table.

The table show all models analyzed ranked by the Deviance Information Criterion (DIC) which we use as a performance measure (small DIC values are better than large values). All models which have a jump component, SVCJ (stochastic volatility with correlated jumps) and SVJ (stochastic volatility with jumps), strictly outperform the pure SV (stochastic volatility) models that are clustered at the bottom of the table. The full paper can be downloaded here