Non-Technical SummaryUnderstanding the fundamental economic risks that drive asset prices is a central research question in finance. Derivatives markets, in conjunction with their underlying stock markets, provide us with a rich set of data to study this topic. It is well established that there are two main types of risks driving asset prices. First, there is diffusive volatility, which measures the amount of uncertainty generated by 'usual' movements in economic fundamentals In asset pricing models, this risk is mostly represented by normally distributed innovations. Second, there are large, and infrequent shocks which generate rapid (and mostly adverse) changes in these fundamentals. These are usually represented by jumps. Due to the sheer size of the movements in state variables (and consequently in prices) conditional on the occurrence of a jump, this type of risk is usually much more dramatic than that generated by diffusive factors, it is harder to hedge and thus has much severer implications for wealth dynamics and risk premia. In many models it is assumed that the risk of such a jump occurring is the higher, the higher the current level of diffusive volatility, which in these models implies a perfect correlation of both risk types. We show in this paper that a simple separation of volatility and jump risk suffices for the model to match two basic and easily observable characteristics of the implied volatility (IV) smile for S&P 500 index options, namely its level and its slope. This improvement in explanatory power is achieved in addition to the matching of basic asset pricing moments like the equity premium, the volatility of the equity premium, the variance premium, and excess return predictability by the price-dividend ratio and the variance risk premium. The important feature of our model from an economic standpoint is therefore that the probability of a large shock is not perfectly correlated with the 'usual' uncertainty represented by diffusive variance. Roughly speaking, the level of the IV smile represents the amount of volatility, while the slope measures jump risk. In contrast to the hypotheses implied by standard models, the correlation between level and slope is far from perfectly positive, and it is even negative with a value around -0.3 for our sample for the S&P 500 index from 1996 to 2015, and even in a general nonlinear sense, the goodness of fit for slope as a function of level is rather low. Our model with separate processes for volatility and jump risk is able to explain these key properties of the data, while standard models are clearly not. The weak link between level and slope is not just of technical interest in the context of the asset pricing model discussed in our paper, but the two risk types related to level and slope are also fundamentally different economically. Overall, we find that both level and slope are related to macro variables, but the degree to which level can be explained by a collection of such variables is much higher than for slope. To sum up, we propose a simp...