Do option markets correctly price the probabilities of movement of the underlying asset?

We answer this question by comparing te risk-neutral density estimated in complete markets from cross-section of S&P 500 option prices to the risk-neutral density inferred from the time series density of the S&P 500 index. If investors are risk-averse, the latter density is different from the actual density that could be inferred from the time series of S&P 500 returns. Naturally, the observed asset returns do not follow the risk-neutral dynamics, which are therefore not directly observable. In contrast to the existing literature, we avoid making any assumptions on investors' preferences, by comparing two risk-adjusted densities, rather than a risk-adjusted density from option prices to an unadjusted density from index returns. Our only maintained hypothesis is a one-factor structure for the S&P 500 returns. We propose a new method, based on an empirical Girsanov's change of measure, to identify the risk-neutral density from the observed unadjusted index returns. We design four different tests of the null hypothesis that the S&P 500 options are efficiently priced given the S&P 500 index dynamics, and reject it. By adding a jump component to the index dynamics, we are able to partly reconcile the differences between the index and option-implied risk-neutral densities, and propose a peso-problem interpretation of this evidence.