Option-implied probability distributions: How reliable? How jagged?*

•A spline model to estimate state price vectors from option prices is proposed.•Computationally inexpensive LAD and Bayesian estimators of state prices are derived.•Bayesian procedures allow to easily compute credible intervals for the state prices.•S&P 500 options data allows to recover state prices with high precision.•More precise estimates of state prices are obtained by imposing uni-modality constraints.

Estimates of option-implied probability distributions are routinely used in central banks, as well as in other institutions, but their reliability is often difficult to assess. To address this issue, we propose a semi-nonparametric model that allows to compute exact credible intervals around estimated distributions. By analyzing a panel of S&P 500 options, we find that the estimates of the distributions are quite precise. We also provide evidence that the multi-modality often found in option-implied distributions could be an artifact due to over-fitting, and that models with uni-modality constraints have high posterior odds.