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.