We propose a novel method to estimate risk-neutral quantiles that uses sorting to minimize an objective function given by a convex combination of call and put option prices over the range of available strike prices. We demonstrate that this new method significantly improves the accuracy of...

We propose a non-parametric method based on a model-free formula to evaluate the tails of a risk-neutral distribution using the full cross-section of option prices at a fixed horizon. The method leads to the joint estimation of risk-neutral tail probabilities and tail expectations beyond the...