Index Option Returns and Generalized Entropy Bounds

I develop a continuum of new nonparametric bounds. They stem from the solution of an optimization problem that is complementary to the Hansen and Jaganathan (1991) approach and are shown to complete the nonparametric bound universe the literature has so far discovered. Through the lens of these bounds, I estimate rare event distributions using index option returns. Standard disaster models and their perturbations are shown unable to meet the bounds implied by simple static option trading strategies. My results suggest more sophisticated modeling of disaster models in order to reconcile with the index option data.