Recovering Probabilistic Information From Options Prices and the Underlying

This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper …rst explores non-parametric procedures for reconstructing densities directly from options market data. I then consider local volatility functions, both through implied volatility trees and volatility interpolation. I then turn to alternative speci…cations of the stochastic process for the underlying. I estimate a mixture of log normals model, apply it to exchange rate data, and illustrate how to conduct forecast comparisons. I …nally turn to the estimation of jump risk by extracting bipower variation.