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This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper first explores non-parametric procedures for recon- structing 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- fications 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 finally turn to the estimation of jump risk by extracting bipower variation.

Recovering Probabilistic Information from Options Prices and the Underlying