Estimating Implied PDFs From American Options on Futures: A New Semiparametric Approach

This article develops a new methodology for estimating implied probability density functions for futures prices from American options. The restricting Black–Scholes assumption of a lognormal distribution for the underlying asset is relaxed with the use of the more flexible distributional form of an Edgeworth series expansion around a lognormal distribution. The model is applied to the crude oil market. The results provide strong evidence that the market consensus can be accurately reflected in the risk‐neutral densities recovered from observed option prices. The recovered distributions are tested and found to differ significantly from a single lognormal distribution. In addition, the recovered distributions are more robust than those recovered with a model, which assumes a mixture of two lognormal distributions. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:1–30, 2002