This approach to generating implied distributions seems to have generated some interest many years ago, eg www.cmap.polytechnique.fr/~rama/dea/kelly.pdf, but not a whole lot since. I am wondering if anyone has encountered the practical problems with this approach. It does seem attractive, eg analytic form for the distribution and no need to extrapolate beyond high and low strikes.

What they suggest in this paper is minimising the Kullback-Liebler divergence ("Kullback's cross-entropy function"), which is difference of information (measured by the Shannon entropy) between the probability estimate and the data. The data are historical and information from option prices is accounted for in the estimated distribution - which is not purely risk-neutral (?). This is equivalent to the standard maximum likelihood estimation (modulo sign), constrained with option prices in this case, hence a pretty standard approach... (e.g. I use MLE and KL interchangeably only to analyse different information criteria for my models.)KL divergence: http://en.wikipedia.org/wiki/Kullback%E ... divergence