The minimum local cross-entropy criterion for inferring risk-neutral price distributions from traded options prices

A quantity known as the Local Cross-Entropy (LCE) for a density is proposed, defined
to be the local derivative of the Cross-Entropy between a density and a ’kernel-smoothed’ version of itself, with respect to bandwidth of the smoothing. This criterion is argued to be of the ’smoothness’ type and is also argued to be more sensible and ’natural’ than the
frequently used ’Maximum Entropy’ criterion for many applications. When applied to price
distributions in conjunction Options constraints the minimum LCE criterion is shown to produce estimates which share the best theoretical properties of the Maximum Entropy approach with the best practical properties of the estimators identified by Jackwerth and Rubinstein