Principled pasting: attaching tails to risk-neutral probability density functions recovered from option prices

The popular ‘curve-fitting’ method of using option prices to construct an underlying asset's risk neutral probability density function (RND) first recovers the interior of the density and then attaches left and right tails. Typically, the tails are constructed so that values of the RND and risk neutral cumulative distribution function (RNCDF) from the interior and the tails match at the attachment points. We propose and demonstrate the feasibility of also requiring that the left and right tails accurately price the options with strikes at the attachment points. Our methodology produces a RND that provides superior pricing performance than earlier curve-fitting methods for both those options used in the construction of the RND and those that were not. We also demonstrate that Put-Call Parity complicates the classification of in and out of sample options.