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The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical problems arise. In order to obtain a full well-behaved density, the option market prices must be smoothed and interpolated, and some way must be found to complete the tails beyond the range spanned by the available options. This paper develops an approach that solves both problems, with a combination of smoothing techniques from the literature modified to take account of the market's bid-ask spread, and a new method of completing the density with tails drawn from a Generalized Extreme Value distribution.
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