Department of Economics and Business Economics

Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach

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We propose a non-structural pricing method to retrieve the risk-neutral density implied by options contracts on the CBOE VIX. The method is based on orthogonal polynomial expansions around a kernel density and yields the risk-neutral density of the underlying asset without the need for modeling its dynamics. The method imposes only mild regularity conditions on shape of the density. The approach can be thought of as an alternative to Hermite expansions where the kernel has positive support. .e family of Laguerre kernels is extended to include the GIG and the generalized Weibull densities, which, due to their flexible rate of decay, are better suited at modeling the density of the VIX. Based on this technique, we propose a simple and robust way to estimate the expansion coefficients by means of a principal components analysis. We show that the proposed methodology yields an accurate approximation of the risk-neutral density also when the no-arbitrage and efficient option prices are contaminated by measurement errors. A number of numerical illustrations support the adequacy and the flexibility of the proposed expansions in a large variety of cases.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages41
Publication statusPublished - 4 Jul 2016
SeriesCREATES Research Papers
Number2016-20

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