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

Andrea Barletta (), Paolo Santucci de Magistris () and Francesco Violante ()
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Andrea Barletta: Aarhus University, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Paolo Santucci de Magistris: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Aarhus University, Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: 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.

Keywords: VIX options; orthogonal expansions; non-structural modeling; principal components (search for similar items in EconPapers)
JEL-codes: C01 C02 C58 G12 G13 (search for similar items in EconPapers)
Date: 2016-06-28
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