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

Author

Listed:
  • Andrea Barletta

    () (Aarhus University)

  • Paolo Santucci de Magistris

    () (Aarhus University and CREATES)

  • Francesco Violante

    () (Aarhus University and CREATES)

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.

Suggested Citation

  • Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2016-20
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    References listed on IDEAS

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    More about this item

    Keywords

    VIX options; orthogonal expansions; non-structural modeling; principal components;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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