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Asymptotic Expansion of Risk-Neutral Pricing Density

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  • Thomas Mazzoni

    (Department of Economics and Finance, University of Greifswald, 17489 Greifswald, Germany)

Abstract

A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov -backward-equation is approximated by using a complete set of orthogonal Hermite -polynomials. The derived model is calibrated and tested on a collection of 1075 European-style ‘Deutscher Aktienindex’ (DAX) index options and is shown to generate very precise option prices and a more accurate implied volatility surface than conventional methods.

Suggested Citation

  • Thomas Mazzoni, 2018. "Asymptotic Expansion of Risk-Neutral Pricing Density," IJFS, MDPI, vol. 6(1), pages 1-26, March.
    • Handle: RePEc:gam:jijfss:v:6:y:2018:i:1:p:30-:d:135806
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