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Int. J. Financial Stud. 2018, 6(1), 30; doi:10.3390/ijfs6010030

Asymptotic Expansion of Risk-Neutral Pricing Density

Department of Economics and Finance, University of Greifswald, 17489 Greifswald, Germany
Received: 14 December 2017 / Revised: 7 February 2018 / Accepted: 27 February 2018 / Published: 12 March 2018
(This article belongs to the Special Issue Recent Developments in Numerical Methods for Option Pricing)
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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. View Full-Text
Keywords: Kolmogorov-backward-equation; asymptotic expansion; Hermite-polynomials; implied volatility surface Kolmogorov-backward-equation; asymptotic expansion; Hermite-polynomials; implied volatility surface

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Mazzoni, T. Asymptotic Expansion of Risk-Neutral Pricing Density. Int. J. Financial Stud. 2018, 6, 30.

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