Asymptotic Expansion of Risk-Neutral Pricing Density

Thomas Mazzoni
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Thomas Mazzoni: Department of Economics and Finance, University of Greifswald, 17489 Greifswald, Germany

IJFS, 2018, vol. 6, issue 1, 1-26

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.

Keywords: Kolmogorov -backward-equation; asymptotic expansion; Hermite -polynomials; implied volatility surface (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2018
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