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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," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(1), pages 1-1, March.
    • Handle: RePEc:gam:jijfss:v:6:y:2018:i:1:p:30-:d:135806
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    References listed on IDEAS

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    2. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
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    6. Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    More about this item

    Keywords

    Kolmogorov -backward-equation; asymptotic expansion; Hermite -polynomials; implied volatility surface;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • F42 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Policy Coordination and Transmission

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