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Hermite Binomial Trees: A Novel Technique For Derivatives Pricing

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  • ARTURO LECCADITO

    (Dipartimento di Scienze Economiche, Statistiche e Finanziarie, Università della Calabria, Ponte Bucci cubo 3C, Rende (CS), 87030, Italy)

  • PIETRO TOSCANO

    (BlackRock Institutional Trust Company, N.A., 400 Howard Street, San Francisco, CA 94105, USA)

  • RADU S. TUNARU

    (Business School, University of Kent, Park Wood Road, Canterbury CT2 7PE, UK)

Abstract

Edgeworth binomial trees were applied to price contingent claims when the underlying return distribution is skewed and leptokurtic, but with the limitation of working only for a limited set of skewness and kurtosis values. Recently, Johnson binomial trees were introduced to accommodate any skewness-kurtosis pair, but with the drawback of numerical convergence issues in some cases. Both techniques may suffer from non-exact matching of the moments of distribution of returns. A solution to this limitation is proposed here based on a new technique employing Hermite polynomials to match exactly the required moments. Several numerical examples illustrate the superior performance of the Hermite polynomials technique to price European and American options in the context of jump-diffusion and stochastic volatility frameworks and options with underlying asset given by the sum of two lognormally distributed random variables.

Suggested Citation

  • Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-36.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:n:s0219024912500586
    DOI: 10.1142/S0219024912500586
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    3. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.

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