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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)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 15 (2012)
    Issue (Month): 08 ()
    Pages: 1250058-1-1250058-36

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:p:1250058-1-1250058-36

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    Related research

    Keywords: Option pricing; binomial trees; Hermite expansion; skewness and kurtosis;

    References

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    2. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
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    Cited by:
    1. Tommaso Paletta & Arturo Leccadito & Radu Tunaru, 2013. "Pricing and Hedging Basket Options with Exact Moment Matching," Science & Finance (CFM) working paper archive 1312.4443, Science & Finance, Capital Fund Management.

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