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Achieving smooth asymptotics for the prices of European options in binomial trees

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  • Mark Joshi

Abstract

A new binomial approximation to the Black-Scholes model is introduced. It is shown that, for digital options and vanilla European call and put options, a complete asymptotic expansion of the error in powers of n-1 exists. This is the first binomial tree for which an asymptotic expansion has been shown to exist.

Suggested Citation

  • Mark Joshi, 2009. "Achieving smooth asymptotics for the prices of European options in binomial trees," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 171-176.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:2:p:171-176
    DOI: 10.1080/14697680802624955
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    References listed on IDEAS

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    1. Dietmar Leisen & Matthias Reimer, 1996. "Binomial models for option valuation - examining and improving convergence," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 319-346.
    2. Martin Widdicks & Ari D. Andricopoulos & David P. Newton & Peter W. Duck, 2002. "On the enhanced convergence of standard lattice methods for option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(4), pages 315-338, April.
    3. Leisen, Dietmar P. J., 1998. "Pricing the American put option: A detailed convergence analysis for binomial models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1419-1444, August.
    4. Yisong Tian, 1993. "A modified lattice approach to option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(5), pages 563-577, August.
    5. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 271-293, April.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Dong Zou & Pu Gong, 2017. "A Lattice Framework with Smooth Convergence for Pricing Real Estate Derivatives with Stochastic Interest Rate," The Journal of Real Estate Finance and Economics, Springer, vol. 55(2), pages 242-263, August.
    2. Kyoung-Sook Moon & Hongjoong Kim, 2013. "A multi-dimensional local average lattice method for multi-asset models," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 873-884, May.
    3. Yury Lebedev & Arunava Banerjee, 2024. "Gaussian Recombining Split Tree," Papers 2405.16333, arXiv.org.
    4. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.

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