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Tree methods

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  • Jérôme Lelong

    ()
    (LJK - Laboratoire Jean Kuntzmann - CNRS : UMR5224 - Université Joseph Fourier - Grenoble I - Université Pierre-Mendès-France - Grenoble II - Institut Polytechnique de Grenoble - Grenoble Institute of Technology, INRIA Rocquencourt - MATHFI - INRIA - École des Ponts ParisTech (ENPC) - Université Paris-Est Créteil Val-de-Marne (UPEC))

  • Antonino Zanette

    (INRIA Rocquencourt - MATHFI - INRIA - École des Ponts ParisTech (ENPC) - Université Paris-Est Créteil Val-de-Marne (UPEC))

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    Abstract

    Tree methods are among the most popular numerical methods to price financial derivatives. Mathematically speaking, they are easy to understand and do not require severe implementation skills to obtain algorithms to price financial derivatives. Tree methods basically consist in approximating the diffusion process modeling the underlying asset price by a discrete random walk. In this contribution, we provide a survey of tree methods for equity options, which focus on multiplicative binomial Cox-Ross-Rubinstein model.

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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00776713.

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    Date of creation: 15 May 2010
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    Publication status: Published, Encyclopedia of Quantitative Finance, John Wiley & Sons, Ltd. (Ed.), 2010, 7 pages
    Handle: RePEc:hal:journl:hal-00776713

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00776713
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    1. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    2. Philipp J. Schönbucher, 2000. "A Tree Implementation of a Credit Spread Model for Credit Derivatives," Bonn Econ Discussion Papers bgse17_2001, University of Bonn, Germany.
    3. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-50.
    4. P. Forsyth & K. Vetzal & R. Zvan, 2002. "Convergence of numerical methods for valuing path-dependent options using interpolation," Review of Derivatives Research, Springer, vol. 5(3), pages 273-314, October.
    5. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
    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.
    7. 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.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    9. Jér�me Barraquand & Thierry Pudet, 1996. "Pricing Of American Path-Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51.
    10. Bardia Kamrad & Peter Ritchken, 1991. "Multinomial Approximating Models for Options with k State Variables," Management Science, INFORMS, vol. 37(12), pages 1640-1652, December.
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