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The valuation of contingent claims using alternative numerical methods

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  • Chang, Chuang-Chang
  • Lin, Jun-Biao
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    Abstract

    This study compares the computational accuracy and efficiency of three numerical methods for the valuation of contingent claims written on multiple underlying assets; these are the trinomial tree, original Markov chain and Sobol-Markov chain approaches. The major findings of this study are: (i) the original Duan and Simonato (2001) Markov chain model provides more rapid convergence than the trinomial tree method, particularly in cases where the time to maturity period is less than nine months; (ii) when pricing options with longer maturity periods or with multiple underlying assets, the Sobol-Markov chain model can solve the problem of slow convergence encountered under the original Duan and Simonato (2001) Markov chain method; and (iii) since conditional density is used, as opposed to conditional probability, we can easily extend the Sobol-Markov chain model to the pricing of derivatives which are dependent on more than two underlying assets without dealing with high-dimensional integrals. We also use 'executive stock options' (ESOs) as an example to demonstrate that the Sobol-Markov chain method can easily be applied to the valuation of such ESOs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of International Financial Markets, Institutions and Money.

    Volume (Year): 20 (2010)
    Issue (Month): 5 (December)
    Pages: 490-508

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    Handle: RePEc:eee:intfin:v:20:y:2010:i:5:p:490-508

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    Web page: http://www.elsevier.com/locate/intfin

    Related research

    Keywords: Trinomial tree method Markov chain methods Low-discrepancy Multivariate contingent claims Executive stock options;

    References

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    1. Brian J. Hall & Kevin J. Murphy, 2000. "Stock Options for Undiversified Executives," NBER Working Papers 8052, National Bureau of Economic Research, Inc.
    2. Ekvall, Niklas, 1996. "A lattice approach for pricing of multivariate contingent claims," European Journal of Operational Research, Elsevier, vol. 91(2), pages 214-228, June.
    3. Huddart, Steven & Lang, Mark, 1996. "Employee stock option exercises an empirical analysis," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 5-43, February.
    4. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    5. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    6. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75.
    7. Antonio Camara, 2005. "Option Prices Sustained by Risk-Preferences," The Journal of Business, University of Chicago Press, vol. 78(5), pages 1683-1708, September.
    8. 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.
    9. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
    10. 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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