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High-order accurate implicit methods for the pricing of barrier options

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  • J. C. Ndogmo
  • D. B. Ntwiga

Abstract

This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or discretely. In addition to the high-order accuracy of the scheme, and the stretching effect of the coordinate transformation, the main feature of this approach lies on a probability-based optimal determination of boundary conditions. This leads to much faster and accurate results when compared with similar pricing approaches. The strength of the present scheme is particularly demonstrated in the valuation of discretely monitored barrier options where it yields values closest to those obtained from the only semi-analytical valuation method available.

Suggested Citation

  • J. C. Ndogmo & D. B. Ntwiga, 2007. "High-order accurate implicit methods for the pricing of barrier options," Papers 0710.0069, arXiv.org.
    • Handle: RePEc:arx:papers:0710.0069
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    References listed on IDEAS

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    1. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    2. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    3. Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers 99s-15, CIRANO.
    4. A. Mayo, 2004. "High-order accurate implicit finite difference method for evaluating American options," The European Journal of Finance, Taylor & Francis Journals, vol. 10(3), pages 212-237.
    5. Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104.
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    Cited by:

    1. J. C. Ndogmo, 2008. "Classification of barrier options," Papers 0806.4676, arXiv.org.

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