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Pricing problems of perpetual Bermudan options


  • Yoshifumi Muroi

    (Bank of Japan)

  • Takashi Yamada

    (Tokyo Institute of Technology)


The pricing problem of options with an early exercise feature, such as American options, is one of the important topics in mathematical finance. The pricing formulas for American options, however, have not been found in general and the numerical methods are required to derive the price of these options, besides some exceptions, such as perpetual American options. Although the closed form pricing formula for perpetual American options in the Black and Scholes economy is known explicitly, it seems that the pricing formula for perpetual Bermudan options is not known. The value function of perpetual Bermudan options is characterized with the partial differential equation and this is solved numerically in this article

Suggested Citation

  • Yoshifumi Muroi & Takashi Yamada, 2006. "Pricing problems of perpetual Bermudan options," Computing in Economics and Finance 2006 345, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:345

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    References listed on IDEAS

    1. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    2. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
    3. M. A. H. Dempster & J. P. Hutton, 1999. "Pricing American Stock Options by Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 229-254.
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    More about this item


    perpetual Bermudan options; optimal stopping problems; linear complementarity problem; PSOR algorithm; linear programming methods; interior point methods;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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