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Pricing problems of perpetual Bermudan options

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  • Yoshifumi Muroi

    (Bank of Japan)

  • Takashi Yamada

    (Tokyo Institute of Technology)

Abstract

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

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 345.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:345

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Related research

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

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  1. 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.
  2. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  3. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May.
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