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Mathematical Pseudo-Completion Of The Bgm Model

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  • TAKASHI YASUOKA

    (Financial Engineering Office, Fuji Research Institute Corporation, 3-1, Kandanishiki-cho, Chiyoda-ku, Tokyo 101-8443, Japan)

Abstract

In this paper, the BGM model is generalized such that it does not need the instantaneous forward rates in the framework of HJM, but includes the original BGM theory as a special case with smooth volatility. Our two convergence theorems show that the original BGM theory is topologically dense in our framework. This topological result makes the BGM model mathematically complete for numerical pricing with piecewise continuous volatility. In addition, we shall make some remarks on the BGM calibration for business use in connection with our theorems.

Suggested Citation

  • Takashi Yasuoka, 2001. "Mathematical Pseudo-Completion Of The Bgm Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 375-401.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:03:n:s0219024901001048
    DOI: 10.1142/S0219024901001048
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
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