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Mathematical Pseudo-Completion Of The Bgm Model

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III)

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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, 2002. "Mathematical Pseudo-Completion Of The Bgm Model," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 11, pages 247-274, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812778451_0011
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    Keywords

    Quantitative Analysis; Financial Markets;

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