MATHEMATICAL PSEUDO-COMPLETION OF THE BGM MODEL

Takashi Yasuoka
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Takashi Yasuoka: Financial Engineering Office, Fuji Research Institute Corporation, 3-1, Kandanishiki-cho, Chiyoda-ku, Tokyo 101-8443, Japan

Chapter 11 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume III), 2002, pp 247-274 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn 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.

Keywords: Quantitative Analysis; Financial Markets (search for similar items in EconPapers)
Date: 2002
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