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

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 03, 375-401

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.

Keywords: Generalized BGM theory; interest rate option pricing; lognormal LIBOR model; stability of the stochastic differential equation; term structure of volatility (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901001048

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