Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates

Li Chen () and H. Vincent Poor
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H. Vincent Poor: Princeton University

Finance from University Library of Munich, Germany

Abstract: In this paper, a class of regular quadratic Gaussian processes is defined to characterize quadratic term structure models (QTSMs) in a general Markovian setting. The primary motivation for this definition is to provide a more general model for the quadratic term structure of the forward curve, while maintaining the analytical tractability of the traditional QTSMs. It is demonstrated that the tractability of QTSMs does not necessarily rely on the Ornstein-Uhlenbeck state processes used in their traditional definition. Rather, the crucial element that provides analytical solutions for the prices of zero-coupon bonds and their options is a so-called quadratic Gaussian property as defined in this paper. In order to retain this property for a general Markov process, it is shown that, under the regularity conditions, no jumps are allowed in the infinitesimal generator of the process. It is further shown that the coefficient functions defined in the quadratic Gaussian property can be determined by multi-variate Riccati equations with a unique admissible parameter set. The implications of this result for modeling the term structure of risk-free rates and defaultable rates are discussed.

Keywords: Quadratic term structure models; option pricing; defaultable rates; time-homogenous Markov processes (search for similar items in EconPapers)
JEL-codes: C39 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2003-03-31
New Economics Papers: this item is included in nep-fmk and nep-mac
Note: Type of Document - pdf; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 20; figures: included/request from author/draw your own. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.
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Citations: View citations in EconPapers (21)

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