Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates
AbstractIn 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.
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Length: 20 pages
Date of creation: 31 Mar 2003
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Quadratic term structure models; option pricing; defaultable rates; time-homogenous Markov processes;
Find related papers by JEL classification:
- C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-04-09 (All new papers)
- NEP-FMK-2003-04-09 (Financial Markets)
- NEP-MAC-2003-04-09 (Macroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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