Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates
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.
|Date of creation:||31 Mar 2003|
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- Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
- Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
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- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
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