Quadratic term structure models for risk-free and defaultable rates

Li Chen, Damir Filipović, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


In this paper, quadratic term structure models (QTSMs) are analyzed and characterized in a general Markovian setting. The primary motivation for this work is to find a useful extension of the traditional QTSM, which is based on an Ornstein-Uhlenbeck (OU) state process, while maintaining the analytical tractability of the model. To accomplish this, the class of quadratic processes, consisting of those Markov state processes that yield QTSM, is introduced. The main result states that OU processes are the only conservative quadratic processes. In general, however, a quadratic potential can be added to allow QTSMs to model default risk. It is further shown that the exponent functions that are inherent in the definition of the quadratic property can be determined by a system of Riccati equations with a unique admissible parameter set. The implications of these results for modeling the term structure of risk-free and defaultable rates are discussed.

Original languageEnglish (US)
Pages (from-to)515-536
Number of pages22
JournalMathematical Finance
Issue number4
StatePublished - Oct 2004

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Economics and Econometrics
  • Accounting
  • Finance
  • Social Sciences (miscellaneous)


  • Option pricing
  • Quadratic term structure models
  • Risk-free and defaultable rates
  • Time-homogenous Markov processes


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