Quadratic Term Structure Models for Risk-Free and Defaultable Rates

22 Pages Posted: 21 Sep 2004

See all articles by Li Chen

Li Chen

Princeton University - Department of Electrical Engineering

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

H. Vincent Poor

Princeton University - Department of Electrical Engineering

Abstract

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.

Suggested Citation

Chen, Li and Filipovic, Damir and Poor, H. Vincent, Quadratic Term Structure Models for Risk-Free and Defaultable Rates. Mathematical Finance, Vol. 14, No. 4, pp. 515-536, October 2004. Available at SSRN: https://ssrn.com/abstract=591377

Li Chen (Contact Author)

Princeton University - Department of Electrical Engineering ( email )

Princeton, NJ 08544
United States

Damir Filipovic

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

H. Vincent Poor

Princeton University - Department of Electrical Engineering ( email )

Princeton, NJ 08544
United States

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