QUADRATIC TERM STRUCTURE MODELS FOR RISK‐FREE AND DEFAULTABLE RATES

Li Chen · Damir Filipović · H. Vincent Poor

108 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Credit Risk and Financial Regulations Economic theories and models

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.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 2000Transform Analysis and Asset Pricing for Affine Jump-diffusions 1999Modeling Term Structures of Defaultable Bonds 1997A Markov Model for the Term Structure of Credit Risk Spreads 1998On cox processes and credit risky securities 2003Affine processes and applications in finance 2002Quadratic Term Structure Models: Theory and Evidence 2002Asset Pricing under the Quadratic Class

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