Arbitrage-Based Estimation of Nonstationary Shifts in the Term Structure of Interest Rates




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    • Graduate School of Business, University of Chicago and College and Graduate School of Business, University of Texas at Austin, respectively. The authors acknowledge the helpful comments and suggestions of Kung-Sik Chan, Larry Fisher, Ron Gallant, Ed George, Tom Ho, Al Madansky, Krishna Ramaswamy, and the participants at finance seminars at Washington University in St. Louis and the University of Houston. An earlier draft of this paper was presented at the May 1988 CRSP Conference. This project was begun when the second author was visiting at the University of Chicago. Chu Zhang provided research assistance. The authors remain solely responsible for any errors contained herein. Financial support from the University of Chicago Graduate School of Business, the Research Foundation of the Institute of Chartered Financial Analysts, and the Institute for Quantitative Research in Finance is gratefully acknowledged.


The purpose of this paper is to provide a test of a state-dependent multinomial model of intertemporal changes in the term structure of interest rates. The theoretical background for the model comes from Ho and Lee (1986). The current paper extends their model in several significant ways. First, we perform diagnostic tests on the data to demonstrate that the empirical results reject a binomial model in favor of a trinomial one. After theoretically deriving the appropriate trinomial model, the current paper extends their model to allow for state-dependent shifts which are determined by the set of ex ante observable state variables. The methodology for the study utilizes OLS regressions to identify the exogenous explanatory variables which drive the hypothesized trinomial process of term structure evolution. The empirical tests indicate that the set of state variables explains a significant portion of the variability in the shifts of the term structure over time. The model also identifies and quantifies a set of variables which impact on changes in the term structure of interest rates.