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The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables

Published online by Cambridge University Press:  06 April 2009

Frank de Jong  and
Pedro Santa-Clara
Frank de Jong
Affiliation:
Finance Group, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands
Pedro Santa-Clara
Affiliation:
Anderson Graduate School of Management, UCLA, Westwood Plaza, Los Angeles, CA 90095-1481
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Abstract

The objective of this paper is twofold. First, the paper develops a class of models of the term structure of interest rates, in the Heath, Jarrow, and Morton (1992) framework, with dynamics characterized by the evolution of a small set of state variables. Second, the paper exploits this characterization of the dynamics of the term structure in an estimation exercise that makes use of both the time series and cross-section of bond prices. In this way, our class of models bridges the gap between traditional models, such as Cox, Ingersoll, and Ross (1985) and Vasicek (1977), that emphasize the dynamics of interest rates and the models of Heath, Jarrow, and Morton (1992) that stress fitting the cross-section of bond prices.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 34 , Issue 1 , March 1999 , pp. 131 - 157
Copyright
Copyright © School of Business Administration, University of Washington 1999

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References

Amin, K. I., and Morton, A.. “Implied Volatility Functions in Arbitrage Free Term Structure Models.” Journal of Financial Economics, 35 (1994), 141–180.CrossRefGoogle Scholar
Bliss, R. R., and Ritchken, P.. “Empirical Tests of Two State-variable Heath-Jarrow-Morton Models.” Journal of Money, Credit and Banking, 28 (1996), 452–476.CrossRefGoogle Scholar
Boudoukh, J.; Whitelaw, R. F.; Richardson, M.; and Stanton, R.. “Pricing Mortgage-Backed Securities in a Multifactor Interest Rate Environment: A Multivariate Density Approach.” Review of Financial Studies, 10 (1997), 405–446.CrossRefGoogle Scholar
Brace, A., and Musiela, M.. “A Multifactor Gauss Markov Implementation of Heath, Jarrow, Morton.” Mathematical Finance, 2 (1994), 259–283.CrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “Savings Bonds, Retractable Bonds, and Callable Bonds.” Journal of Banking and Finance, 3 (1977), 133–156.CrossRefGoogle Scholar
Brown, S., and Dybvig, P.. “The Empirical Implications of the CIR Theory.” Journal of Finance, 41 (1986), 617–632.CrossRefGoogle Scholar
Carverhill, A. “When is the Short Rate Markovian?” Mathematical Finance, 4 (1994), 305–312.CrossRefGoogle Scholar
Chan, K. C.; Karolyi, G. A.; Longstaff, F. A.; and Sanders, A. B.. “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate.” Journal of Finance, 47 (1992), 1209–1227.Google Scholar
Chen, R.-R., and Scott, L.. “ML Estimation for a Multifactor Equilibrium Model of the Term Structure.” Journal of Fixed Income, 3 (1993), 14–31.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385–407.CrossRefGoogle Scholar
Dai, Q., and Singleton, K. R.. “Specification Analysis of Affine Term Structure Models.” Working Paper, Stanford Univ. (1997).CrossRefGoogle Scholar
de Jong, F. “Time Series and Cross-Section Information in Affine Term Structure Models.” CentER Discussion Paper 9786, Tilburg Univ. (1997).Google Scholar
Duan, J., and Simonato, J.. “Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter.” Working Paper, CIRANO (1995).Google Scholar
Duffie, D., and Kan, R.. “A Yield-Factor Model of Interest Rates.” Mathematical Finance, 6 (1996), 379–406.CrossRefGoogle Scholar
El Karoui, N., and Lacoste, V.. “Multifactor Models of the Term Structure of Interest Rates.” Working Paper, Université de Paris VI (1992).Google Scholar
Flesaker, B. “Arbitrage Free Pricing of Interest Rate Futures and Forward Contracts.” Journal of Futures Markets, 13 (1993a), 77–91.CrossRefGoogle Scholar
Flesaker, B. “Testing the Heath-Jarrow-Morton/Ho-Lee Model of Interest Rate Contingent Claims Pricing.” Journal of Financial and Quantitative Analysis, 28 (1993b), 483–495.CrossRefGoogle Scholar
Geyer, A. L. J., and Pichler, S.. “A State-Space Approch to Estimate the Term Structure of Interest Rates: Some Empirical Evidence.” Working Paper, Univ. of Economics, Vienna (1995).Google Scholar
Gouriéroux, C.; Monfort, A.; and Trognon, A.. “Pseudo Maximum Likelihood Methods: Theory.” Econometrica, 52 (1984), 681–700.CrossRefGoogle Scholar
Harvey, A. C.The Econometric Analysis of Time Series. Second Edition, MIT Press (1990).Google Scholar
Harvey, A. C.Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge Univ. Press (1989).Google Scholar
Heath, D.; Jarrow, R. A.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica, 60 (1992), 77–105.CrossRefGoogle Scholar
Ho, T. S. Y., and Lee, S.. “Term Structure Movements and Pricing Interest Rate Contingent Claims.” Journal of Finance, 41 (1986), 1011–1029.CrossRefGoogle Scholar
Hull, J., and White, A.. “Bond Option Pricing on a Model for the Evolution of Bond Prices.” Advances in Options and Futures Research, 6 (1993), 1–13.Google Scholar
Jamshidian, F. “Bond and Option Evaluation in the Gaussian Interest Rate Model.” Research in Finance, 9 (1991), 131–170.Google Scholar
Pearson, N. D., and Sun, T. S.. “Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model.” Journal of Finance, 49 (1994), 1279–1304.CrossRefGoogle Scholar
Richard, S. F. “A Model of the Term Structure of Interest Rates with Variance Proportional to the Cube of the Short Rate.” Unpubl. Manuscript, Miller, Anderson and Sherrerd (1994).Google Scholar
Ritchken, P., and Sankarasubramanian, L.. “Volatility Structures of Forward Rates and the Dynamics of the Term Structure.” Mathematical Finance, 5 (1995), 55–72.CrossRefGoogle Scholar
Santa-Clara, P. “Markovian Arbitrage-Free Models of the Term Structure of Interest Rates.” Working Paper, Anderson School at UCLA (1995).Google Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (1977), 177–188.CrossRefGoogle Scholar
White, H. “Maximum Likelihood Estimation of Misspecified Models.” Econometrica, 50 (1982), 1–25.CrossRefGoogle Scholar