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Another Look at Models of the Short-Term Interest Rate

Published online by Cambridge University Press:  06 April 2009

Robin J. Brenner ,
Richard H. Harjes  and
Kenneth F. Kroner
Robin J. Brenner
Affiliation:
Brenner, Merrill Lynch, World Financial Center, North Tower, 15th Floor, New York, NY 10281
Richard H. Harjes
Affiliation:
Advanced Strategies and Research Group, Wells Fargo Nikko Investment Advisors, 45 Fremont Street, San Francisco, CA 94105
Kenneth F. Kroner
Affiliation:
University of Arizona (departments of economics and finance) and Advanced Strategies and Research Group, Wells Fargo Nikko Investment Advisors, 45 Fremont Street, San Francisco, CA 94105.
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Abstract

The short-term rate of interest is fundamental to much of theoretical and empirical finance, yet no consensus has emerged on the dynamics of its volatility. We show that models which parameterize volatility only as a function of interest rate levels tend to over emphasize the sensitivity of volatility to levels and fail to model adequately the serial correlation in conditional variances. On the other hand, serial correlation based models like GARCH models fail to capture adequately the relationship between interest rate levels and volatility. We introduce and test a new class of models for the dynamics of short-term interest rate volatility, which allows volatility to depend on both interest rate levels and information shocks. Two important conclusions emerge. First, the sensitivity of interest rate volatility to interest rate levels has been overstated in the literature. While this relationship is important, adequately modeling volatility as a function of unexpected information shocks is also important. Second, we conclude that the volatility processes in many existing theoretical models of interest rates are misspecified, and suggest new paths toward improving the theory.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 31 , Issue 1 , March 1996 , pp. 85 - 107
Copyright
Copyright © School of Business Administration, University of Washington 1996

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References

Ball, C. A., and Torous, W. N.. “A Stochastic Volatility Model for Short Term Interest Rates and the Detection of Structural Shifts.” Unpubl. Manuscript, Anderson School of Management, Univ. of California at Los Angeles (1994).Google Scholar
Bliss, R. R., and Smith, D. C.. “Stability of Interest Rate Processes.” Unpubl. Manuscript, Indiana Univ. (1994).Google Scholar
Bollerslev, T. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 (1986), 307–327.CrossRefGoogle Scholar
Bollerslev, T.; Chou, R. T.; and Kroner, K. F.. “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence.” Journal of Econometrics, 52 (1992), 5–59.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “Analyzing Convertible Bonds.” Journal of Financial and Quantitative Analysis, 15 (1980), 907–929.CrossRefGoogle Scholar
Broze, L.; Scaillet, O.; and Zakoian, J.-M.. “Testing for Continuous-Time Models of the Short Term Interest Rate.” Unpubl. Manuscript, CORE, Belgium (1993).Google Scholar
Cai, J. “A Markov Model of Unconditional Variance in ARCH.” Journal of Business and Economic Statistics (1994).Google Scholar
Cecchetti, S.; Cumby, R.; and Figlewski, S.. “Estimation of the Optimal Futures Hedge.” Review of Economics and Statistics, 70 (1988), 623–630.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
Cox, J. “Notes on Option Pricing I: Constant Elasticity of Variance Diffusions.” Unpubl. Manuscript, Stanford Univ. (1975).Google Scholar
Cox, J.; Ingersoll, J.; and Ross, S.. “An Analysis of Variable Rate Loan Contracts.” Journal of Finance, 35 (1980), 389–403.CrossRefGoogle Scholar
Cox, J.; Ingersoll, J.; and Ross, S.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 145–166.CrossRefGoogle Scholar
Dietrich-Campbell, B., and Schwartz, E.. “Valuing Debt Options: Empirical Evidence.” Journal of Financial Economics, 16 (1986), 321–343.CrossRefGoogle Scholar
Dothan, U. “On the Term Structure of Interest Rates.” Journal of Financial Economics, 6 (1978), 59–69.CrossRefGoogle Scholar
Engle, R. E. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation.” Econometrica, 50 (1982), 987–1008.CrossRefGoogle Scholar
Engle, R. F.; Lilien, D.; and Robins, R.. “Estimating Time Varying Risk Premia in the Term Structure:The ARCH-M Model.” Econometrica, 55 (1987), 391–407.CrossRefGoogle Scholar
Engle, R. F.; Ng, V.; and Rothschild, M.. “Asset Pricing with a Factor ARCH Covariance Structure: Empirical Estimates for Treasury Bills.” Journal of Econometrics, 45 (1992), 213–238.CrossRefGoogle Scholar
Evans, M. “Interpreting the Term Structure Using the Intertemporal Capital Asset Pricing Model: An Application of the Non-linear ARCH-M Model.” Unpubl. Manuscript, New York Univ. (1989).Google Scholar
Flannery, M.; Hameed, A.; and Harjes, R.. “Asset Pricing, Time-Varying Risk Premia and Interest Rate Risk.” Unpubl. Manuscript, Univ. of Florida (1992).Google Scholar
Gagnon, L.; Morgan, I. G.; and Neave, E. H.. “Pricing Eurodollar Time Deposit Futures.” Unpubl. Manuscript, School of Business, Queen's Univ. (1993).Google Scholar
Gibbons, M. R., and Ramaswamy, K.. “A Test of the Cox, Ingersoll and Ross Model of the Term Structure.” Review of Financial Studies, 6 (1993), 619–658.Google Scholar
Hamilton, J. D., and Susmel, R.. “Autoregressive Conditional Heteroskedasticity and Changes in Regime.” Unpubl. Manuscript, Department of Economics, Univ. of California, San Diego (1992).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 Evaluation.” Econometrica, 60 (1992), 77–105.CrossRefGoogle Scholar
Kloeden, P. E., and Platen, E.. Numerical Solution of Stochastic Differential Equations. New York, NY: Springer-Verlag (1992).Google Scholar
Longstaff, F., and Schwartz, E.. “Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model.” Journal of Finance, 47 (1992), 1259–1282.Google Scholar
Marsh, T., and Rosenfeld, E.. “Stochastic Processes for Interest Rates and Equilibrium Bond Prices.” Journal of Finance, 38 (1983), 635–646.CrossRefGoogle Scholar
Merton, R. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Newey, W. K., and Steigerwald, D. G.. “Consistency of Quasi-Maximum Likelihood Estimators for Models with Conditional Heteroskedasticity.” Unpubl. Manuscript, Department of Economics, Univ. of California, Santa Barbara (1994).Google Scholar
Oldfield, G. S., and Rogalski, R. J.. “The Stochastic Properties of Term Structure Movements.” Journal of Monetary Economics, 19 (1987), 229–245.Google Scholar
Sanders, A., and Unal, H.. “On the Intertemporal Behavior of the Short-Term Rate of Interest.” Journal of Financial and Quantitative Analysis, 23 (1988), 417–423.CrossRefGoogle Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (1977), 177–188.Google Scholar
Wooldridge, J. M. “A Unified Approach to Robust, Regression-Based Specification Tests.” Econometric Theory, 6 (1990), 17–43.CrossRefGoogle Scholar