Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T18:23:06.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation in the Cox-Ingersoll-Ross Model

Published online by Cambridge University Press:  11 February 2009

Ludger Overbeck  and
Tobias Rydén
Ludger Overbeck
Affiliation:
University of California
Tobias Rydén
Affiliation:
University of California
Get access Rights & Permissions [Opens in a new window]

Abstract

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are discussed, and we also compare their performance in a simulation study.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 3 , June 1997 , pp. 430 - 461
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCE

Abken, P.A. (1993) Innovations in modeling the term structure of interest rates. In Financial Derivatives: New Instruments and Their Uses, pp. 107–128. Atlanta: Federal Reserve Bank of Atlanta.Google Scholar
Bergstrom, A.R. (1984) Continuous time stochastic models and issues of aggregation over time. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, vol. 2, pp. 1145–1212. Amsterdam: North-Holland.CrossRefGoogle Scholar
Bibby, B.M. & Serensen, M. (1995) Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1, 17–39.CrossRefGoogle Scholar
Brennan, M.J. & Schwartz, E.S. (1980) Analyzing convertible bonds. Journal of Financial and Quantitative Analysis 15, 907–929.CrossRefGoogle Scholar
Carroll, R.J. & Ruppert, D. (1988) Transformation and Weighting in Regression. New York: Chapman and Hall.CrossRefGoogle Scholar
Chan, K.C., Karolyi, G.A., Longstaff, F.A., & Sanders, A.B. (1992) An empirical comparison of alternative models of the short-term interest rate. The Journal of Finance 47, 1209–1227.Google Scholar
Chen, R.-R. & Scott, L. (1992) Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of the term structure. The Review of Financial Studies 5, 613–636.Google Scholar
Chen, R.-R. & Scott, L. (1993) Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates. The Journal of Fixed Income 3 (3), 14–31.Google Scholar
Cox, J.C., Ingersoll, J.E., & Ross, S.A. (1985) A theory of the term structure of interest rates. Econometrica 53, 385–407.CrossRefGoogle Scholar
Crowder, M. (1987) On linear and quadratic estimating functions. Biometrika 74, 591–597.CrossRefGoogle Scholar
Dacunha-Castelle, D. & D. Florens-Zmirou (1986) Estimation of the coefficients of a diffusion from discrete observations. Stochastics 19, 263–284.CrossRefGoogle Scholar
Davidian, M. & Carroll, R.J. (1987) Variance function estimation. Journal of the American Statistical Association 82, 1079–1091.CrossRefGoogle Scholar
Devroye, L. (1986) Non-Uniform Random Variate Generation. New York: Springer-Verlag.CrossRefGoogle Scholar
Dohnal, G. (1987) On estimating the diffusion coefficient. Journal of Applied Probability 24, 105–114.CrossRefGoogle Scholar
Durrett, R. (1991) Probability: Theory and Examples. Pacific Grove, California: Wadsworths & Brooks/Cole.Google Scholar
Feller, W. (1951) Two singular diffusion problems. Annals of Mathematics 54, 173–182.CrossRefGoogle Scholar
Florens-Zmirou, D. (1993) On estimating the diffusion coefficient from discrete observations. Journal of Applied Probability 30, 790–804.CrossRefGoogle Scholar
Godambe, V.P. & Heyde, C.C. (1987) Quasi-likelihood and optimal estimation. International Statistical Review 55, 231–244.CrossRefGoogle Scholar
Gourieroux, C. & Monfort, A. (1995) Testing, encompassing, and simulating dynamic econometric models. Econometric Theory 11, 195–228.CrossRefGoogle Scholar
Gourieroux, C , Monfort, A., & Renault, E. (1993) Indirect inference. Journal of Applied Econometrics 8, S85-SU8.Google Scholar
Gradshteyn, I.S. & Ryzhik, I.M. (1980) Table of Integrals, Series, and Products. New York: Academic Press.Google Scholar
Ibragimov, I. A. & Hasminskii, R.Z. (1981) Statistical Estimation. New York: Springer-Verlag.CrossRefGoogle Scholar
Jacod, J. & Shiryaev, A.N. (1987) Limit Theorems for Stochastic Processes. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Kawazu, K. & Watanabe, S. (1971) Branching processes with immigration and related limit theorems. Theory of Probability and Its Applications 16, 36–54.CrossRefGoogle Scholar
Klimko, L.A. & Nelson, P.I. (1978) On conditional least squares estimation for stochastic processes. Annals of Statistics 6, 629–642.CrossRefGoogle Scholar
Kloeden, P.E. & Platen, E. (1992) Numerical Solution of Stochastic Differential Equations. Berlin: Springer-Verlag.CrossRefGoogle Scholar
LeCam, L. & Yang, G. (1990) Asymptotics in Statistics. New York: Springer-Verlag.CrossRefGoogle Scholar
Lehmann, E.L. (1990) Theory of Point Estimation. Pacific Grove, California: Wadsworths & Brooks/Cole.Google Scholar
Longstaff, F.A. & Schwartz, E.S. (1992) Interest rate volatility and the term structure: A twofactor general equilibrium model. The Journal of Finance 47, 1259–1282.Google Scholar
Overbeck, L. (1995) Estimation for Continuous-State Branching Processes. Preprint. Pfanzagl, J. (1994) Parametric Statistical Theory. Berlin: Walter de Gruyter.Google Scholar
Pitman, J. & Yor, M. (1982) A decomposition of Bessel bridges. Zeitschrift fiir Wahrscheinlichkeitstheorie und Verwandte Cebiete 59, 425–457.CrossRefGoogle Scholar
Revuz, D. & Yor, M. (1991) Continuous Martingales and Brownian Motion. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Wefelmeyer, W. (1996a) Adaptive estimators for the parameters of the autoregression function of a Markov chain. Journal of Statistical Planning and Inference, forthcoming.Google Scholar
Wefelmeyer, W. (1996b) Quasi-likelihood models and optimal inference. Annals of Statistics 24, 405–422.CrossRefGoogle Scholar
Wei, C.Z. & Winnicki, J. (1990) Estimation of the means in the branching process with immigration. Annals of Statistics 18, 1757–1773.CrossRefGoogle Scholar
Winnicki, J. (1990) Estimation of the variances in the branching process with immigration. Probability Theory and Related Fields 88, 77–106.CrossRefGoogle Scholar