Skip to main content
SpringerLink
Log in

Gaussian Estimation and Forecasting of Multi-Factor Term Structure Models with an Application to Japan and the United Kingdom

  • Published:
Asia-Pacific Financial Markets Aims and scope Submit manuscript

Abstract

In this paper we extend the exact discrete model of Bergstrom (1966) first used in empirical finance by Brennan and Schwartz (1979) to estimate their two-factor term structure model to estimate other two-factor term structure models using the recent assumption in Nowman (1997) for single factor models. Following Nowman (1997) we use the exact Gaussian estimation methods of Bergstrom (1983–1986, 1990) to estimate two-factor CKLS, Vasicek and CIR models. We estimate the models using monthly UK and Japanese interest rate data and our results indicate that the estimation method works well in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agbeyegbe, T. D. (1984) The exact discrete analog to a closed linear mixed-order system, J. Econom. Dynam. Control 7, 363-375.

    Google Scholar 

  • Agbeyegbe, T. D. (1987) The exact discrete analog to a closed linear first-order system with mixed sample, Econometric Theory 3, 142-149.

    Google Scholar 

  • Agbeyegbe, T. D. (1988) An exact discrete analog of an open order linear non-stationary first-order continuous time system with mixed sample, J. Econometrics 39, 237-250.

    Google Scholar 

  • Andersen, T. G. and Lund, J. (1997) Estimating continuous time stochastic volatility models of the short term interest rate, J. Econometrics 77, 343-377.

    Google Scholar 

  • Babbs, S. H. and Nowman, K. B. (1999) Kalman filtering of generalized Vasicek term structure models, J. Financ. Quantitat. Anal. 43, 115-130.

    Google Scholar 

  • Beaglehole, D. R. and Tenney, M. S. (1991) General solutions of some interest rate-contingent claim pricing equations, J. Fixed Income 1, 69-83.

    Google Scholar 

  • Bergstrom, A. R. (1966) Non-recursive models as discrete approximations to systems of stochastic differential equations, Econometrica 34, 173-182.

    Google Scholar 

  • Bergstrom, A. R. (1983) Gaussian estimation of structural parameters in higher-order continuous time dynamic models, Econometrica 51, 117-152.

    Google Scholar 

  • Bergstrom, A. R. (1984) Continuous time stochastic models and issues of aggregation over time. In Z. Griliches and M. D. Intriligator (eds), Handbook of Econometrics, Volume II, Elsevier Science, Amsterdam.

    Google Scholar 

  • Bergstrom, A. R. (1985) The estimation of parameters in nonstationary higher-order continuous time dynamic models, Econometric Theory 1, 369-385.

    Google Scholar 

  • Bergstrom, A. R. (1986) The estimation of open higher-order continuous time dynamic models with mixed stock and flow data, Econometric Theory 2, 350-373.

    Google Scholar 

  • Bergstrom, A. R. (1989) Optimal forecasting of discrete stock and flow data generated by a higher-order continuous time system, Computers Mathematics Applications 17, 1203-1214.

    Google Scholar 

  • Bergstrom, A. R. (1990) Continuous Time Econometric Modelling, Oxford University Press, Oxford.

    Google Scholar 

  • Bergstrom, A. R. (1997) Gaussian estimation of mixed order continuous time dynamic models with unobservable stochastic trends from mixed stock and flow data, Econometric Theory 13, 467-505.

    Google Scholar 

  • Bergstrom, A. R. and Nowman, K. B. (1999) Gaussian estimation of a two-factor continuous time model of the short-term interest rate, Economic Notes 28, 25-41.

    Google Scholar 

  • Byers, S. L. and Nowman, K. B. (1998) Forecasting U.K. and U.S. interest rates using continuous time term structure models, Int. Rev. Financ. Anal. 7, 191-206.

    Google Scholar 

  • Byers, S. L. and Nowman, K. B. (2000) Further evidence on the forecasting performance of two factor continuous time interest rate models in international and Asia-Pacific financial markets, Managerial Finance, forthcoming.

  • Brennan, M. J. and Schwartz, E. S. (1979) A continuous time approach to the pricing of bonds, J. Banking Finance 3, 133-155.

    Google Scholar 

  • Chambers, M. J. (1991) Discrete models for estimating general linear continuous time systems, Econometric Theory 7, 531-542.

    Google Scholar 

  • Chambers, M. J. (1999) Discrete time representation of stationary and non-stationary continuous time systems, J. Econom. Dynam. Control 23, 619-639.

    Google Scholar 

  • Chan, K. C., Karolyi, G. A., Longstaff, F. A., and Sanders, A. B. (1992) An empirical comparison of alternative models of the short-term interest rate, J. Finance 47, 1209-1227.

    Google Scholar 

  • Chen, R. and Scott, L. (1995) Multi-factor Cox-Ingersoll-Ross models of the term structure: Estimates and tests from a Kalman filter model, paper, Rutgers University.

  • Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985) A theory of the term structure of interest rates, Econometrica 53, 385-407.

    Google Scholar 

  • Dahlquist, M. (1996) On alternative interest rate processes, J. Banking Finance 20, 1093-1119.

    Google Scholar 

  • Duffie, D. and Kan, R. (1996) A yield-factor model of interest rates, Mathematical Finance 6, 379-406.

    Google Scholar 

  • James, J. and Webber, N. (2000) Interest Rate Modelling, John Wiley & Sons.

  • Longstaff, F. and Schwartz, E. (1992) Interest rate volatility and the term structure: A two factor general equilibrium model, J. Finance 47, 1259-1282.

    Google Scholar 

  • Malinvaud, E. (1966) Statistical Methods of Econometrics, North-Holland, Amsterdam.

    Google Scholar 

  • Nowman, K. B. (1991) Open higher-order continuous time dynamic model with mixed stock and flow data and derivatives of exogenous variables, Econometric Theory 7, 404-408.

    Google Scholar 

  • Nowman, K. B. (1997) Gaussian estimation of single-factor continuous time models of the term structure of interest rates, J. Finance 52, 1695-1706.

    Google Scholar 

  • Nowman, K. B. (1998) Continuous time short term interest rate models, Appl. Financ. Econom. 8, 401-407.

    Google Scholar 

  • Nowman, K. B. and Sorwar, G. (1999) An evaluation of contingent claims using the CKLS interest rate model: An analysis of Australia, Japan, and United Kingdom, Asia-Pacific Financ. Markets 6, 205-219.

    Google Scholar 

  • Phillips, P. C. B. (1972) The structural estimation of a stochastic differential equation system, Economtrica 40, 1021-1041.

    Google Scholar 

  • Saltoglu, B. (1996) Forecasting with a continuous time interest rate model: A comparision between continuous time and discrete time estimation methods, unpublished paper.

  • Saltoglu, B. (2000) Comparing forecasting ability of parametric and nonparametric methods: An application with Canadian monthly interest rates, unpublished paper.

  • Vasicek, O. (1977) An equilibrium characterization of the term structure, J. Financ. Econom. 5, 177-188.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics and Finance, University of Durham, 23/26 Old Elvet, Durham, DH1 3HY, U.K.

    K. Ben Nowman

Authors
  1. K. Ben Nowman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nowman, K.B. Gaussian Estimation and Forecasting of Multi-Factor Term Structure Models with an Application to Japan and the United Kingdom. Asia-Pacific Financial Markets 8, 23–34 (2001). https://doi.org/10.1023/A:1011436907037

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011436907037

Search

Navigation