Blätter der DGVFM

, Volume 26, Issue 2, pp 369–387 | Cite as

Anpassung eines CIR-k-Modells zur Simulation der Zinsstrukturkurve

  • Tom Fischer
  • Angelika May
  • Brigitte Walther
Article

Zusammenfassung

In dieser Arbeit wird erläutert, wie die Theorie des Kalman-Filters für die Parameterschätzung eines Cox-Ingersoll-Ross-Modells mitk Faktoren genutzt werden kann. Die zunächst theoretische Ausführung der Vorgehensweise wird anhand des deutschen Rentenmarkts konkretisiert. Schätzwerte für die Fällek=1,2 und 3 werden angegeben und die Cox-Ingersoll-Ross-Modelle für die ermittelten Parameterwerte verglichen. Mit Hilfe stochastischer Simulation erzeugte Szenarien von Zinsstrukturkurven werden diskutiert.

Simulation of the yield curve: comparing CIR-k models

Summary

This paper is devoted to the Cox-Ingersoll-Ross model withk factors. We give an outline of the theory of the Kalman filter and show how it can be applied for parameter estimation. For an empirical study, we use the German debt securities market. We present estimates fork=1, 2 and 3 and compare the respective Cox-Ingersoll-Ross models for the computed values of the model parameters. Some scenarios of the term structure generated by means of stochastic simulation are discussed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    T. Beletski und A. Szimayer (2002):Estimating Exponential-Affine Term Structure Models by Kalman Filtering: Studying the DEM/Euro-Market, Arbeitspapier, Forschungszentrum caesar, BonnGoogle Scholar
  2. [2]
    D. Brigo und F. Mercurio (2001):Interest Rate Models - Theory and Practice, SpringerGoogle Scholar
  3. [3]
    P.J. Brockwell und R.A. Davis (1987):Time Series: Theory and Methods, SpringerGoogle Scholar
  4. [4]
    R. Chen und L. Scott (1992):Pricing Interest Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure, The Review of Financial Studies 5, No. 4, 613–636CrossRefGoogle Scholar
  5. [5]
    R. Chen und L. Scott (1993) -Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates, Journal of Fixed Income 4, 14–31Google Scholar
  6. [6]
    J. Cox, J. Ingersoll und S. Ross (1985):A Theory of the Term Structure of Interest Rates, Econometrica 53, 385–407CrossRefMathSciNetGoogle Scholar
  7. [7]
    Deutsche Bundesbank (1997):Schätzung von Zinsstrukturkurven, Monatsbericht Oktober, 61–66Google Scholar
  8. [8]
    L. Devroye (1986):Non-Uniform Random Variate Generation, SpringerGoogle Scholar
  9. [9]
    J.C. Duan und J.G. Simonato (1999):Estimating Exponential-Affine Term Structure Models by Kalman Filter, Review of Quantitative Finance and Accounting 13, 111–135CrossRefGoogle Scholar
  10. [10]
    D. Duffie und R. Kan (1996):A Yield-Factor Model of Interest Rates, Mathematical Finance 6, 379–406MATHCrossRefGoogle Scholar
  11. [11]
    J. Eichenauer und J. Lehn (1986):A Non-linear Congruential Pseudo Random Number Generator, Statistical Papers 27: 315–326MATHMathSciNetGoogle Scholar
  12. [12]
    T. Fischer, A. May und B. Walther (2003):Anpassung eines CIR-1-Modells zur Simulation der Zinsstrukturkurve. Blätter der DGFVM XXVI, Heft 2, 193–206Google Scholar
  13. [13]
    J.D. Hamilton (1994):Time Series Analysis, Princeton University Press, Princeton, New JerseyMATHGoogle Scholar
  14. [14]
    A.C. Harvey (1990):Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, CambridgeMATHGoogle Scholar
  15. [15]
    P. Hellekalek (1995):Inversive Pseudorandom Number Generators: Concepts, Results and Links, Proceedings of the 1995 Winter Simulation Conference, 255–262Google Scholar
  16. [16]
    P.E. Kloeden und E. Platen (1992):Numerical Solution of Stochastic Differential Equations, SpringerGoogle Scholar
  17. [17]
    S.T. Schich (1997):Schätzung der deutschen Zinsstrukturkurve, Diskussionspapier 4/97, Volkswirtschaftliche Forschungsgruppe der Deutschen BundesbankGoogle Scholar
  18. [18]
    M. Sørensen (1997):Estimating Functions for Discretely Observed Diffusions: A review, Basawa, I.V., Godambe, V.P. and Taylor, R.L. (eds.): Selected Proceedings of the Symposium on Estimating Functions. IMS Lecture Notes -Monograph Series, Vol. 32, 305–325Google Scholar
  19. [19]
    L.E.O. Svensson (1994):Estimating and Interpreting Forward Interest Rates: Sweden 1992 – 94, IWF Working Paper 114, SeptemberGoogle Scholar

Copyright information

© DAV/DGVFM 2003

Authors and Affiliations

  • Tom Fischer
    • 1
  • Angelika May
    • 2
  • Brigitte Walther
    • 3
  1. 1.Darmstadt
  2. 2.Bonn
  3. 3.Darmstadt

Personalised recommendations