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Anpassung eines CIR-k-Modells zur Simulation der Zinsstrukturkurve

Simulation of the yield curve: comparing CIR-k models

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Blätter der DGVFM

Zusammenfassung

In dieser Arbeit wird erläutert, wie die Theorie des Kaiman-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.

Summary

This paper is devoted to the Cox-Ingersoll-Ross model withk factors. We give an outline of the theory of the Kaiman 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.

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Literatur

  1. T. Beletski und A. Szimayer (2002):Estimating Exponential-Affine Term Structure Models by Kaiman Filtering: Studying the DEM/Euro-Market, Arbeitspapier, Forschungszentrum caesar, Bonn

  2. D. Brigo und F. Mercurio (2001):Interest Rate Models-Theory and Practice, Springer

  3. P. J. Brockwell und R.A. Davis (1987):Time Series: Theory and Methods, Springer

  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, 613–636

    Article  Google Scholar 

  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, 14–31

    Article  Google Scholar 

  6. J. Cox, J. Ingersoll und S. Ross (1985):A Theory of the Term Structure of Interest Rates, Econometrica 53, 385–407

    Article  MathSciNet  MATH  Google Scholar 

  7. Deutsche Bundesbank (1997):Schätzung von Zinsstrukturkurven, Monatsbericht Oktober, 61–66

  8. L. Devroye (1986):Non-Uniform Random Variate Generation, Springer

  9. J.C. Duan und J.G. Simonato (1999):Estimating Exponential-Affine Term Structure Models by Kaiman Filter, Review of Quantitative Finance and Accounting 13, 111–135

    Article  Google Scholar 

  10. D. Duffie und R. Kan (1996):A Yield-Factor Model of Interest Rates, Mathematical Finance 6, 379–406

    Article  MATH  Google Scholar 

  11. J. Eichenauer und J. Lehn (1986):A Non-linear Congruential Pseudo Random Number Generator, Statistical Papers 27: 315–326

    MathSciNet  MATH  Google Scholar 

  12. T. Fischer, A. May und B. Walther (2003):Anpassung eines CIR-1-Modellszur Simulation der Zinsstrukturkurve. Blätter der DGVFM XXVI, Heft 2, 193–206

  13. J.D. Hamilton (1994):Time Series Analysis, Princeton University Press, Princeton, New Jersey

    MATH  Google Scholar 

  14. A.C. Harvey (1990): Forecasting,Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge

    Chapter  Google Scholar 

  15. P. Hellekalek (1995):Inversive Pseudorandom Number Generators: Concepts, Results and Links, Proceedings of the 1995 Winter Simulation Conference, 255–262

  16. P.E. Kloeden und E. Platen (1992):Numerical Solution of Stochastic Differential Equations, Springer

  17. S.T. Schich (1997):Schätzung der deutschen Zinsstrukturkurve, Diskussionspapier 4/97, Volkswirtschaftliche Forschungsgruppe der Deutschen Bundesbank

  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, 305–325

  19. L.E.O. Svensson (1994):Estimating and Interpreting Forward Interest Rates: Sweden 1992 – 94, IWF Working Paper 114, September

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Author information

Authors and Affiliations

  1. Darmstadt

    Tom Fischer & Brigitte Walther

  2. Bonn

    Angelika May

Authors
  1. Tom Fischer
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  2. Angelika May
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  3. Brigitte Walther
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Additional information

Die Autoren danken Stefan Hartmann, caesar, Bonn, für zahlreiche Verbesserungsvorschläge.

Der Autor wird unter Projektnummer 03LEM6DA durch das Bundesministerium für Bildung und Forschung (BMBF) gefördert.

Die Autorin wird unter Projektnummer 03MAM6CA durch das BMBF gefördert.

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Fischer, T., May, A. & Walther, B. Anpassung eines CIR-k-Modells zur Simulation der Zinsstrukturkurve. Blätter DGVFM 26, 369–387 (2004). https://doi.org/10.1007/BF02858081

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  • DOI: https://doi.org/10.1007/BF02858081

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