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Short Rate as a Sum of Two CKLS-Type Processes

  • Zuzana BučkováEmail author
  • Jana Halgašová
  • Beáta Stehlíková
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

Abstract

We study the short rate model of interest rates, in which the short rate is defined as a sum of two stochastic factors. Each of these factors is modelled by a stochastic differential equation with a linear drift and the volatility proportional to a power of the factor. We show a calibration methods which - under the assumption of constant volatilities - allows us to estimate the term structure of interest rate as well as the unobserved short rate, although we are not able to recover all the parameters. We apply it to real data and show that it can provide a better fit compared to a one-factor model. A simple simulated example suggests that the method can be also applied to estimate the short rate even if the volatilities have a general form. Therefore we propose an analytical approximation formula for bond prices in such a model and derive the order of its accuracy.

Keywords

Interest Rate Term Structure Bond Price Short Rate Interest Rate Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The work was supported by VEGA 1/0251/16 grant and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE – Novel Methods in Computational Finance).

References

  1. 1.
    Brigo, D., Mercurio, F.: Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit. Springer, Berlin (2007)zbMATHGoogle Scholar
  2. 2.
    Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.B.: An empirical comparison of alternative models of the short-term interest rate. J. Financ. 47(3), 1209–1227 (1992)CrossRefGoogle Scholar
  3. 3.
    Chen, R.R., Scott, L.: Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates. J. Fixed Income 3(3), 14–31 (1993)CrossRefGoogle Scholar
  4. 4.
    Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rates. Econometrica 53(2), 385–407 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Halgašová, J., Stehlíková, B., Bučková, Z.: Estimating the short rate from the term structures in the Vasicek model. Tatra Mountains Math. Publ. 61, 1–17 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kwok, Y.K.: Mathematical Models of Financial Derivatives. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  7. 7.
    Stehlíková, B.: A simple analytic approximation formula for the bond price in the Chan-Karolyi-Longstaff-Sanders model. Int. J. Numer. Anal. Model. Ser. B 4(3), 224–234 (2013)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Ševčovič, D., Urbánová Csajková, A.: Calibration of one factor interest rate models. J. Electr. Eng. 55(12/s), 46–50 (2004)zbMATHGoogle Scholar
  9. 9.
    Ševčovič, D., Urbánová Csajková, A.: On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model. Cent. Eur. J. Oper. Res. 13, 169–188 (2005)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Vasicek, O.: An equilibrium characterization of the term structure. J. Financ. Econ. 5(2), 177–188 (1977)CrossRefGoogle Scholar
  11. 11.
    EMMI - European Money Markets Institute. Euribor Rates. http://www.emmi-benchmarks.eu/euribor-org/euribor-rates.html

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Zuzana Bučková
    • 1
    • 2
    Email author
  • Jana Halgašová
    • 1
    • 3
  • Beáta Stehlíková
    • 1
  1. 1.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia
  2. 2.Chair of Applied Mathematics/Numerical AnalysisUniversity of WuppertalWuppertalGermany
  3. 3.ČSOB BankBratislavaSlovakia

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