# Calibration of the Vasicek model of interest rates using bicriteria optimization

## Main Article Content

## Abstract

The Vasicek model of the interest rates is one of the most frequently used short rate models to describe the movements of the interest rates. For the model to work properly it has to be adequately calibrated. Based on different approaches, there are several techniques to calibrate the Vasicek model. In this paper, we combine two criteria: fitting term structures of the interest rates and comparison of the estimated short rate with its estimate from the Kalman filter, which takes probability distributions into account. Doing so, we obtain the risk-neutral parameters as well as the estimate for the short rate. The proposed algorithm is then applied to the real market data and we analyze the results.

## Article Details

How to Cite

Jašurková, T., & Stehlíková, B.
(2020).
Calibration of the Vasicek model of interest rates using bicriteria optimization.

*Proceedings Of The Conference Algoritmy,*, 211 - 220. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1585/838
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Articles

## References

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[8] Z. Bučková, J. Halgašová, and B. Stehlı́ková, Estimating the short rate from the term structure in the Vasicek model, Tatra Mountains Mathematical Publications, 61 (2014), pp. 87-103.

[9] Z. Bučková, J. Halgašová, and B. Stehlı́ková, Short Rate as Sum of Two CKLS-Type Processes, Numerical Analysis and Its Applications, (2017), pp. 243-251.

[10] K. C. Chan, G. A. Karolyi, F. A. Longstaff, and A. B. Sanders, An empirical comparison of alternative models of the short-term interest rate, The journal of finance, 47(3) (1992), pp. 1209-1227.

[11] T. Corzo Santamaria and E. S. Schwartz, Convergence within the EU: Evidence from interest rates, Economic Notes, 29(2) (2000), pp. 243-266.

[12] M. Ehrgott, Multicriteria optimization (Vol. 491), Springer Science & Business Media, 2005.

[13] M. Ehrgott, Multiobjective optimization, Ai Magazine, 29(4) (2008), pp. 47-57.

[14] T. Fischer, A. May, and B. Walther, Fitting Yield Curve Models Using the Kalman Filter, Proceedings in Applied Mathematics and Mechanics, 3 (2003), pp. 507-508.

[15] J. James and N. Webber, Interest Rate Modelling, John Wiley & Sons Inc., Hoboken, 2000.

[16] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Transaction of the ASME—Journal of Basic Engineering, 82(Series D) 1960, pp. 35-45.

[17] J. Koski and R. Silvennoinen, Norm methods and partial weighting in multicriterion optimization of structures, International Journal for Numerical Methods in Engineering, 24(6) (1987), pp. 1101-1121.

[18] P. S. Maybeck, Stochastic models, estimation, and control, Volume 1, Academic Press, New York, 1979.

[19] K. Mikula, B. Stehlı́ková, and D. Ševčovič, Analytical and numerical methods for pricing financial derivatives, Nova Science, Hauppauge, 2011.

[20] K. B. Nowman, Continuous-time short term interest rate models, Applied Financial Economics, 8(4) (1998), pp. 401-407.

[21] H. W. Sorenson, Least-Squares estimation: from Gauss to Kalman, IEEE Spectrum, 7 (1970), pp. 63-68.

[22] D. Ševčovič and A. Urbánová - Csajková, On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model, Central European Journal of Operations Research, 13(2) (2005).

[23] O. Vašı́ček, An equilibrium characterization of the term structure, Journal of financial economics, 6 (1977), pp. 177-188.

[2] J. S. Arora and R. Y. Marler, Survey of multi-objective optimization methods for engineering, Struct. Multidisc. Optim., 26 (2004), pp. 369-395.

[3] S. H. Babbs and K. B. Nowman, Kalman Filtering of Generalized Vasicek Term Structure Models, Journal of Financial and Quantitative Analysis, 34 (1999), pp. 115-130.

[4] D. J. Bolder, Affine Term-Structure Models: Theory and Implementation, Working Paper, Bank of Canada, Ottawa, 2001.

[5] D. Brigo and F. Mercurio, Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer Science & Business Media, Berlin, 2007.

[6] D. Brigo and F. Mercurio, A deterministic shift extension of analytically–tractable and time–homogeneous short–rate models, Finance and Stochastics, 5 (2001), pp. 369-387.

[7] R. G. Brown and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering: with MATLAB Exercises and Solutions, John Wiley & Sons Inc., Hoboken, 1996.

[8] Z. Bučková, J. Halgašová, and B. Stehlı́ková, Estimating the short rate from the term structure in the Vasicek model, Tatra Mountains Mathematical Publications, 61 (2014), pp. 87-103.

[9] Z. Bučková, J. Halgašová, and B. Stehlı́ková, Short Rate as Sum of Two CKLS-Type Processes, Numerical Analysis and Its Applications, (2017), pp. 243-251.

[10] K. C. Chan, G. A. Karolyi, F. A. Longstaff, and A. B. Sanders, An empirical comparison of alternative models of the short-term interest rate, The journal of finance, 47(3) (1992), pp. 1209-1227.

[11] T. Corzo Santamaria and E. S. Schwartz, Convergence within the EU: Evidence from interest rates, Economic Notes, 29(2) (2000), pp. 243-266.

[12] M. Ehrgott, Multicriteria optimization (Vol. 491), Springer Science & Business Media, 2005.

[13] M. Ehrgott, Multiobjective optimization, Ai Magazine, 29(4) (2008), pp. 47-57.

[14] T. Fischer, A. May, and B. Walther, Fitting Yield Curve Models Using the Kalman Filter, Proceedings in Applied Mathematics and Mechanics, 3 (2003), pp. 507-508.

[15] J. James and N. Webber, Interest Rate Modelling, John Wiley & Sons Inc., Hoboken, 2000.

[16] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Transaction of the ASME—Journal of Basic Engineering, 82(Series D) 1960, pp. 35-45.

[17] J. Koski and R. Silvennoinen, Norm methods and partial weighting in multicriterion optimization of structures, International Journal for Numerical Methods in Engineering, 24(6) (1987), pp. 1101-1121.

[18] P. S. Maybeck, Stochastic models, estimation, and control, Volume 1, Academic Press, New York, 1979.

[19] K. Mikula, B. Stehlı́ková, and D. Ševčovič, Analytical and numerical methods for pricing financial derivatives, Nova Science, Hauppauge, 2011.

[20] K. B. Nowman, Continuous-time short term interest rate models, Applied Financial Economics, 8(4) (1998), pp. 401-407.

[21] H. W. Sorenson, Least-Squares estimation: from Gauss to Kalman, IEEE Spectrum, 7 (1970), pp. 63-68.

[22] D. Ševčovič and A. Urbánová - Csajková, On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model, Central European Journal of Operations Research, 13(2) (2005).

[23] O. Vašı́ček, An equilibrium characterization of the term structure, Journal of financial economics, 6 (1977), pp. 177-188.