Calibration of term structure models
Alexandra UrbŠnovŠ CsajkovŠ
PhD thesis advisor: Daniel ©evŤoviŤ

PhD thesis - Full text    (PDF 1.2M)
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Summary: The main goal of this thesis was to identify and analyze a lot of possibilities of using one factor interest rate models in the context of the European and new member states markets. Of course, there exist many different papers dealing with these models, but many of them are focusing only on particular aspect connected with the one factor models. We attempted to add a new value and insight in this theses. We proposed new and hopefully interesting issues and topics which came out during the analysis and expertise of the possibilities of usage of these models for real data.

The core results of this theses could be divided into two main parts. The first part is the so-called internal calibration method. This method is based on the new two phase minmax optimization method for parameter estimation of the CIR and Vasicek one factor interest rate model. It is based on minimization of the loss functional together with the maximization of the likelihood function restricted to the set of minimizers. We have tested the estimation method on various term structures including stable west Europe inter-bank offered rates as well as those of the new EU member states. Based on our results of parameter estimation for the CIR one factor model we can state that the western European term structure data are better described with CIR model compared to the new EU member states represented by Central European countries. It is very important to emphasize the possibility of the parameter reduction in the CIR and Vasicek model too. This is utilized during all introduced methods and approaches in this theses.

Before turning to the second part of our analysis and results, we insert a somehow new view on the internal calibration method. This is the calibration based on binding interval approach. It means that we do not try to calibrate all the parameters of the one factor models to be a point, but we allow some freedom of a parameter. The endogenity of this method remains, because all the parameters are obtained from the data.

Final part of the theses deals with the external calibration method. In this case the exogenity of this approach is coming from an externally provided parameter. Based on that information which is the expected long-term interest rate interval we have calibrated the remained parameters of the one factor interest rate models. We assumed that the BRIBOR and PRIBOR rates in 2005 will converge to the mean values of EURIBOR with specific maturity in 2006. We prefer the results for BRIBOR from the point of view of negative market price of risk. Our assumption about the expected long-term interest rate interval is not justified for PRIBOR.

Related papers
[1] ©evŤoviŤ, D. and UrbŠnovŠ CsajkovŠ, A., On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model,
Central European Journal of Operational Research 13 (2005), 169--188.
Full text    (PDF 5.6M)

[2] ©evŤoviŤ, D. and UrbŠnovŠ CsajkovŠ, A., Calibration of one factor interest rate models,
Journal of Electrical Engineering 55, No. 12/s (2004), 46-50.
Full text    (PDF 216K)

[3] UrbŠnovŠ CsajkovŠ, A., Min-max calibration for interest rate models and its application to central European financial markets,
Proceedings of 4th International scientific seminar of doctoral students, May 21 (2004), 371--376.
Full text    (PDF 3.5M)