Fraunhofer Institute for Industrial Mathematics ITWM
Fraunhofer Institute for Industrial Mathematics ITWM

Calibration Methods in Financial Market Applications

Once the appropriate financial mathematical model has been selected, its calibration is a critical challenge in financial market applications such as interest rate modeling. Calibration is the process of determining suitable model parameters in order to map the real world as accurately as possible. Historical market data, expert opinions and forecasts are used for this purpose.    

 

Models Should Be Versatile 

The model parameters are often only calibrated with regard to one criterion; for example, the gap between selected market and model prices is minimized. In practice, however, financial market models are required and used in very different areas of application. In order to achieve standardization with regard to model selection and thus ensure the comparability of different contexts in the application, the requirements for the selected model increase, which must be taken into account during calibration.

Standard Calibration Procedure Is Examined and Expanded  

Based on an established financial mathematical capital market model for simulating interest rate and share price developments (see »Classification of Private Pension Products«), we examine the standard procedure for calibrating these financial market models, which is described in the literature, and extend it accordingly.

This includes the following aspects:

  • the derivation of model-independent criteria for a calibration to measure the calibration quality,
  • examining the financial market data used (e.g. interest rate derivatives when calibrating an interest rate model) with regard to the various calibration criteria,
  • the investigation of the optimization problem arising in the calibration,
  • the systematic decomposition of the total error into model errors and calibration or estimation errors,
  • the comparison of different estimation methods.

Data science methods support calibration

Due to the potentially large amount of real financial market data that can be used for calibration, the methodological integration of data science methods into the calibration process will be discussed. In addition, for the above-mentioned optimization problem, the extent to which its extension to a multi-criteria optimization problem improves the quality of the calibration will be examined.

 

Results Relevant for Long-Term Projects

The doctorate is thematically close to the department's long-term projects that fall within the department's focus on “Retirement Provision and Life Insurance”, such as the cooperation with Produktinformationsstelle Altersvorsorge gGmbH (PIA), so that the results of the doctorate can be integrated into these projects.

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