Robust calibration methods for asset price models

For the application of sophisticated asset price models in practice a reliable and stable calibration procedure is a prerequisite. Typically the parameters of the model should be chosen in a way to optimally fit the prices of standard European options written on the asset, i.e. to minimize (in some sense) the gap between their model and market prices. This is a classic example of an inverse problem. While the calculation of the model prices (the forward problem) is well studied in the mathematical finance literature, calibration routines (the inverse problem) have only recently attracted major attention of researchers in this field. In this talk we will discuss some fundamental properties of the calibration problem -- in particular its ill-posedness -- and show how the theory of Tikhonov-regularization can be used to stabilize it. We will also outline the implementation of regularization techniques in some special cases.