On the calibration of local jump-diffusion market models

We show that for the originally ill-posed inverse problem of calibrating a localized jump-diffusion process to given option price data, Tikhonov regularization can be used to get a well-posed optimization problem. Furthermore we prove stability as well as convergence of the regularized parameters using the forward partial integrodifferential equation associated to the European call price. By providing a precise link between these parameters and the corresponding market models we are able to extend the results to the associated market models and hence to the model prices of exotic derivatives. Finally we indicate some possible applications.