Johannes StadlerJumps and Uncertainties in Financial Markets

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In financial markets Lévy processes, such as the Generalized Hyperbolic, the Normal Inverse Gaussian, and the Variance Gamma processes, are used for modelling time series affected by jumps and fat tails. This work first compares the results of risk-neutral and historical fitting methods of Lévy processes in a univariate and a multivariate setting and analyses the differences. In the following, approaches to explain asymmetric volatilities are developed.

Until now, no methods exist for the estimation of appropriate initial values for the historical calibration of the Generalized Hyperbolic model. Therefore, a new algorithm is specifically developed for the estimation of the initial values which itself is a new and quick estimation method.

Besides, by using EUREX option data, the sensitivity of the volatility-smile is analysed in relation to ad- hoc news triggered by changes in the capital structure of companies. In addition to an empirical event study, a theoretical mathematical model is presented to explain the sensitivity on the basis of the Geske compound option model. The empirical results contribute to the in literature intensely discussed existence of the leverage effect by creating a linkage between capital structure and implied volatilities.

This work provides new insights into stochastic models, Lévy processes, fitting methods, and into the relation between implied volatility and the leverage effect.

Ihr Werk im Verlag Dr. Kovač

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