Forschung
Forschungsschwerpunkte
The arbitrage theory of the term structure of interest rates serves as the main tool for the pricing and hedging of interest rate dependent derivatives. It provides the basis for the risk management of banks and financial institutions with regard to interest-rate-dependent derivatives such as options on bonds, financial futures and interest rates (caps, floors and swaptions). Many models of the term structure are formulated with respect to continuously compounded interest rates. These rates are not identical to observable interest rates. One observation is, that the expected roll over returns are finite even within in log-normal framework if instead of continuously compounded rates the stochastic dynamics of nominal rate are the modelling ele-ments. One of the most important term structure models, the so called LIBOR-Market Model covers this case. Among others the famous Black formula for caps and floors has shown to be arbitrage free. In a recent study on the term structure of futures rates new no-arbitrage conditions on the volatility surface of the term structure of interest rates are derived.
Non-standard financial products with broken compounding periods, time delayed payment dates, average payoffs, barrier conditions or individual exercise opportuni-ties are frequently offered by financial institutions. In many cases the pricing of these products is derived by numerical procedures relative to a specific model assumption. A more robust approach than the numerical approximation relies on super hedging ideas. These approaches are usually based on weaker model assumptions. Furthermore, the extension of the uncertain volatility approach to the term structure of interest rates is not yet derived. The research agenda is to extent the ideas of super hedging and uncertain volatility to the pricing and hedging of a larger class of interest rate dependent claims.
Equity linked life and pension insurance contracts are related to financial risk 8interest rate, price and index) as well as to non-financial risk (e.g. death and survival risk, premature exercise). The valuation and hedging of these contracts is related to the diversification technique within a cohort of insured persons and to the dynamic duplication by the financial market. In addition periodic premium and long time to maturity complicates the hedging problem for the insurer. So far these problems are addressed only within very specific modelling framework. The research project considers robust contract specifications in the sense of close approximation by super hedging strategies and model independency. The solution involves the contract design as well as the construction of the underlying financial portfolio.
The current financial crisis has pushed compensation policy like Executives´ Stock Options (ESOs) at the forefront of the public debate. An on-going discussion is whether ESOs have in fact encouraged the managers to take on too large risks which might improve their own benefits but jeopardize the firm. People doubt that ESOs have always positive effects on the firm's performance. Sustainability and incentive compatibility are the main qualitative keywords within the present discussion. The approach is considering executive non-traditional performance-based stock option schemes which discourage managers from excessive risk taking. Promising candidates are Parisian and constrained Asian executives' stock option plans. Both contracts impose a restriction on the path of the firm's assets process. Both schemes make the exaggerated risk taking through the executives less likely. Within this research project we focus on the comparison of a larger class of ESO schemes and their welfare implications in a utility based framework.
