Quasi-Monte Carlo for Portfolio-Credit-Derivates

It is the aim of this project on the one hand to develop refined models for the valuation of portfolio credit derivatives with the help of quasi-Monte Carlo methods, and on the other hand the further development of quasi-Monte Carlo methods (especially with respect to the analysis of low-discrepancy point sequences and of weighted quasi-Monte Carlo techniques), and finally the application and the testing of the new models and techniques in concrete examples. In detail we are planning the following work: a) Concerning Modelling, Simulation and Valuation of Portfolio Credit Derivatives We will investigate credit risk models where the firm values in a portfolio are modeled using Levy processes, which admits much better fit to market data than models ordinarily used by practitioners. For inhomogeneous portfolios with relatively high risk one has to drop some assumptions which otherwise make exact computation possible. One therefore has to resort to simulation methods, which are very time-consuming. We want to speed up the computation by using quasi-Monte Carlo methods. b) Concerning low-discrepancy Point Sets and Weighted Quasi-Monte Carlo Methods A new class of low-discrepancy point sets, which should be especially useful for quasi-Monte Carlo simulations (generalized Halton-Niederreiter sequences) will be analysed in detail with respect to estimation of discrepancy, weighted discrepancy, and with respect to existence properties. Further we will study if weighted quasi-Monte Carlo methods (in the sense of Sloan and Wozniakowski) are applicable for the modelling provided in part a) and how we optimally have to choose the sets of weights for these problems. In exhaustive numerical tests we finally will test the efficiency of the point sequences and the techniques for the valuation of portfolio credit derivatives.