Adaptive Wavelet Methods for Structured Financial Products

• Applicant: Professor Dr. Karsten Urban
• Subject Area: Mathematics
• Term: from 2008 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 79623460

In recent years financial market required the introduction of increasingly complex financial structures. Up to now the risk management and valuation of these structures is not sufficiently understood as the current credit crisis shows. Subject of our project is the development of efficient, reliable and fast valuation methods for so-called Collateralized Debt Obligations (CDOs) and exotic derivatives on tranches of CDOs. Our strategy will be based on Partial Differential Equations (PDEs) using an adaptive wavelet method for valuation. The equations to be considered will be Partial Integro-Differential Equations (PIDE). Exotic options lead to obstacle problems which we plan to treat by means of an adaptive projection scheme. Moreover, we investigate parameter dependencies and sensitivities both analytical (if possible) and by Automatic Differentiation. Finally, we compare this approach with (quasi-)Monte Carlo models in order to investigate the performance of PDE-based models.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1324: Extraction of Quantifiable Information from Complex Systems
• Participating Person: Professor Dr. Rüdiger Kiesel