Semi-analytische und simulative Kreditrisikomessung synthetischer Collateralized Debt Obligations bei heterogenen Referenzportfolios

Abstract

Collateralized Debt Obligations (CDOs) have nowadays become an integral part of all asset-backed securities issuances. It is noteworthy that credit derivative-based synthetic CDO structures dominate the German CDO market, in contrast to the U.S. market, notwithstanding the True Sale initiative taken by KfW. A thorough and comprehensive understanding of the distinguishing characteristics of synthetic CDO transactions, and the application of powerful risk measurement systems and adequate applicable valuation concepts are indispensable for a successful transaction with respect to investors, originators, rating agencies, and supervisory authorities.This thesis develops a comprehensive and coherent concept for measuring the credit risk of various transactional elements and computing their value. Essential theories are equally presented and discussed as viable methods of model implementation and calibration. At the outset, a modified asset-value credit risk portfolio model is constructed incorporating analytical formulas, whenever possible, or semi-analytical techniques, if necessary, rather than utilizing simulations. The credit risk portfolio model is applicable to heterogeneous portfolios, with heterogeneity relating to the credit engagements nominal values, probabilities of default, and maturities. For developing the model, the idea of transforming the Brownian motion with respect to time and of utilizing time-invariant default barriers in parallel, initially suggested by Overbeck and Schmidt, is adopted and subject to further advancement.The semi-analytical model constitutes the basis for evaluating and quantifying the credit risk of CDO transactions. Taking into account the distinguishing characteristics of synthetic CDO transactions in particular, the research focuses on loss probability distributions of the CDO tranches, as well as on loss probability distribution-based credit risk figures. For the first time, the influence of loan amortization schedules, portfolio replenishments, replenishment triggers on loss probability distributions, and credit risk figures of CDO reference portfolios is subject to systematic analysis. Furthermore, the structure of a limited-interest subparticipation to sell first-loss tranches in financial markets is duly examined. Using KfW s PROMISE design, numerous problems at hand are debated from a practical point of view.With the objective of evaluating CDOs, formulas for computing present cash values, as well as (fair) risk premiums that are appropriate for either advance or subsequent regular credit fee payments are derived by following the no-arbitrage concept. Theoretical considerations with respect to duplicating CDO cash flows support the CDO evaluation formulas. By selecting special cases for further examination of various formula components, the overall structure of the CDO evaluation formulas is analyzed in detail. Thereupon, a comprehensive account and examination of the cash flow of synthetic CDO transactions is given, taking into consideration the payment amounts, as well as the contingent payment structure. The results permit discussion of several significant deficiencies in the timing of cash inflows and cash outflows on a special-purpose vehicle level.This thesis is directed toward scientific researchers and practitioners alike, who are concerned with modern techniques for evaluating and measuring the credit risk of synthetic Collateralized Debt Obligations.