Modeling and analysis of structured finance products [Elektronische Ressource] / vorgelegt von Florian Kramer

Modeling and AnalysisofStructured Finance ProductsDissertationzur Erlangung des Doktorgrades Dr. rer. nat.der Fakult¨at fu¨r Mathematik und Wirtschaftswissenschaftender Universit¨at Ulmvorgelegt vonFlorian KramerausKaufbeurenUlm, September 2008Amtierender Dekan: Prof. Dr. Frank Stehling1. Gutachter: Prof. Dr. Gunter L¨offler2. Gutachter: Prof. Dr. Ru¨diger KieselTag der Promotion: 12.12.2008ContentsList of Symbols and Notation viiList of Abbreviations xiList of Figures xivList of Tables xvi1 Introduction 11.1 Motivation and Formulation of the Problem . . . . . . . . . . . . . 11.2 Outline and Contributions . . . . . . . . . . . . . . . . . . . . . . . 42 A Model for a Vector of Stopping Times 112.1 Definition of the Stopping Times Model. . . . . . . . . . . . . . . . 122.2 Single Survival and Jump Probabilities . . . . . . . . . . . . . . . . 172.3 Joint Survival Probabilities. . . . . . . . . . . . . . . . . . . . . . . 232.4 Construction of the Stopping Times . . . . . . . . . . . . . . . . . . 282.5 Model-Implied Dependence Structure . . . . . . . . . . . . . . . . . 312.5.1 Conditional Independence and Contagion . . . . . . . . . . . 312.5.2 A Characterization Result for the Dependence Structure . . 352.6 The Loss Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.6.1 Formulation by Means of Orthogonal Point Processes andTime-Change . . . . . . . . . . . . . . . . . . . . . . . . . . 472.6.