Credit Barrier and Dynamic Correlation Techniques for Pricing CDOs of SMEs
by Louis Loizou of the University of Oxford
July 2006
Abstract: This thesis develops a framework for pricing synthetic tranches of collateralized debt obligations (CDOs) backed by loans to small and medium-sized enterprises (SMEs). By using functional calculus the pricing of SME CDOs is done in the light of a constructive, functional analytic and intuitive approach, while it overcomes the Monte Carlo simulation noise of copula implementation schemes. In addition, the functional calculus framework is rich and flexible enough to accommodate both jumps and dynamic correlation structures within the credit quality process of the SME obligors and hence the CDO pricing kernel.
Furthermore, the mathematical components enter the pricing framework in an intuitive way. Firstly, the construction of the Credit Barrier Model (CBM) satisfies both the fundamental theorem of finance and the theorem of measure changes. Secondly, the pricing framework is justified from an economic perspective, by taking on board special issues arising in the SME structured finance. For instance, the complex correlation interrelationships of the SMEs with large enterprises and financial observables and the fact that the asset side of an SME CDO consists of hundreds names.
The calibration is performed under both the statistical (real-world) and risk-neutral (pricing) measure. Under the statistical measure the model is calibrated by using historical credit ratings data for SMEs at the aggregate level. Then, the CBM and the dynamic correlation techniques are combined to price an actual SME synthetic CDO from the German securitization market. The pricing and the calculation of the various hedge ratios of the different tranches with or without trading management constraints (unwind constraints) has been successful.
Keywords: Credit Derivatives, Credit Barrier Models, Dynamic Correlation, Collateralized Debt Obligations, Structured Finance, Small and Medium-sized Enterprises.
