Mathematical models of credit management and credit derivatives

Abstract

The first two chapters give the background, history and overview of the dissertation, together with the necessary mathematical preliminaries. Thereafter, the next four chapters deal with credit risk and credit derivatives. The final part of the dissertation is devoted to the Basel II bank regulatory framework and the mathematical modeling of asset allocation in bank management, pertaining to credit risk.Credit risk models can be categorized into two groups known as structural models and reduced form models. These models are used in pricing and hedging credit risk. In this thesis we review a variety of credit risk instruments described by models of the said types. One of the strategies utilized by companies to mitigate credit risk is by using credit derivatives.In this thesis, five main types of risk derivatives have been considered: credit swaps, credit linked notes, credit spreads, total return swaps and collaterized debt obligations. Valuation models for the first three derivatives that are mentioned above, are also presented in this dissertation. The material presented include some of the most recent developments in the literature. Our methods range from single-period modeling to application of stochastic optimal control theory. We expand on the material presented from the literature by way of simplifying or clarifying proofs, and by adding illustrative examples in the form of calculations, tables and simulations.Also, the entire Chapter 6 is a new original contribution to the existing literature on mathematical modeling of credit risk. Key words: credit risk; default risk; structural approach; reduced form approach; incomplete information approach; investment strategy; Basel II regulatory framework