MATH5995 is a Mathematics Level V course. See the course overview below.

Units of credit: 6

Prerequisites:

Cycle of offering: A new topic will be offered yearly.

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. (This pdf will usually be updated by the end of the first week of the semester.)

The Online Handbook entry contains up-to-date timetabling information.

The goal of the course is to present the most important mathematical tools that are used for the arbitrage valuation of defaultable claims, which are usually referred to as credit derivative. We first provide a concise summary of the main developments within the so-called "structural approach'' to modelling and valuation of credit risk. In particular, we study the first-passage-time approach and a random barrier case. The next part of the lectures will be devoted to the "reduced-form approach''. This approach is purely probabilistic in nature and, technically speaking, it has a lot in common with the reliability theory. Subsequently, we examine hedging strategies under the assumption that some defaultable assets (such as, e.g., corporate bonds or credit default swaps) are traded. Finally, we give a brief survey of practical methods that are currently used in modelling of dependent defaults and credit migrations and we briefly discuss valuation and hedging of multi-name credit derivatives, such as: credit default index swaps and synthetic collateralized debt obligations.