Dynamic Copulas: Applications to finance and economics
by Daniel Totouom-Tangho of MINES ParisTech
November 6, 2007
Abstract: Credit derivatives are one of the fastest developing parts of market finance at present. Not only have the nominal amounts increased phenomenally, but new products are continually being created. After reviewing the evolution of these products since their inception in the early 90s, we demonstrate that this development has been market driven, with the mathematical models used for pricing lagging behind. As the market developed, the weak points of the models became apparent and improved models had to be developed. In October 2003 when the work on this thesis started, CDOs (Collateralised Debt Obligations) were becoming standard products. A new generation of products which we will refer to as third generation credit derivatives were starting to come on line: these include forward-starting CDS, forward-starting CDOs, options on CDOs and CPDOs. In contrast to early products, these derivatives require a dynamic model of the evolution of the "correlation" between the names over time, something which base correlation was not designed to do. The aim of this doctorate has been to develop a mathematical consistent framework for pricing these types of products.
Keywords: Default risk, CDOs, Forward Starting CDOs, correlation smile, LÚvy Process, Non Gaussian Ornstein-Uhlenbeck process, Sub Prime, Archimedean copulas, multivariate stochastic processes, lower tail dependence.