Pricing models for collateralized debt obligations

One of the most controversial and innovative finnancial products in recent years has been collateralised debt obligations (CDOs). Much of the blame for the current credit crisis is being attributed to the mathematical models and quantitative methods associated with these credit derivatives. In recent years, there has been rapidly growing research on credit derivatives and correlated defaults and in this thesis we examine the possible replacement of current copula based approaches with intuitive contagion models for percolation on nite networks. We propose that modelling the probability of default in a correlated portfolio is similar to modelling the probability of default of contagion spreading in a network. In the rst part of our thesis we review current models from the literature that have been suggested to price CDOs. From the literature review we noted that the critical input in the pricing of a CDO is an estimate of the default dependence (default correlation) between the underlying names in a portfolio. Dependency modelling with copula functions, introduced by Li (2000), has become a market standard in the pricing of CDOs. We compute the default distribution for both the Gaussian and student t4 copulas by implementing both a Monte Carlo and theoretical approach. We then compare these copulas ability to t market data. In the second part of our thesis we begin by introducing some of the earliest network models proposed by Paul Erd}os and Alfr ed R enyi. We show how similar to component sizes on a network being related to contagion on a network, it is possible then to compute the probability of default for a portfolio of names using network percolation. We present the nite and in nite network models used to model the default dependency between names in a portfolio and thus extend the in nite network model to compute the probability of default for a CDO portfolio. We nally compare the percolation model, Gaussian and Student t4 copulas to market data and from our results determine that the percolation model provides a better t to market data than the Gaussian and Student t4 copulas.