Abstract:
A review of the credit risk models that were used for pricing credit derivatives and risk management during the financial crisis of 2008 shows that the models fail to capture the severe event that a lot of firms default simultaneously and measure credit losses dynamically. As a result, the models underestimate credit risk and misprice complex credit derivatives, for example, Collateralized Debt Obligations (CDOs). The aim of the study is to propose the model that has the capacity to produce strong default dependency for pricing CDOs. Our proposed model is a kind of the intensity based models. To create default correlation among the CDO's underlying firms, we construct firms' default intensity processes based on market factor intensity processes. The market factors are modeled as the jump-diffusion distribution that has a drift-diffusion component and a jump component. Unlike any existing models, our model corporates in correlated market factor intensity processes. In addition, we use the Gamma-Poisson mixture process as the counting process of jumps in market factor intensities. Another objective of this research is to develop efficient methods which are used to implement our correlated market factor model for computing the portfolio loss distribution. The methods that we suggest are a recursive method and a Mimicking Markov chain method. The empirical results show that our model prices CDO tranches better than the traditional jump-diffusion model. The correlations between the market factor intensities are economically interpretable. Gamma-Poisson mixture processes governing arrival of jumps in intensities have an immense impact to the tails of the portfolio loss distribution.
