In a credit portfolio, events can lead to the default of a single component or simultaneous defaults of multiple components. Modeling dependent defaults in a portfolio is important in credit risk management. In this thesis, we introduce a multivariate default model which takes the dependence structure between components into account. Based on subordinators, a default time is constructed as the first time that the subordinator process exceeds a unit-mean exponential random variable. We call this the multivariate default model. The survival probability for the univariate model, as well as the joint survival probability for the bivariate and the multivariate model are calculated and proved to have Marshall– Olkin form. The implied copulas of the default times for the bivariate and the multivariate model are found to be a Marshall–Olkin survival copulas. Under certain conditions, the implied copula of the bivariate model is a Cuadras–Aug´e survival copula. Based on the multivariate default model, we derive the portfolio loss process and derive closed-form expressions for the unconditional and conditional probability of defaults. These formulas enable to estimate the default probability given certain conditions and reevaluate the default probability based on observed defaults. In the end, this model is applied to collateralized debt obligations (CDOs) pricing. A Monte Carlo simulation example is given to estimate the premium spread for di↵erent tranches of a CDO. The multivariate default model employs multi–dimensional subordinators, it provides a better understanding of the model in a higher–dimensional setting. Besides, it yields a computationally efficient method for simulating default times.     «

In a credit portfolio, events can lead to the default of a single component or simultaneous defaults of multiple components. Modeling dependent defaults in a portfolio is important in credit risk management. In this thesis, we introduce a multivariate default model which takes the dependence structure between components into account. Based on subordinators, a default time is constructed as the first time that the subordinator process exceeds a unit-mean exponential random variable. We call this...     »