Modeling Multi-name default Correlations

Tsui, Lung (2011) Modeling Multi-name default Correlations. Doctoral Dissertation, University of Pittsburgh.

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Abstract

This thesis focuses on the study of credit default dependence and related mathematical and computational issues.Firstly, we derive an integral expression of the joint survival probability for the 2D first-passage-time model with default index being correlated Brownian motion and then apply it to give an alternative derivation (PDE approach) of the classical analytical formula of the default time density distribution which was first derived by Iyengar (Probabilistic approach). Furthermore, we prove that for this model both the coefficients of lower and upper tail dependence are zero.Secondly, we create a new model, the crisis model, which is a generalization of the stress event model. In the study of this model, we provide a novel identification of a set of independence conditions of defaults which enables us to derive a series expansion for the unconditional loss of a portfolio. Contrary to most bottom-up approach dynamic models, the distribution of the independence condition in the crisis model has a closed form expression which speeds up computations. We discover that by using a series expansion the loss distribution of a portfolio under the stress event model, which is a special case of the crisis model, can be computed accurately and extremely efficient. Furthermore, the computational cost for additional common factors to the stress event model is mild. This allows more flexibility for calibrations and opens up the possibility to study the multi-factor default dependence of a portfolio via a bottom-up approach. We demonstrate the effectiveness of our approach by calibrating it to investment grade CDS index tranches.

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