Large Deviations in Portfolio Credit Risk

Specialeforsvar: David Haoyang Xu

Titel: Large Deviations in Portfolio Credit Risk

Abstract: Credit risk analysis is a critical concern for financial institutions, where the main problem is the probability of the portfolio loss exceeding a threshold. This thesis focuses on the asymptotic behavior of the tail loss distribution in large credit
portfolios by analyzing two distinct regimes. The first regime examines the tail of the loss distribution at increasingly high loss thresholds, while the second regime considers the scenario where the individual obligor’s default probability approaches zero. Both regimes are studied under the condition of an expanding portfolio size.
We begin by formulating the factor model used in the analysis, extending the basic model to include generic distribution types and then to account for multiple obligor types.
Our analysis reveals significant qualitative distinctions between the two regimes across both models. In the generic distribution model, the large loss regime is characterized by idiosyncratic factors that determine an increasing threshold, with the tail distribution of the common factors quantifying this threshold. In the small default probability regime, the tail distribution of the
common factors alone governs the loss probability, driven by the decreasing default probability.
In the multiple obligor type model, the large loss regime exhibits a power law decay in the tail loss threshold, while the small default probability regime follows an exponential decay.

Vejleder: Jeffrey Collamore
Censor: Camilla Schaldemose, Topdanmark