Large portfolios credit risk analysis with LT-Archimedean copulas and application to a case of securitised ABS

The primary focus of this thesis centers on the investigation of an innovative quantitative framework for evaluating credit risk, particularly within the context of margin loans pricing. Given that these credit derivatives are grounded in large credit portfolios, the accurate quantification of their inherent credit risk is imperative, necessitating the evaluation of loss tail quantiles and Conditional Value at Risk. To accomplish this, the study harnesses the power of LT-Archimedean Copulas, specialized mathematical tools for elucidating tail-risk interdependencies among obligors. This analysis begins by deriving precise analytical asymptotic expressions, which serve as the foundation for the development of a variance reduction algorithm known as the Conditional Monte Carlo method, employed to enhance the outcomes of the conventional Monte Carlo approach. Then, the empirical application of this novel methodology is undertaken, utilizing an ABS loan data tape provided by Intesa Sanpaolo S.p.A. Within the data structure, critical parameters are meticulously computed and estimated. The assessment of interdependence strength within the asset pool is accomplished through an adapted application of the Kendall's Tau concordance measure, while the evaluation of each individual obligor's loan quality is achieved through an innovative spread-based methodology. Subsequently, the derived loss tail probabilities assume a central role, serving as the foundation for pricing the associated security. The results are then compared with existing market practices, offering insight into the reliability and precision of this innovative quantitative method.