Copyright © 2009 Diresh Jewan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This research work investigates the theoretical foundations and computational aspects of constructing optimal bespoke CDO structures. Due to the evolutionary nature of the CDO design process, stochastic search methods that mimic the metaphor of natural biological evolution are applied. For efficient searching the optimal solution, the nondominating sort genetic algorithm (NSGA-II) is used, which places emphasis on moving towards the true Paretooptimal region. This is an essential part of real-world credit structuring problems. The algorithm further demonstrates attractive constraint handling features among others, which is suitable for successfully solving the constrained portfolio optimisation problem. Numerical analysis is conducted on a bespoke CDO collateral portfolio constructed from constituents of the iTraxx Europe IG S5 CDS index. For comparative purposes, the default dependence structure is modelled via Gaussian and Clayton copula assumptions. This research concludes that CDO tranche returns at all levels of risk under the Clayton copula assumption performed better than the sub-optimal Gaussian assumption. It is evident that our research has provided meaningful guidance to CDO traders, for seeking significant improvement of returns over standardised CDOs tranches of similar rating.