Journal of Applied Mathematics and Decision Sciences
Volume 2009 (2009), Article ID 925169, 32 pages
Research Article

Optimal Bespoke CDO Design via NSGA-II

1Department of Statistical Sciences, University of Cape Town, Private Bag, Rhodes' Gift, Rondebosch 7701, Cape Town, South Africa
2Peregrine Quant, PO Box 44586, Claremont, Cape Town, 7735, South Africa

Received 28 November 2008; Accepted 9 January 2009

Academic Editor: Lean Yu

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.


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.