Optimal Bespoke CDO Design via NSGA-II

摘要

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 thatmimic the metaphor of natural biological evolution are applied. For efficient searching the optimal solution, the nondominatingsort genetic algorithm (NSGA-II) is used, which places emphasis on moving towards the true Paretooptimalregion. This is an essential part of real-world credit structuring problems. The algorithm further demonstratesattractive constraint handling features among others, which is suitable for successfully solving the constrained portfoliooptimisation problem. Numerical analysis is conducted on a bespoke CDO collateral portfolio constructed fromconstituents of the iTraxx Europe IG S5 CDS index. For comparative purposes, the default dependence structure ismodelled via Gaussian and Clayton copula assumptions. This research concludes that CDO tranche returns at alllevels of risk under the Clayton copula assumption performed better than the sub-optimal Gaussian assumption. It isevident that our research has provided meaningful guidance to CDO traders, for seeking significant improvement ofreturns over standardised CDOs tranches of similar rating.