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.
Highlights
Bespoke CDOs provides tailored credit solutions to market participants
Understanding the risk/return trade-off dynamics underlying the bespoke CDO collateral portfolios is crucial when maximising the utility provided by these instruments
The single-tranche deal can be put together in a relatively short period of time. This is aided by the development of numerous advance pricing, risk management and portfolio optimisation techniques
Summary
Bespoke CDOs provides tailored credit solutions to market participants. They provide both long-term strategic and tactical investors with the ability to capitalise on views at the market, sector and name levels. Investors often express preferences on individual names, and there is likely to be credit rating constraint and industry concentration limits imposed by the investors and rating agencies 2 Given these various investor defined requirements, the structurer is required to optimise the portfolio to achieve the best possible tranche spreads for investors. The main features of these algorithms are the implementation of a fast nondominated sorting procedure and its ability to handle constraints without the use of penalty functions The latter feature is essential for solving the multiobjective CDO optimisation problem. A robust and practical CDO valuation framework based on the application of the single-factor copula models given, is presented This is in conjunction with weighted Monte Carlo techniques used in options pricing. The final section highlights the improtant research findings and discusses several areas of future study
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