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CDO and structured financial products: a modeling prospective

Credit derivatives were the fastest growing financial products in capital markets. They assumed complex structures and forms and were vilified by some, and called financial weapons of mass destruction, and celebrated by many others who bought, sold, and invested in such products. Banks, insurance companies, hedge funds, pension funds, asset managers, and structured finance vehicles have used and are likely to continue to use credit derivatives for arbitrage, speculation, hedging, securitization, and pass through their credit risks. Essentially these structured products combine insurance and financial innovation to allow risks to be shared far more extensively than vanilla options and typical insurance and credit products.

Collateralized Debt Obligations (CDO), as their name implies, are used as a generic structured credit product, similar to asset-backed securities and structured finance products. In a CDO a portfolio of bonds, loans, or other fixed income securities is gathered together, and used to create a new set of fixed income securities. This allows for a technique called "credit tranching" by which insured losses from the portfolio are repackaged as sliced notional tranches that are marketed to separate investors that seek return-loss characteristics. CDOs thus allow financial firms to market and transfer their credit risk to other parties either OTC or through securitization. These (credit) pass through products have desirable characteristics that explain their popularity. For example, for banks holding loans, their covenant can be structured with their rights and securities used as collaterals.

There are many types, forms, structures, and names for CDOs. Some are securitized portfolios of bonds, real estate properties, assets backed securities (ABS), portfolios backed by the revenues and the obligations of mortgages (MBS) or CDS (Synthetic CDOs), and so on. Currently, financial products such as forward starting CDO and possibly options on CDO tranches, market values CDO, CFO (Collateralized Fund Obligations), Constant Proportion Portfolio Insurance (CPPI), Constant proportion debt obligations (CPDO), and so on, are engineered to face regulation to be imposed on such products. Their usefulness fuel a continuous financial innovation to provide liquidity and at the same time provide sources of profit to financial institutions. Their pricing remains, however, challenging.

A CDO’s risk-rewards properties and the prices of its tranches are in general a function of the CDO structure, defined in terms of: (1) the definition of the portfolio assets (such as bonds, MBS, ABS, etc.), their returns and losses (whether deterministic or stochastic), their individual statistical dependence and their aggregate dependence on rare events, contagions, macroeconomic factors, and so on, that define the prospective portfolio returns and losses and their distribution across tranches; (2) tranches or layering the portfolio in risk-reward classes; (3) defining the rights and the obligations for each risk class including (also called payment waterfall) the sequencing and the schedule of returns allocation to tranche holders, the sequencing and the schedule of losses allocated to tranches, and the legal rights and the recourse to each tranche holder (many of which are defined as clauses in the offering circular); and (4) rating and securitizing the portfolios by selling it in a financial market, rate the portfolios appreciably to secure their acceptability by investors, marketing the portfolios to meet the need of investors, and managing the risks and pricing the portfolios risk classes.

The complexity and the pricing of CDOs is as a result mathematically complex. Due to the many risks embedded in such products, multivariate probability models (or multivariate stochastic processes) are used. Due to a lack of sufficiently rich information required to capture their dependence and their evolution over time, simplifications are also made that can lead to mispricing. For example, dynamic copulas are used to model the statistical and time dependence structure of the many random factors that contribute to the gains and losses of the CDO notional. While these approaches are useful, they remain hypotheses made about a future embedded in the fundamental framework of state price preference theory.

In our latest article, we provide a tractable mathematical model of CDO models, their essential economic (risk-rewards) characteristics embedded in specific structures of the probability distribution of underlying assets or losses in a CDO. Due to CDOs’ variety and broad applications, our paper focuses attention to selected examples that emphasize the structure, the returns and the losses, and the complexity of CDOs of assets as well as bonds.

Our article provides both a retrospective and perspective for CDOs, their usefulness as well as a generic and tractable quantitative formulation that allows one to simulate and price CDO tranches. If you wish to know more about our pricing models please refer to the article at:


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