Intelligent Information Management, 2010, 2, 149-158 doi:10.4236/iim.2010.22018 Published Online February 2010 (http://www.scirp.org/journal/iim) On the Mechanism of CDOs behind the Current Financial Crisis and Mathematical Modeling with Lévy Distributions Hongwen Du1, Jianglun Wu2, Wei Yang3 1School of Finance and Economics, Hangzhou Dianzi University, Hangzhou, China 2Department of Mathematics, Swansea University, Swansea, UK 3Department of Mathematics, Swansea University, Swansea, UK Email: [email protected], {j.l.wu,mawy}@swansea.ac.uk Abstract This paper aims to reveal the mechanism of Collateralized Debt Obligations (CDOs) and how CDOs extend the current global financial crisis. We first introduce the concept of CDOs and give a brief account of the de- velopment of CDOs. We then explicate the mechanism of CDOs within a concrete example with mortgage deals and we outline the evolution of the current financial crisis. Based on our overview of pricing CDOs in various existing random models, we propose an idea of modeling the random phenomenon with the feature of heavy tail dependence for possible implements towards a new random modeling for CDOs. Keywords: Collateralized Debt Obligations (CDOs), Cashflow CDO, Synthetic CDO, Mechanism, Financial Crisis, Pricing Models, Lévy Stable Distributions Collateralized debt obligations (CDOs) were created in lateralized Bond Obligations, or CBO), loans (Co- 1987 by bankers at Drexel Burnham Lambert Inc. Within llateralized Loan Obligations, or CLO), funds (Coll- 10 years, the CDOs had become a major force in the ateralized Fund Obligations, or CFO), mortgages credit derivatives market, in which the value of a deriva- (Collateralized Mortgage Obligations, or CMO) and oth- tive is “derived” from the value of other assets. But ers. And frequently, they source their collaterals from a unlike some fairly straightforward derivatives such as combination of two or more of these asset classes. options, calls, and Credit Default Swaps (CDSs), CDOs Collectively, these instruments are popular referred to as are not “real”, which means they are constructs, and CDOs, which are bond-like instruments whose cashflow sometime even built upon other constructs. CDOs are structures allocate interest income and principal repay- designed to satisfy different type of investors, low risk ments from a collateral pool of different debt instruments with low return and high risk with high return. to a prioritized collection of CDO securities to their In early 2007, following the burst of the bubble of investors. The most popular life of a CDO is five years. housing market in the United States, losses in the CDOs However, 7-year, 10-year, and to a less extent 3-year market started spreading. By early 2008, the CDO crisis CDOs now trade fairly actively. had morphed into what we now encountered the world- A CDO can be initiated by one or more of the wide financial crisis. CDOs are at the heart of the crisis followings: banks, non-bank financial institutions, and and even extend the crisis. asset management companies, which are referred to as the sponsors. The sponsors of a CDO create a company 1. Introduction to CDOs so-called the Special Purpose Vehicle (SPV). The SPV works as an independent entity and is usually bankruptcy remote. The sponsors can earn serving fees, adminis- Collateralized Obligations (COs) are promissory notes tration fees and hedging fees from the SPV, but otherwise backed by collaterals or securities. In the market for COs, has no claim on the cash flow of the assets in the SPV. the securities can be taken from a very wide spectrum of According to how the SPV gains credit risks, CDOs alternative financial instruments, such as bonds (Col- are classified into two kinds: cashflow CDOs and syn- Copyright © 2010 SciRes IIM 150 H. W. DU ET AL. thetic CDOs. If the SPV of a CDO owns the underlying the least risky tranche in CDOs with lowest fixed interest debt obligations (portfolio), that is, the SPV obtains the rate, followed by mezzanine tranche, junior mezzanine credit risk exposure by purchasing debt obligations (eg. tranche, and finally the first loss piece or equity tranche. bonds, residential and commercial loans), the CDO is A CDO makes payments on a sequential basis, depen- referred to as a cashflow CDO, which is the basic form ding on the seniority of tranches within the capital struc- in the CDOs market in their formative years. In contrast, ture of the CDO. The more senior the tranches investors if the SPV of a CDO does not own the debt obligations, are in, the less risky the investment and hence the less instead obtaining the credit risk exposure by selling they will be paid in interest. The way it works is fre- CDSs on the debt obligations of reference entities, the quently referred to as a “waterfall” or cascade of cash- CDO is referred to as a synthetic CDO; the synthetic flows. We well give a specific illustration in Section 3. structure allows bank originators in the CDOs market to In perfect capital markets, CDOs would serve no pur- ensure that client relationships are not jeopardized, and pose; the costs of constructing and marketing a CDO avoids the tax-related disadvantages existing in cashflow would inhibit its creation. In practice, however, CDOs CDOs. The following graph (Figure 1) illustrates a construction of a cashflow CDO. address some important market imperfections. First, ban- After acquiring credit risks, SPV sells these credit ris- ks and certain other financial institutions have regulatory ks in tranches to investors who, in return for an agreed capital requirements that make it valuable for them to payment (usually a periodic fee), will bear the losses in securitize and sell some portion of their assets, reducing the portfolio derived from the default of the instruments the amount of (expensive) regulatory capital that they in the portfolio. Therefore, the tranches holders have the must hold. Second, individual bonds or loans may be ultimate credit risk exposure to the underlying reference illiquid, leading to a reduction in their market values. portfolio. Securitization may improve liquidity, and thereby raise Tranching, a common characteristic of all securisa- the total valuation to the issuer of the CDO structure. tions, is the structuring of the product into a number of In light of these market imperfections, at least two different classes of notes ranked by the seniority of in- classes of CDOs are popular: the balance-sheet CDO and vestor's claims on the instruments assets and cashflows. the arbitrage CDO. The balance-sheet CDO, typically in The tranches have different seniorities: senior tranche, the form of a CLO, is designed to remove loans from the Figure 1.Cashflow colateralised mortgage obligation. Copyright © 2010 SciRes IIM H. W. DU ET AL. 151 balance sheets of banks, achieving capital relief, and ssess the advantage that they call for minimal resources perhaps also increasing the valuation of the assets thr- in terms of management expertise and time and reduce ough an increase in liquidity. An arbitrage CDO, often costs involved in trading. However, when they declined underwritten by an investment bank, is designed to cap- in value, investors were unable to do anything to reverse ture some fraction of the likely difference between the that decline as credit quality began to deteriorate. There- total cost of acquiring collateral assets in the secondary fore, actively managed CDOs were rapidly gaining in market and the value received from management fees popularity. The growth of managed products, however, and the sale of the associated CDOs structure. was also helped by the growing maturity of the CDO market and by the increasing number of managers with 2. The Development of CDOs proven experience in managing credit in general and credit derivatives in particular. Although a market for CMOs—the forerunner of modern CDOs—was taking shape in the US market by the early 3. The Mechanism of CDOs 1980s, the market for CDOs is generally believed to date back to the late 1980s and the rapid revolution of CDOs In this section, we try to describe the mechanism of is very much a story of the 1990s. CDOs in a vivid, therefore not so rigorous, way. We By the late 1990s, the structure of the international simplify the collaterals as mortgages. Then the process to market for CDOs of all kinds was becoming characte- create a CDO can be seen in the following manner: rized by a number of conspicuous and interrelated trends. investment banks buy mortgages and then pool them into Firstly, issuance volume was rising exponentially, as was Mortgage Backed Securities (MBSs) with different ra- understanding and acceptance of the CDO technique. Se- tings. Financial institutions seeking new markets pur- condly, the cross-border investment flowing into CDOs chase these MBSs, pool them with other similarly rated were rising steeply. Thirdly, more and more asset classes MBSs and sometimes derivatives, and then issue new were being used as security for COs. Finally, in 1999 and securities. This process of buying mortgages, creating 2000 the concept of the COs was popularised across MBSs, and packaging these MBSs into CDOs is desi- continental Europe with strikingly high speed and, mean- gned to apportion credit risk to those parties who are while, changes to legislation and regulation were emer- willing to take it on. ging as important sources of support for new issuance in First of all, we have a CDO manager who decides to the CDOs market in Europe. create a CDO. He/She has a bottle (SPV). In order to fill In 2000 CDOs were made legal and at the same time the bottle, he/she can buy collaterals (anything he/she were prevented from being regulated, by the Commodity wants: the loans, credit card debt and student loans).