PDF Ebook Default Clustering and Valuation of Collateralized Debt Obligations
The recent financial crisis, which led to the collapse of some major financial institutions such as Bear Sterns, Fannie Mae, Freddie Mac, Merrill Lynch, Lehman Brothers, Washington Mutual, and Wachovia, has changed the financial landscape completely. It is too early to tell the full impact of the crisis, as the events are still unfolding. But in terms of research, two issues are clear: (1) We need better models to incorporate the default clustering effect, i.e., one default event tends to trigger more default events both across time and cross-sectionally. (2) We need better models for multi-name credit securities, such as collateralized debt obligations (CDOs), the mispricing of which contributed significantly to the current financial crisis. This paper attempts to study these two issues.
By extending the intensity based model of Duffie and G?rleanu (2001), we propose a credit risk model based on cumulative default intensities that can incorporate the default clustering effect. Furthermore, the model is tractable enough to provide a direct link between single-name credit securities, such ascredit default swaps (CDS), and multi-name credit securities, such as CDOs. The calibration of our model to the market data of CDOs and CDS on March 14, 2008, when Bear Sterns was near bankruptcy, and the data on September 16, 2008, right after Lehman Brothers filed for bankruptcy protection, shows that the model is promising.
There are two types of credit derivatives: the single-name derivatives, whose payoffs depend on the credit events of a single reference name, and the portfolio credit derivatives, whose payoffs depend on the credit events of a portfolio of reference names. For example, a popular single-name credit derivative is the CDS, which is a bilateral contract between a default protection buyer and a protection seller. More precisely, the protection buyer pays a periodic premium to the protection seller, in return for the cover of loss if the reference name defaults.
The best-known portfolio credit derivative is perhaps the CDO. A CDO is a debt security that is secured by a portfolio of defaultable assets, such as bonds and CDS. A CDO partitions its underlying portfolio into tranches, each of which corresponds to a specific portion of the default losses of the portfolio. A typical CDO structure is shown in Fig. 1, where the portfolio underlying the CDO has 125 names and the CDO comprises 6 tranches. The investor of the first tranche takes the first 3% default losses. The investor of the second tranche begins to take losses when the cumulative portfolio losses exceed 3% and continues to do so until the cumulative losses reach 6%, and so on for other tranches. In return, the investors receive periodic coupon payments. The first tranche is called the equity tranche, which is the most risky and hence offers the highest coupon. The last tranche is called the senior tranche, which is the last to take default losses (see Duffie and Singleton, 2003, for a comprehensive discussion of CDOs).
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PDF Ebook Default Clustering and Valuation of Collateralized Debt Obligations
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