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Leveraged Finance: Concepts, Methods, and Trading of High-Yield Bonds, Loans, and Derivatives by FRANK J. FABOZZI, DOUGLAS J. LUCAS, STEPHEN J. ANTCZAK

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CHAPTER 13
Default Correlation The Basics
Default correlation measures whether credit risky assets are more likely to default together or separately. For example, default correlation answers the following question: If 10 bonds each have a 10% probability of default, does that mean: (1) One and only one is definitely going to default? Or (2) is there a 10% chance all of them will default and a 90% chance none of them are going to default? If the answer is “in between,” where in between?
Default correlation is essential to understanding the risk of credit portfolios and is the subject of this chapter. Along with default probability and loss in the event of default, default correlation determines the credit risk of a portfolio.
In this chapter, we look closely at the definition of default correlation and discuss its drivers. We then provide pictorial representations of default probability and default correlation and present mathematical formulas relating default correlation to default probability. The difficulty of the problem becomes evident when we show that pairwise default correlations are not sufficient to understand the behavior of a credit risky portfolio and introduce “higher orders of default correlation.” In the next chapter, we continue our discussion of default correlations where we cover empirical results and problems related to default correlation, as well as our opinion on proposed solutions to the problem of incorporating default correlation into credit analysis. ...

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