he dramatic meltdown in the subprime market during 2007-2008 raised many red flags among market participants about their potential exposure to broad, systemic credit shocks. These heightened concerns have produced dramatic declines in market liquidity and access to credit, flights to quality, sharp increases in market volatility, and rising risk premiums in many financial markets. As a result, prices of the most credit sensitive securities in the market may actually play the role of "the canary in the coal mine" in providing information about how market participants collectively assess the risk of systemic or macroeconomic credit shocks.In this article, we describe using the prices of indexed credit derivatives to extract market expectations about the nature and magnitude of the credit risks facing financial markets. Since their inception in 2002, the indexed credit derivatives markets have exploded in size and participation. Broad indices are now traded for the U.S. (Markit CDX) and European (Markit iTraxx) credit markets, which usually have high liquidity, and indices are traded to a lesser degree for the Japanese and U.K. credit markets. As of the end of 2007, the investment-grade CDX was in its ninth generation and its European counterpart, in its eighth generation. Even more striking than the success of the indices, however, are the launch and success of tranches on the indices. Tranches can be best thought of as call spreads on the credit losses of a portfolio. Investors can use tranches to control their exposure to particular loss thresholds.To extract the information from these credit derivatives, we first developed a simple linearized version of the collateralized debt obligation (CDO) pricing model of Longstaff and Rajan (2008). They proposed a three-jump model that is directly calibrated to the traded spreads of tranches and indices. The model allows for the possibility that credit spreads might be a composite of several types of credit risk. Specifically, they found that the creditloss distribution embedded in index tranche prices includes a component for the risk of idiosyncratic or company-specific defaults, a component for the risk of broader, sectorwide or industrywide defaults, and a component for the risk of a massive economywide default scenario. 1 In the study reported in this article, we fit the linearized version of the model to the market prices of the credit indices and tranches.
The Linearized Three-Jump ModelFollowing Longstaff and Rajan (2008), we let L denote the proportion of portfolio losses realized on a credit portfolio (so, L 0 = 0 losses). We write the proportion of portfolio losses as (1) where the i parameters (where i = 1, 2, 3) denote jump sizes and N i are independent Poisson counters that correspond to the number of jumps. 2 Note that Equation 1 allows for L to be greater than 1, but in practice, such large values of L are never
