Jul 09

CDS Index tranches (FRM AIMs in the news)

by David Harper, CFA, FRM, CIPM

FRM |

Martin Scheicher of European Central Bank (ECB) gives a helpful, non-technical summary of the mechanics of CDS Index tranches on the way to finding pricing differences between CDS and iTraxx.

From my notes:

Two issues make CDO valuation more complex than the pricing of many other financial instruments.

  • For most CDOs there is no active trading. Most CDO transactions are tailor made and often held on books until maturity.
  • Theoretical valuation of CDOs is complex: "requires accurate and up-to-date estimation of the co-movement of defaults among the entities in the credit portfolio backing the CDO."

The dependence (co-movement) problem has at least two aspects: first, the known problems with using historical correlations in order to extrapolate "out of sample" into the future. Second, Jorion's curse of dimensionality: n credits implies (n)(n+1)/2 pairwise correlations. For example, 50 credits implies (50)(51)/2 pairwise correlations or elements in the covariance matrix.

CDO market consists of two segments:

  • Actively traded segment: underlying credit portfolio is based on the standardized portfolio of a CDS index such as the iTraxx (European) or CDX (North American) index. These index-based CDOs (a.k.a., CDS index tranches) are the "tip of the iceberg" of the CDO market segment.
  • Illiquid "buy and hold" segment. Tailor-made instruments (a.k.a., bespoke securities) which have been the source of sizable losses for many market participants. Frequently sold in private transactions where institutional buyer chooses (designs) underlying credit portfolio or the structure of cash-flows. "The specific features in these transactions limit the development of an active secondary market and investors have to hold these securities until maturity. When banks sell these non-standard CDOs in the primary market they rely on the market prices of the CDS index tranches for the pricing of the bespoke instruments. "

Both iTraxx and CDX have six tranches (e.g., equity = 0% to 3%) with slightly difference attachment/detachment points:

"Collectively, the six tranches represent the entire capital structure of the CDS index portfolio and can be interpreted as options on the joint loss distribution. In total, the six tranches cover all the possible losses arising from defaults in the CDS index portfolio. In parallel, all cash flows from the CDS index portfolio are paid out, starting from the senior tranches and ending with the equity tranche. Tranche trading takes place in the over-the-counter market among banks and brokers. Because the instruments are constructed as synthetic single-tranche CDOs investors can buy or sell all tranches individually."

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