Back Matter

References

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  • Andritzky, Jochen, 2006, Sovereign Default Risk Valuation (New York: Springer).

  • Cossin, Didier, Tomas Hricko, Daniel Aunon-Nerin, and Zhijiang Huang, 2002, “Exploring for the Determinants of Credit Risk in Credit Default Swap Transaction Data: Is Fixed-Income Markets’ Information Sufficient to Evaluate Credit Risk?Research Paper Series No. rp65 (Brussels: HEC–University of Lausanne).

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  • Duffie, Darrell, 1999, “Credit Swap Valuation,” Financial Analyst’s Journal, Vol. 55 (January-February), pp. 7387.

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1

We like to thank for helpful comments from Bojan Bistrovic, Jane Brauer, Michael Dooley, Frank Packer, Paul Söderlind, Haibin Zhu, and seminar participants at the Quant Congress 2005, New York; the EFMA Annual Meetings 2006, Madrid; the Annual Pacific Basin Finance, Economics, and Accounting Conference 2006, Taipei; the NFA Annual Meetings 2006, Montreal; the University of California, Santa Cruz; and the International Monetary Fund. Jochen Andritzky acknowledges financial support from the Swiss National Science Foundation (SNF).

2

Permitted currencies are generally the G-7 currencies and also those OECD currencies that carry a rating of AAA on their local currency debt (e.g., the Mexican peso and South Korean won, both issued by OECD countries, are not permitted currencies as the local currency debt is rated below AAA).

3

According to market participants, physical delivery is the preferred clause to avoid price disputes in the typically illiquid cash markets following a credit event. This is problematic when there is a short supply of CTDs, as it recently occurred when the U.S. auto parts maker Delphi filed for bankruptcy in 2005. In this case, an auction to determine the CTD price can be called with protection sellers offering the choice between physical delivery or cash settlement at the auction price.

4

This is the underlying idea of the widespread recovery of market value (RMV) concept which assumes the expected recovery value ψ to be a portion of the market value. See Duffie and Singleton, 1999.

5

When marking CDS contracts to market, this up-front payment reduces the exposure of protection sellers since less of the protection leg is at risk. Therefore, when spreads tighten (widen), the mark-to-market gain (loss) will be smaller.

6

Other standard terms are (i) “modified restructuring (MR),” first applied in 2001 and for nonsovereigns today by far the most popular contract in the United States, which limits the delivery option to bonds with a maturity of 30 months or less after the maturity of the respective CDS contract, and (ii) “modified-modified restructuring (MMR),” first used in 2003 and often applied in European markets for nonsovereigns, which allows slightly more flexibility in the delivery option than the modified restructuring terms.

8

This is exactly true only if the bond price always stays at par.

9

The following example illustrates this. If a bond to be insured by a CDS trades at 200 basis points and ψ is assumed to be 50 percent homogeneously for all bonds, this gives λ =400bps. If the CTD (regardless of the price of the bond the CDS contract is intended to insure) is expected to trade constantly at 0.75 per unit of face value, the relevant recovery rate ω for pricing the CDS becomes ω=50%·0.75, resulting in a CDS spread of 250 basis points.

10

The recovery fraction is assumed to be constant and deterministic here, a presumption which deserves some further analysis though.

11

The same effect is apparent from Figure 2 in Duffie and Singleton (1999), page 703. Remember that the implied default probability (during the first increment of time) must be one if we set the fractional recovery of face ω equal to the current bond price.

12

This is called partial protection. The corresponding argument for the protection seller would indicate that for achieving a neutral position when providing protection for a par value of 100 units of currency the protection seller would need to short more than 100 units of par value in the underlying bond.

13

This threshold is typically seen as a good proxy for distress. See Pescatori and Sy (2004).

14

As measured by the British Bankers Association according to the EMBI+ subindex.

15

As evidence from Uruguay shows, even very plain maturity extension deals do not result in a constant ψ for all bonds. In practice, even soft restructurings resemble a mixed recovery framework where the recovery value is comprised by two recovery fractions ω and ψ. See Andritzky, 2006, p. 105.

16

These figures are created for illustrative reasons (instead of plotting solely ω and ψ), and incorporate additional assumptions. The graphed recovery value is discounted with the risk-free rate from the 75 percent quantile default time, i.e., the point in the future at which the cumulative default probability hits 75 percent. The recovery fraction of market value, ψ, is multiplied with the current clean price of the CTD which does not take into account fluctuations in the expected pre-default price. Results are illustrated only for one underlying. For the three-year tenor, Brazil 2006 US$10.25 percent was the most liquid bond and has the best maturity match.Results for the Brazil 2005 US$9.625 percent bond look comparable. For the five-year tenor, results for the other bonds look similar.

The Pricing of Credit Default Swaps During Distress
Author: Mr. Manmohan Singh and Mr. Jochen R. Andritzky