This was driven from a requirement to ensure that traders couldn't enter spreads that had a negative implied default rate. For example if a 3 year CDS is priced at 50 bps and a 5  year at 60 bps, the 4 year must be between 37.5 and 75 to avoid an arbitrage -

3 * 50 = 150bps

5 * 60 = 300bps

(this example is given in Chaplin)

Obviously this was simplified example (not taking interest rates into account), so more digging was required - I found the following on Wilmott

http://www.wilmott.com/messageview.cfm?catid=4&threadid=37690

http://www.wilmott.com/messageview.cfm?catid=8&threadid=9830

and in particular, the JP paper that details how the calculation is done

http://www.wilmott.com/attachments/CDS_JPM1.zip

I got the majority of the calculations working but couldn't get from the yld to discount factor. However, looking at Moorad Chouldry's new book, it appears that he is happy to use the spot rate for his calculations, so I have done likewise, although this will mean that my results differ slightly from Bloomberg.

Taking a typical curve (ACCOR), Bloomberg CDSW (using JPMorgan model), gives the following

The things to note here are:

• Using EUR swap curve
• Quarterly calculation/payments
• Fees accrued on ACT/360 basis
• Recovery of 40%

TODO: Bootstrap swap curve

So for the 5 year default, we are showing 0.028 compared to 0.0276

We can also use the spreadsheet to calculate DV01

although we differ from Bloomberg's figure of 4678.

UPDATE: The 4678 figure is wrong - I hadn't adjusted the deal spread from default of 100 bps.

Note that my original calculation

http://www.noelwatson.com/blog/PermaLink,guid,5c54efd9-9b42-480a-bb1a-01386a2c9d48.aspx

gives a DV01 of 4484, so this is more accurate - close but no cigar.

However, the spreadsheet enables us to check for negative default rate. For example, if we multiply the two year spread by 10, we can see that the probability of default is higher at two years than at three. This would lead to an arbitrage situation (I would sell you two year protection and buy three year protection), so should be flagged.

Attachment: Spreadsheet (note that the 2 year spread has the x10 value)

CDSWv1.xls (40.5 KB)

• Credit Derivatives by Geoff Chaplin (Page 97) http://www.amazon.co.uk/exec/obidos/ASIN/047002416X/qid=1141718528/sr=1-1/ref=sr_1_2_1/026-0058056-7028455

• Moorad Choudry: The Credit Default Swap Basis (Page 160)

http://www.amazon.co.uk/Credit-Default-Swap-Basis/dp/1576602362/sr=1-1/qid=1162898932/ref=sr_1_1/026-8787779-9446068?ie=UTF8&s=books