How to invert the bonds yields to find out the expected time to default?

[beerbaron]

Sometimes we see comments like the yield of Italy is 2.6% and Germany's is 1% implying that Italy would default on it's debt every X years. What's the formula to get the implies default rate?

 

Thanks

BeerBaron

[peter1234]

I thought using Credit Default Swaps CDS is more straight forward.

[wknecht]

CDS data usually leads bond I believe. But using bonds, you can derive a spread (yield to worst minus treasury of same duration), and use the shortcut formula in the link below. Should try to pick a bond maturing around the horizon you're interested in. I suppose this would work for Euro sovereigns in your example also, but maybe in that case they use German bonds as risk free proxies in the spread calculation.

 

Paper you might find interesting:

http://www-2.rotman.utoronto.ca/~hull/downloadablepublications/hpwpaperoncdsspreads.pdf

 

Shortcut formula (in this formula, folks typically assume 35% or 40% recovery for senior unsecured obligations):

http://www.kamakuraco.com/Blog/tabid/231/EntryId/217/Kamakura-Blog-The-Links-between-CDS-Spreads-and-Default-Probabilities.aspx

 

 

If you have CDS data, you can use the ISDA standard model (believe this is based on the "JP Morgan" model which you can google for more info) to imply PDs also:

http://www.cdsmodel.com/cdsmodel/

 

[beerbaron]

Thank, quite comprehensive.

 

BeerBaron