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


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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:



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




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:



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