CDS Implied Default Probability

[optionshedge]

I read an interesting article on Bloomberg:

"Credit-default sellers on Sept. 17 demanded as much as $2.1 million upfront and $513,000 a year to protect $10 million in Morgan Stanley bonds from default for five years. The price implied a 65 percent chance the company would go bust within five years, based on a valuation model created by JPMorgan. The cost has since dropped to $500,000 a year, implying it has a more than one-in-three chance of failing."

http://www.bloomberg.com/apps/news?pid=20602007&sid=aT.Q3P5imhVg&refer=govt_bonds

How do you calculate the implied default probability for these CDS?

 

[David Harper CFA FRM]

Thanks for link to interesting article.

A crude approach (but I imagine conceptually similar to JP Morgan's) is to take the Hull model (here it is on member page). Note that model takes probability of default as an input and solves for CDS spread. So, you could simply "goal-seek" on the PD that produces a spread equal to the market CDS spread (much like we reverse-engineer implied volatility of a call option by solving for the volatility input that gives a model option value equal to observed market value).

But it's crude because our (Hull's) assumes a constant PD. JP morgan likely bootstrapped a survival curve. So, you take the first observed market spread, solve for the default assumption that produces a model credit spread = market spread (with the same premise as we study in CDS: the PV of the payment leg = PV of payoff leg). Then you use that to "bootstrap" the next implied default, building a term structure. It employs, in a way, both the implied volatility procedure (in call option) and the bootstrap procedure used to build out a forward interest rate term structure.

David