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But the rate plays a role: as long as the product remains "Marked to Model" (theoretical pricing and not actual quote from a market, which is only available for the most liquid ones, like iTraxx basket and the like, see www.markit.com - nothing is free there).
The "Model" price is a math model of the probability of a default by the time the CDS expires. This gives you a value "averaged over all possible futures weighted by their respective probabilities".
Most of those math models try to extract "implicit" information from the market: notably, when a borrower has issued bond, they have a yield (coupon set a issue divided by price set by market), which has a spread (how many % more than Fed rate is it ??). Risky borrowers have high spreads, which means they must pay exorbitant rates to borrow, thus increasing their riskiness ("on ne prête qu'aux riches")
So the math models computes the risk of default of company ACME in years 1,2,3... based on the spreads of its quoted bonds of maturities 1,2,3 years: actually, you are making a poll of the opinion of traders about if/when ACME will default, except (market quotes + untested math + historical default events to calibrate) replace a lot of phone calls... (+ tricky poll maths)
And the problem is that in the past years, markets have been so in love with risk that the spread range between "sovereign debt" and "total junk" is only a few percentage points.
So basically when the auction at BearStearns & Merril Lynch says that securities traded for 30 to 80 cents on the dollar, it means their spreads are up by 1-20 percentage points. Which means that the new market opinion, according to the models, should now read as: 100% guaranteed total default across the board for all MBS within the next 6 months. Either that, or the calibration is out the window and bankers are now shit scared about risky loans like they haven't been in decades (= total credit crunch)
Most institutions with MBS marked to models should now be basically writing them off, which would require a gov'nmt bail out...
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