Stochastic cascades, credit contagion, and large portfolio losses

September 30, 2008 8:14 AM

"In the limit of an infinite economy, the number of initial downgrades is Poisson distributed.This captures the idea that the shock initially affects only a small number of firms. Nonetheless, the distribution of the total number of defaults has slowly decaying tails ... A firm might well be able to absorb its shock, but it might not be able to absorb both the shock and the resulting deterioration in the average rating. The initial downgrades may thus trigger additional defaults that, in turn, further deteriorate the average rating, and so on. In a large economy, this cascade can be described by a branching process." Ulrich Horst, Journal of Economic Behavior & Organization, 2007. (Internet supplement!)

More from Hurst on his website, this is the best description of the credit crisis I have yet to come across. Here's part of the conclusion:

"We characterized the tail behavior of the distribution of aggregate portfolio losses. If the interaction between firms are too strong, then aggregate losses turned out to be heavy-tailed even if individual losses are thin-tailed. This illustrates that counterparty relationships are in fact an additional source of intrinsic risk that should be accounted for. However, the risk can be considerably reduced if the firms’ financial standing is measured on a finer scale. In the limiting case of continuous adjustments, the additional risk is simply specified by the size of the external shock."

The solution to bad models? More models!

posted by geoff. (8 comments total)

I call red herring.

Don't hate me.
posted by Durn Bronzefist at 8:46 AM on September 30, 2008 [1 favorite has favorites]

Interestingly prophetic paper. I'm a bit disappointed by the apparent lack of motivation to quantitatively apply this nice model to an actual real live system like...say....the US financial sector. I know it's hard, but maybe try anyways? Would've been nice if he had used this to analyze financial firms back in 2004 and said "OH MY GOD the US economy is a time bomb! You investment banks need to reassess your risk portfolios right now!" But I appreciate the theoretical effort anyway.
posted by Salvor Hardin at 8:58 AM on September 30, 2008

I wonder when these differential equation / calculus dorks are ever going to realize that multi-agent modeling would make their lives much easier (though without the joy of having a QED).
posted by rbs at 9:15 AM on September 30, 2008

Interestingly prophetic paper. ...
posted by Salvor Hardin

My head asplode.
posted by ROU_Xenophobe at 9:30 AM on September 30, 2008

Isn't Hari Seldon supposed to show up in times like these?
posted by dhoe at 9:48 AM on September 30, 2008 [2 favorites has favorites]

Yes, Hari Seldon may send us a message, but we can't depend on him! We must act as if we know nothing of Seldon's psychohistory. Otherwise there may be a much longer delay before the rise of the second American Empire from the chaos of these times. Now excuse me while I organize the priests for my new religion of the holy science to secure our place in this troubled corner of the galaxy.

Ok, sorry for the threadjack. Back to real live economics.

ROU_Xenophobe: what, too meta for you?
posted by Salvor Hardin at 1:01 PM on September 30, 2008

What does this have to do with fish?
posted by TwelveTwo at 9:38 PM on September 30, 2008

Just forwarded the paper to a few. Thanks!
posted by ruelle at 12:48 PM on October 1, 2008