Stochastic cascades, credit contagion, and large portfolio losses
September 30, 2008 8:14 AM Subscribe
"In the limit of an infinite economy, the number of initial downgrades is Poisson distributed.
posted by geoff. (8 comments total)
3 users marked this as a favorite
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!