Tuesday, November 25, 2008

Crashing the credit network

It appears that those coping with the credit crisis aren't sufficiently ramped up on network theory. This paper by Zhao et al, titled "Tolerance of scale-free networks against attack-induced cascades", has a paragraph which captures the current situation.

... the presence of such a small set of important nodes means that the network can be fragile because attack on one or a few nodes in this group can have a devastating effect. In particular, considering that those nodes typically handle a substantial fraction of loads necessary for the normal operation of the network, an attack to disable one or few of these nodes means that their loads will be redistributed to other nodes. Because the amount of the redistributed loads can typically be large, this can cause other nodes in the network to fail, if their loads exceed their capacities, which in turn causes more loads to be redistributed, and so on. This cascading process can continue until the network becomes disintegrated. Indeed, simulations show, for instance, that for a realistic power-grid network, attack on a single node can disable more than half of the nodes, essentially shutting down the network...

Lehman Brothers was a well-connected, load-bearing node in a complex network of credit. Its sudden disappearance crashed the credit network. In a disintegrated credit network, no one will lend out money; that condition describes the credit crunch we're experiencing now, where governments and central banks are having to step in as lenders of last resort. Under normal functioning conditions, the loss of a random node won't crash the network. We're not in normal conditions. Calls to "amputate" or otherwise permit major credit nodes to fail apparently reflect a failure to recognize the failure modes that networks can exhibit.

Cascading failure is evident in the commentary on the collapse on a Krugman's blog entry.

What the article really adds, though, is the details of the chain reaction that did the damage... Lehman’s fall led to (1) a run on money market funds, causing commercial paper rates to soar (2) soaring rates on credit default swaps, driving AIG over the edge and sending LIBOR sky-high.