# Unwinding CDS’s

As pointed out several times by Steve Hsu recently, a major instigator of our current financial crisis is the Credit Default Swap (CDS). As far as financial instruments go, this one is almost understandable. Basically, it is an insurance policy that is exchanged between two firms. So, say you just loaned a bunch of money and you want to insure it. Well, you can buy a CDS for some fee from someone who will pay you some agreed upon amount if the loan goes bad. It is a zero sum game, which is why the amounts insured (notional amount) can be larger than the GDP of the entire world. Although the notional amounts of these CDS’s could be large, the big banks and hedge funds that traded them are often hedged so that the net gain or loss are manageable. The problem was that when Lehman Brothers went down, the whole network became unbalanced and some parties were exposed to huge losses. However, given that there is no market for these things, no one knows who is holding what. Steve drew a complex graph and an example to demonstrate how difficult it would be to unwind everything.

I like to visualize this as a problem of flux balance. For example, let $C_{ij}$ be a CDS payout from party j to i. Then the total net gain or loss (i.e. flux) for party i is given by

$F_i=\sum_j C_{ij} - \sum_j C_{ji}$

We see that the sum over $F_i$ is zero verifying that it is a zero sum game. It actually would be a simple matter to unwind all the obligations if everyone agreed to do it all at once. This could even be done without anyone disclosing any of their trades. People may want to do this so others wouldn’t know how weak they were. The way you would do it is for everyone to compute their net flux $F_i$ and disclose this amount to a central clearinghouse. The clearing house then checks to see if the sum of all the fluxes is zero. If the sum is not zero then either someone made a mistake or tried to cheat. If it sums to zero then those with a negative flux would deposit that amount to the clearinghouse and those with a positive flux could then withdraw from it. It is possible to cheat if you collude with someone else so that the net change to the sum of your two fluxes is zero. However, that would not affect anyone else so it would be like a private deal between two parties.