One example is Protein Folding. The problem is hard for simple lattice models. Once the model gets more complicated (more complicated lattices, more degrees of freedom), the problem is not known to be NP-hard and becomes much easier to approximate.

Why shouldn’t it be the case that certain correlations between mortgage prices allow for better algorithms for detecting bad derivatices? Granted it may be the case that the industry does not use such algorithms, but I do not believe the current work rules out the possibility that in certain prevalent conditions, the problem can be solved.

The second issue is that they don’t address whether or not the solution can be approximated in polynomial time. Even if the buyer cannot establish the exact price within polynomial time, that does not imply that the buyer cannot approximate the price within polynomial time. It may be the case that the buyer can find a sufficiently good approximation of the solution to give sufficient information to make good enough purchasing decisions.

They should also consider addressing the question of whether or not the problem is in co-NP. If it is, then the seller could offer a short certificate which could be used to verify that they had not created a biased CDO. The validity of such a certificate could be verified in polynomial time. Mind you, I’m not saying that the problem is in co-NP, just that they should check whether or not it is.

Also, current rating algorithms at the ratings agencies use simple monte-carlo simulation. That definitely will not detect dense subgraphs. The commenter who thinks he can do any version of densest subgraph efficiently should definitely try to publish this algorithm because the experts would be very interested.

I also want to address the issue of simple model vs complicated model. As pointed out in the paper introduction, the simpler model with independent asset yields considered in the paper can be *embedded* (ie is a subcase of) inside more complicated models. That makes the result *stronger* not weaker. In general you want to prove negative results in as simple a model as possible, and a positive result (in this case, that would be a pricing algorithm) in as complicated model as possible.

The details about CDOs in the paper are correct. The commenter Kraut who thinks that issuer keeps the senior tranche is clearly mistaken, as anonymous has noted.

When real life and theory don’t agree, it’s time to refine the theory.

Long-term plan, mind you, since it’d take a good decade or so for the market to recover, but…you’d own the only good liferafts after the ship sank, right?

The other problem is that they are assuming in some way that it is only the seller or bundler who has access to the information. The buyer has access too.

It’s a typical problem with academics who stray outside their sphere of expertise and end up making assumptions that are wrong, and then coming to a conclusion that isn’t valid.

But fuck me, Goldmans and JPM are announcing humungo profits – and didn’t the former engineer the crisis?

The fix is in. The fix has been in since long before you or I were born.

“Trading in derivatives brought down Lehman Brothers” – err, no. What brought down Lehman’s (speaking as an ex-employee) was a) they weren’t GS, and the treasury was looking to prove their moral hazard theory, b) they were too leveraged, c) their funding was too short term. Most of the derivatives desks at Lehmans were very profitable.
Bear in mind that Lehman’s was largely a seller of CDOs, so the article doesn’t make sense.

Anyway, in a CDO the issuer usually keeps the senior or equity tranche, rather than selling it on. Which means that they eat the first X% of the losses that happen before they pass losses on to the next tranche. So the result, while I’m sure it’s theoretically valid (notwithstanding the other comments that the while P=NP issue only arises on large N etc…), it’s not actually relevant to the issue.

@technogeek: Err, no. Index funds are not derivatives, and derivatives are a great way of making money, or insuring yourself against losses. Of course your definition of $(Too Much Time) may differ from mine ;)

I wouldnt say they engineered the crisis, but they definatlty profited from irresponsibility and short term thinking. They are posting huge profits because the American tax payers were forced to bail them out with hundreds of billions of our tax money. Its hard not to make a profit if someone else covers you in the case of a loss.