As Andrew Appel explores in his post Intractability of Financial Derivatives, the computer science world’s Intractability Theory may better explain the derivative world than other theories. (the theory is used for DRM, cryptography, and more). The paper is Computational Complexity and Information Asymmetry in Financial Products (pdf) by Sanjeev Arora, Boaz Barak, Markus Brunnermeier, and Rong Ge.

For those who are interested in the topic and/or understand the math and theory behind the risk shifting involved in this area, check out Andrew’s post. He does a great job explaining how the paper applies to a CDO (collateralized debt obligation). If you need a little more to understand why this paper and its ideas are important, consider Andrew’s take away

In principle, an alert buyer can detect tampering even if he doesn’t know which asset classes are the lemons: he simply examines all 1000 CDOs and looks for a suspicious overrepresentation of some of the asset classes in some of the CDOs. What Arora et al. show is that is an NP-complete problem (“densest subgraph”). This problem is believed to be computationally intractable; thus, even the most alert buyer can’t have enough computational power to do the analysis.

Arora et al. show it’s even worse than that: even after the buyer has lost a lot of money (because enough mortgages defaulted to devalue his “senior tranche”), he can’t prove that that tampering occurred: he can’t prove that the distribution of lemons wasn’t random. This makes it hard to get recourse in court; it also makes it hard to regulate CDOs.

UPDATE: It appears from the comments to Andrew’s post that CDO and derivatives are not precisely the same thing. In addition, the comments explore the limits of the study. It is a good discussion.

ALSO check out the FAQ for the paper. It addresses many issues that the initiated may want to probe.