Intractability of Financial Derivatives

This is interesting, but I'm struck by the sheer amount of serious analysis on this topic. It always struck me as very simple requiring no deep understanding.<p>There's an old saying on wall street, the harder it is to understand the deal the bigger the profit. The truth of this should be self evident. Add to that the fact that the people gambling weren't gambling with their own money. That way if they won then got big bonuses, and if they lost they simply didn't get bonuses. Clearly the only rational action in this situation is to go all in with other people's money.<p>Is it really that complicated? You wouldn't give your money to someone else and send them to Vegas, tell them to gamble if they win you split the profits, if they lose you lose your money.<p>You shouldn't invest in things you don't understand, and mind that old wall street saying.<p>But people do invest in things they don't understand, and pyramid schemes, and tulips, none of this is new. Sure some fancy math was involved this time, but that's only tangential.<p>I think everyone is concentrating on the fancy math because it's like magic, and then it's not their fault, it's not the same old story of everyone just being stupid again like in .COM 1.0, oh no - It's <i>magic</i>!

Economics as it is got going well before complexity theory was established.<p>There's an interesting difference between assuming perfect information and perfect rationality -- idealizations of existing scenarios -- and essentially assuming P=NP; the former makes the math easier at no real penalty (provided you remember not to confuse the map with the territory) but until P is proven to be equal to NP (which probably won't happen) the latter is more like sprinkling pixy dust to make it go.<p>The only school that really takes something like tractability seriously are the Austrians, but their math phobia leaves their approach unrigorous and not very useful outside of as an anti-central-planning argument.<p>The claim that a market will converge on an accurate price (!) for an "intractable" financial asset is pretty dubious; the price-discovery process is supposed to depend on lots of agents running their #s and taking positions depending on if they think current price is different than it ought to be...over time this process will push the market price toward an accurate price.<p>In the case of an intractable asset there'd be no reason to believe that any outside agents crunched accurate #s, which means that even if the price converged there'd be no reason to believe that the converged-to price had any accuracy, which isn't usually the case in most other classes of financial assets.<p>As noted towards the end they need to do some work about estimating "lemon cost" and otherwise establishing how close you can estimate with approximate methods.<p>(!) In general there's not much sense in talking about true or accurate prices for some good; price is what it gets, full stop.<p>In the case of most financial products the notion of accurate price is more justified: a product entitles the owner to some sequence of future cash flows, which can be assigned a value in some straightforward manner. When a financial asset's current price deviates from the value of the underlying sequence of payments in some substantial way it's usually due to some easily-understood dynamic (eg: inflation expectations, doubts about some of the payments coming through) which makes a minor correction to the price it fetches.<p>An "inaccurate price" would be one with no apparent relation to the underlying cash flows.

I know that prof. Appel is a really smart guy from reading his books on optimizing compilers - so I'm going to risk looking like an idiot here, especially because I don't have time to carefully read the paper.. but maybe someone can help me out here.<p>so he says that a buyer cannot determine that a CDO has been maliciously packed with bad assets because this is equivalent to finding the densest subgraph. Is there a reason why an <i>approximate</i> solution to the dense subgraph problem could not allow one to conclude that a CDO was more likely to have been stuffed with garbage?<p>clearly if the problem is truly like encryption as Appel says then an approximate solution is worthless (an approximate encryption key would still give you garbage)

&#62;a CDO (collateralized debt obligation) is a security formed by packaging together hundreds of home mortgages<p>there's actually another layer of abstraction involved. a mortgage backed security, or collateralized mortgage obligation (CMO), is formed by packaging together a large group of home mortgages. a CDO is made by packaging together hundreds of MBS obligations or CMOs.

Even if we had unlimited computation, there are human factors that are tough to determine beforehand.<p>For example, some originators encouraged their borrowers to lie more, and now post-meltdown some servicers are less willing to agree to loan modifications / short-sales.<p>At first traders didn't place much emphasis on the originator, servicer, or bank, because they focused on the loan stats (FICO score, loan type, interest rate, etc).<p>Post-meltdown, the smart players see obvious systematic patterns between originators and servicers, even given the same paper stats. But again, to see it before it happened, it's less a computer problem and more an unscalable human due diligence problem.

The link to the paper seems to be down. A clone can be found at <a href="http://www.princeton.edu/bcf/newsevents/seminar/SanjeevArorapaper.pdf" rel="nofollow">http://www.princeton.edu/bcf/newsevents/seminar/SanjeevArora...</a>