Intractability of Financial Derivatives

http://www.freedom-to-tinker.com/blog/appel/intractability-financial-derivatives

by oscarwao • 17 years ago

59 27 17 years ago

jwb119• 17 years ago

>a CDO (collateralized debt obligation) is a security formed by packaging together hundreds of home mortgages

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.

yangyang• 17 years ago

CDOs are not necessarily just composed of mortgage derivatives. They can be put together from bonds, CDSs (synthetic CDOs), syndicated loans (CLOs), other CDOs (CDOs squared), a mixture of these and other debt instruments.

therealazeem• 17 years ago

Yep. And you can count the leverage at every single level

biohacker42• 17 years ago

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.

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.

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.

You shouldn't invest in things you don't understand, and mind that old wall street saying.

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.

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 magic!

kurtosis5• 17 years ago

Yeah I think you're totally right on here. I would go even further and suggest that these pseudo-scientific valuation models were cynically exploited to make it sound like the risks were calculable.

I think an analogy to medicine is appropriate - for many years the desperation and naivete of the sick was exploited by frauds selling patent medicines. Many makers of these bogus cures undoubtedly sincerely believed in their efficacy. Watching this history would make you suspicious of anyone who claimed that they could cure your illness with a drug. Despite this sordid reputation, there really are wonder drugs. If medicine can be made scientific so can finance.

joe_the_user3• 17 years ago

If medicine can be made scientific so can finance.

Uh, one thing to be careful with in such a statement is reasoning by analogy.

Consider if someone says:

"If physics can be made scientific, so can pertual-motion-machine-construction"

"If chemistry can be made scientific, so can alchemy!"

"If astronomy can be made scientific, so can astrology!"

The problem is clearer. Not every "field" is subject to valid innovation since some fields are inherently bogus. It is a hard problem determining which fields can "scientifized" so you might not be wrong. But I personally think that the real scientific economists are those that have argued that you're not ever going to find a "financial innovation" which adds value to the economy as a whole.

bmalicoat2• 17 years ago

I agree with you entirely. But from the person looking for (or getting) a mortgage, they likely didn't know the lender was going to chop up their mortgage and mix it with bits of hundreds or thousands of others' and sell it to another party. It's obvious, like you say, that the system wasn't incentive compatible and that the people writing and selling the mortgages had no reason to ensure the borrowers paid.

Sadly there are still no regulations preventing this from happening again.

dantheman4• 17 years ago

What issue does the person getting the mortgage with how it's financed? You seem to try and remove the responsibility from the borrower, which is where it should be. This is most likely the biggest financial decision they will ever make and they should understand it.

joe_the_user3• 17 years ago

There's a quandary here. If someone is, say, a medical equipment VC, they have to invest in technologies they can understand only in outline, since no one is going understand everything about them.

But finance is different in the sense that any investor has to understand things down to where the money is coming from. You correctly reason that "innovation" in finance is simply a system for gambling with other people's. That's indeed more or less fraud by your reasoning.

But the tricky part is that an investor in technology has to know where the substantial engineering technology ends and the insubstantial "financial technology" begins. It's OK not to understand the first but deadly, over time, not to understand the second. So the problem can get tricky despite the underlying situation being simple.

frig• 17 years ago

Economics as it is got going well before complexity theory was established.

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.

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.

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.

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.

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.

(!) In general there's not much sense in talking about true or accurate prices for some good; price is what it gets, full stop.

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.

An "inaccurate price" would be one with no apparent relation to the underlying cash flows.

joe_the_user3• 17 years ago

In general there's not much sense in talking about true or accurate prices for some good; price is what it gets, full stop.

Well, if the price is not above the costs of production, you're going to have a hard finding the product in stores for very long. Oppositely, the price and availability of food, say, isn't at a certain level, the whole society may cease to function.

While arguments about intractability, chaos and uncertainty are great and interesting, it's worth considering that if an economy doesn't have a number of important, predictable elements, things stop working.

kurtosis5• 17 years ago

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.

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 approximate solution to the dense subgraph problem could not allow one to conclude that a CDO was more likely to have been stuffed with garbage?

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)

rguzman• 17 years ago

I also don't know anything about this, but ...

I'd guess that even if you can't solve the problem exactly you could find a tractable probabilistic solution that works x% of the time and traders spend their time finding such solutions. The real problem is that for the (1-x)% of the time when it doesn't work it wrecks major havoc.

coliveira• 17 years ago

Like all theorems in complexity, this one is saying something that is true only for the most general problems. Reality is, most problems found in the real world are just special cases of the truly generic NP-hard problems. That is why we can find algorithms for many of them (deterministic or stochastic). So, basically the theorem doesn't really say much about the financial problem, unless you believe that the modeling here is 100% correct - which, considering any non-trivial financial scenario, is not.

slackenerny• 17 years ago

Is there a reason why an approximate solution to the dense subgraph problem could not allow

I haven't read the paper either ;] (just skimmed bibliography to get a sense, as I usually do first) but Arora (one of the authors) is an expert on probabilistic approximations, and they do cite 2001 paper by Feige which is standard ref. on approximations to dense subgraph. Also, what they reduce their model to is a "planted" hidden clique variant of dense subgraph, a problem which is hard "on average" and not only in worst case (propety used in crypto protocols also).

kurtosis5• 17 years ago

I see - thanks for the info. I didn't know the background of the author or recognize the reference. I'm going to read this one over much more carefully.

roundsquare2• 17 years ago

One issue is the vocabulary of the word equivilent.

With poloynomial time problem reductions (which is what is usually used with showig a problem is NP complete, though I too haven't read the paper) equivilent just means something like "an exact solution in A translates to an exact solution in B." Unfortunatly, in general, an approxmimate solution to A doens't translate to an approxmiate solution to B.

Note: This part is me really guessing so please don't take it at face falue.

If I had to guess, I'd say that this is like densest subgraph in the sense that:

The mortgages are the nodes.

High correlation --> Edge connections.

So there might be a straightforward translation of approxmiate solutions. Like I said, just a guess.

leelin• 17 years ago

Even if we had unlimited computation, there are human factors that are tough to determine beforehand.

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.

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).

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.

chasingsparks• 17 years ago

The link to the paper seems to be down. A clone can be found at http://www.princeton.edu/bcf/newsevents/seminar/SanjeevArora...

Intractability of Financial Derivatives

Related Stories