Pricing a CDO – Not only Bad Math, Bad Computation too
from: The Economic Populist, by Robert Oak, Sat, 12/26/2009
A working paper, Computational complexity and informational asymmetry in financial products, Sanjeev Arora, Boaz Barak, Markus Brunnermeier, Rong Ge. sheds some light on the complex mathematical models upon which credit default obligations and other derivatives are based.
What Arora et al. prove is not only are many derivative mathematical models impossible to compute, never mind in real time, because they require more computing power than the world possesses, the missing information to run a mathematical model is a very good place to cheat with.
To understand what CDOs, derivatives are, see this post, complete with video tutorials. For some background on the mathematics behind derivatives, read We Want the Formula and this one on some of the probability functions.
Onto the paper. Firstly this quote:
One of our main results suggests that it may be computationally intractable to price derivatives even when buyers know almost all of the relevant information, and furthermore this is true even in very simple models of asset yields.
They ain’t talking about your new PC cranking through these calculations, they are referring to massive supercomputers.
This result immediately posts a red flag about asymmetric information, since it implies that derivative contracts could contain information that is in plain view yet cannot be understood with any foreseeable amount of computational effort.
So, individual investors or even online brokerage firms can kiss it goodbye in verifying these values easily due to computational complexity of the algorithms themselves.
The practical downside of using derivatives is that they are complex assets that are difficult to price. Since their values depend on complex interaction of numerous attributes, the issuer can easily tamper derivatives without anybody being able to detect it within a reasonable amount of time.
read at: http://www.economicpopulist.org/content/pricing-cdo-not-only-bad-math-bad-computation-too
Is anyone surprised at such shenanigans that appear to be contrived to deliberately deceive? Is it enough to say that the buyers were professionals or “it’s just trading” as Felix Salmon at Reuters points out? Or … The real lesson here isn’t that Goldman did anything scandalous. It’s just that if you’re making a bet and Goldman is your bookmaker, don’t be surprised if you end up losing.
Yves Smith’s comment: ..this is a very important finding, and this take is from an engineer who knows more than a bit about computer science.
Any Computer Science SNSers care to comment?