Unreasonable Effectiveness of Mathematics
September 23rd, 2008 by WaltPeter Woit observes that mathematicians and physicists had a prominent role to play in the current financial crises that threaten to take down the world’s banks. Stochastic calculus has become the main tool of evaluating financial derivatives, which are financial instruments whose payoffs are (usually nonlinear) functions of underlying assets. Overly-optimistic assumptions in pricing derivatives have led to large losses throughout the financial sector. The worst case scenario is the kind of widespread economic dislocation not seen since the Great Depression.
Hey, at least it means we have something to be more embarrassed about than Theodore Kaczynski.
September 24th, 2008 at 7:50 am
I’m not sure that the current crisis can be blamed
squarely on Mathematicians/physicists as conveniently
as Peter Woit seems to suggest.
One could argue that the crisis directly originated in the Fed’s low
interest rates, championed by an economist. Which in turn
made loans cheap, which people got easily thanks to the transference
of risk (securitisation). The first CDO was issued by a company
founded by a Wharton graduate, so that should be blamed on business
graduates. In any case, securitisation is an idea as old as markets,
all that the quants have done is to provide pricing models. Which were
certainly wrong.
On the other hand, quants have done much to improve the estimation
of risk in the business. Quantitative methods provide the fundamental
means of spreading risk around. That’s what makes economies efficient.
Also, not clear why Mathematicians should be immune from the sort of
greed that afflicts everybody else.
So what about poor models? Time for some Mathematician to come up
with a _reasonable_ way of modelling fat tailed processes.
Can’t see economists doing this with any success. Any takers?
[I'd also like to remind people of Jim Simons: his Renaissance Technologies
has delivered a whopping 35%+ annualised since inception on their flagship
fund.]
–Sanatan
September 25th, 2008 at 1:57 pm
We already had string theory to be embarrassed about.
September 25th, 2008 at 7:55 pm
We’re stuck with Kaczynski. By and large the models in question are not the stochastic calculus ones. It’s the mortgage prepayment models. These are jazzed up to sound like statistical estimations, but in fact are parametric and constrained to fit what the traders think the factors are. And no one worth their salt really believed one-parameter Gaussian copula models for the correlation in a pool of securities.
This is much more an issue of mathematics, and technical language in general, being used and subverted for greed. I’m a math PhD, been on Wall Street for 12 years, and the only mathematicians anywhere close to power were pointing out all the faults of the models or actually saying that they’re not even models at all. Most quants are well aware of the assumptions that go into their models and therefore where they are wrong. Unfortunately they’re not the ones who apply the models.
Even if a management committee type was half-convinced, they’d be hard-pressed to forgo the returns our competitors seemed to be getting, for what seemed to them like theoretical issues.
These are issues of power and human nature, not a failure of mathematics. And it may take a generation or two, but there will be another.
September 25th, 2008 at 9:39 pm
I’m a math PhD, been on Wall Street for 12 years
In the wake of this fallout, is anyone still hiring? ‘Cause the academy’s not working great these days. How does a non-financial, non-analyst, non-statistician get hooked up with one of those gigs?
September 26th, 2008 at 2:12 am
By sending in one’s resume to prospective employers:
hedge funds, investment banks, insurence companies.
The smart employers only care about one’s abilities
and that one should know one’s Math, if one claims to.
–Sanatan
September 26th, 2008 at 3:09 pm
We should look at this as an argument to subsidize pure math research. “Look what happens when there are mathematicians who have to take private sector employment ” we should say.
September 26th, 2008 at 5:37 pm
- Yes firms are hiring. They are ‘upgrading’ shall we say, and some are even growing.
- One can get hired as Sanatan says. One also has to be able (and want) to program.
- Actually if the federal government ends up owning pools of debt, it wouldn’t be a bad idea to turn at least part of a national lab over to computable models of correlation with a reasonable number of parameters. Even if it doesn’t make sense to estimate the parameters after such a regime-change in the historical data. Scenario analysis is still useful. In fact, even if the government doesn’t own the ‘bad assets’ it’s probably still in our national interest to do such research.
September 28th, 2008 at 9:16 am
John, I’m guessing the repo man business will be picking up. The life of a repo man is always exciting.
September 28th, 2008 at 9:18 pm
For whatever reason, Peter Woit modded out this submission of mine, which is still on-topic here.
# Jonathan Vos Post Says: Your comment is awaiting moderation.
September 21st, 2008 at 11:33 am
With all due respect to Physicists who migrated to finance “rocket
science” — their models had too many false assumptions. In particular,
the Black-Scholes equation, in all the textbooks, key to a Nobel prize
in Economics, blithely assuming Gaussian distributions.
This led to Long-Term Capital Management (LTCM), the U.S. hedge fund
which failed spectacularly in the late 1990s, leading to a massive
bailout by other major banks. Now that looks like a beta test of the
current $7×10^11 bailout proposal.
What the physicist-quants did not address was the origin of clustered
volatility in real markets. There are some
physicists-turned-complexity theorists at the Santa Fe Institute who
have a good agent-based model.
Keywords: Heteroskedacity and heteroskedasticity.
September 29th, 2008 at 6:14 pm
Do they hire mathematicians as repo men?
September 29th, 2008 at 6:25 pm
In “Repo Man” (the 1984 film written by Alex Cox, directed by Alex Cox,
produced by Peter McCarthy and Jonathan Wacks, starring Emilio Estevez
and Harry Dean Stanton, music by The Plugz) the infamous car (carrying the alien payload in its trunk) has New Mexico license plates labelled with “127-GBH” and “Land Of Enchantment”:
* “Charged GBH” are a UK hardcore punk rock band. GBH also stands for the British legal phrase, grievous bodily harm.
* 127 is a Mersenne prime (2^7 - 1) and as such it is the largest integer that can be represented by a signed byte. Additionally, 127 is related to the perfect number 8,128 (Pythagoras studied perfect numbers for their mystical properties). In 1876, 127 was discovered as a double Mersenne number (2^127 - 1) which was and still is the largest prime ever discovered (by hand calculations).
* At the end of the movie when the entire car is glowing, the car’s license plate appears to be mirrored backwards. This mirroring shows that the strange “glowing effect” of the car was partly created using a photographic negative.
[thanks to Wikipedia for filling in some blanks of what I knew had to be my comment to John Baez]
September 29th, 2008 at 7:52 pm
Do they hire mathematicians as repo men?
I’m beginning to hope so.