A critique of The Black Swan
stat.berkeley.edu
stat.berkeley.edu
My problem with Taleb and all the attention he's been getting lately because of the financial crisis is that I think it's a logical jump to go from those criticisms to "these models are bad, because of black swans". Black swans are defined as unpredictable random events with large impact. 9/11 was a black swan, but I don't think that the financial crisis we're seeing today is a result of a black swan. Insurers ignored systemic risk and over leveraged based on bad asset pricing, but were those assets priced poorly because of black swans? I think that's a tough argument to make, because mortgage foreclosures don't seem nearly as unpredictable as say, terrorists flying airplanes into buildings.
There also seems to be a bit of observation bias in concluding that events are black swans. Prediction markets can't be right 100% of the time. To quote the article: "What does it mean to say such a prediction is right or wrong? In 2008, the day before John McCain was scheduled to announce his VP choice, the Intrade prediction market gave Sarah Palin a 4% chance. Was this right or wrong? Unlikely events will sometimes happen just by chance."
Anyways, do you know if anyone is trying to come up with something better?
Here is a nice paper on risk measures, and points out some of the problems with VaR: http://tinyurl.com/ar3336
My apologies if you're unable to grok the contents of these papers...they're both a little technical but I can't think of anything off the top of my head that's more accessible.
These models are bad because the companies that have been bet on their accuracy go bust.
They go bust because they assume that the probability of "black swans" such as housing prices throughout the country all going down at the same time is vanishingly small when it isn't.
Hi, options guy here. I don't think that model has been used for predicting in a long time. It's now used for pricing. Back in the day before computers couldn't run calculations, market makers could arb using these models, but due to the liquidity of the market it's much harder to now.
Also, BS assumes european-style options, which is not the case on nearly all options trading. I personally use bjerksund stensland as a model, but just for pricing.
If you take any large corpus of text and start counting the frequencies that different words occur you will rapidly notice that a huge fraction of the words have never been seen before or occur only once. Biblical scholars called these words hapax legomena instead of black swans. Methods for estimating the probabilities of these events go back to Alan Turning and his codebreaking work at Blechley Park. One need not assign zero probability to unseen events a la maximum likelihood.
Taleb's rants against VAR and mediocristan have always seemed like borderline straw man bashing to me. Sure there are many fools who believe in the gaussian or lognormal returns model, but the best knowledge in the field doesn't make these assumptions. Why doesn't he give authors like bouchard and potters who have built on mandelbrot's work their due? or does he?
Taleb does give credit to them in terms of them understanding the presence of fat tails and focussing on the failure of the gaussian. However, both Bouchaud and Potters, coming from physics backgrounds, believe that the tail-exponent can be calibrated accurately from a finite sample-set. When in fact estimating the tail-exponent (the 'alpha' of a power law process) is fraught with small-sample effects and one cannot reliably make decisions even when you do come up with an estimate of the tail-exponent. This is Taleb's main beef with the breed of physicists with power-law models.
The best paper to understand this is: Weron 2001: "Levy-stable distributions revisited: Tail index > 2 does not exclude the levy-stable regime" http://citeseer.ist.psu.edu/448515.html
More on my website if you're interested: navanitarakeri.com
A Black Swan is not just a rare event - it is defined as a rare event with _high impact_.
Statistical NLP may handle rare occurrences well (are you talking about smoothing?), but, by it's very nature, a rare event in a block of text is not going to wipe out a library now, is it? So the appearance of a rare word in a block of text is hardly in the same class of problems as epidemics, wars, market crashes etc.
I'll think a more critically the next time I see a straight line drawn on a log-log plot. I remember reading a sermon by cosma shalizi chastising physicists for making basic errors when estimating the exponent of power laws. I'm sure there's a lot of suspect results in the literature due to the error that you described :) maybe even a few bank failures.
Regarding the impact of rare words: misinterpreting certain rare words like "teratogenic" or "mesothelioma" could conceivably have a pretty high impact!
In fact, it may have already been on HN, that's probably where I first read it and have been trying to find it again, ever since.
Taleb is now turning up almost everywhere, so I thought people might find this interesting.
Perhaps it would be an interesting and profitable exercise to look for and measure causes of Black Swan events.