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Comment by paulpauper | Hacker News Reader

Sightly off-topic, but IMHO the theory of random walks, risk neutral pricing, and the black scholes option pricing formula to be the most significant findings of the past 100 years in the field of economics, in term of: practical applications (the option and futures market is huge, and they all involve these formulas), spawning research (if you go on arXiv, the original work done in the late 60's and 70's is still spawning tons of research to this day on asset pricing and asset price dynamics, whereas other economic fields seem to have stagnated), and being mathematically empirically sound (meaning it's a complete theory that does an adequate job describing reality), and is was groundbreaking in that the result was unexpected and answered a nagging question about how to price contracts without having to define a drift variable.

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"black scholes option pricing formula"

There are some issues with it, though. It uses volatility as a proxy for risk---fortunately, past performance is a perfect predictor of future performance and future events can be predicted at least to the extent of normally distributed errors---and assumes a standard normal distribution---the fact that the actual distribution had a much heavier tail[1] can have no material effect, right?

[1] https://seekingalpha.com/amp/article/2291545-a-statistical-a...

> theory of random walks, risk neutral pricing, and the black scholes option pricing formula to be the most significant findings

Random walks, heck yes! Black Scholes not so much. Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously. There's way too much fluctuation in practice than a Gaussian process would fit/predict.

So I would put it as: mathematically sound enough, empirically not quite so.

> Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously.

Options theory is popularly misunderstood. Makes being a former options trader fun and annoying.

First, the impact. You can model almost anything as an option. Equity? Call option on a firm's assets struck at the liabilities. (Literally anything else? A portfolio of Arrow–Debreu options [0].) Modern risk models, and these include some very successful ones, would not work without Black Scholes.

Second, no professional uses a Gaussian assumption without knowing what they're doing. (In any case, people started re-writing Black Scholes for other curves since at least the 1990s.) No model can economically ascertain every possible risk. One must always choose risks one considers negligible. This is true in finance as in life. Sometimes we choose to ignore the wrong risks. When that happens, it's easier to blame highfalutin math than admit "I didn't think about that".

No amount of "fat tailing" will substitute rigorous risk management. Case in point: the multitude of funds launched after 2008 focussing on "black swans" and "fat tails". Pretty much all of them lost money [3]. They missed--with everyone else--Dubai's near default, Greece's actual default, the 2010 Flash Crash, 2011's summer volatility, China's 2015 crash, the following August's international crash, Brexit or practically anything else that one might consider both significant and unexpected. (No shit.)

The real "magic" in Black Scholes? It's not the distribution. It's volatility. Modern models expand this once single term into a multidimensional beast [4]. This is the other reason for the prevalence of Gaussian assumptions. Traders trade computation of the distribution for computation of the volatility surface. The latter (tau) almost always dominates the former (delta) in terms of what's being mispriced.

[0] https://en.wikipedia.org/wiki/Arrow–Debreu_model

[1] https://en.wikipedia.org/wiki/Portfolio_insurance

[2] https://en.wikipedia.org/wiki/Tulip_mania

[3] http://www.businessinsider.com/watch-out-investors-the-black...

[4] http://edoc.hu-berlin.de/series/sfb-649-papers/2005-20/PDF/2...

Vehemently agree, in particular this

> no professional uses a Gaussian assumption without knowing what they're doing

I would say Black Scholes set the theme, but the details had to be modified quite a bit. Unmodified BS is BS.

'Fat tailing' would be very unlikely to give one a better prediction accuracy. It can, however, give one a better appreciation of the risk.

> Unmodified [Black Scholes] is BS

Black-Scholes-Merton is a theory. Analogous to Newtonian mechanics or textbook thermodynamics. They all need modification to work in the real world. That doesn't make them BS.

> [Using a fat-tailed distribution] can, however, give one a better appreciation of the risk

How does one choose a model and parameters for events which are, by definition, hard to predict? Keep in mind that most "black swans" arise from unforeseen dimensions of risk. There's the "my stock lost 90% of its value" fat tail versus "the damn exchange went bust". There's "my clearing bank is broke" and "the Russians invaded my country".

I agree that random walks are the most sensible way to model the financial markets, IMO. Anyone telling you otherwise you should be suspicious of (are they can beat the market?) Especially now with the mountain of evidence that pretty much no one can consistently beat a good market index.

The only issue with that is there are a few groups that have consistently beat the market over time, so perhaps its more pseudorandom than we think. One example might be the Renaissance Medallion Fund.

Right, and I generally respect Renaissance.

I think people who actually can beat the market fall into the general category of "knows something others don't". Renaissance probably is one of the very few firms that could qualify as that on purely technocratic means (instead of the usual, which is shades of grey in what's really insider trading). The other category would be simply HFT, but I'm not sure how profitable that is at this point, though.

Most of the people who seem to beat the market, though, are generally just happy benefactors of survival bias (eg. the 10000 monkeys on typewrites effect)

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