Justin Fox asks, "Why didn't people in finance pay attention to Benoit Mandelbrot?" -- and it's a great question. His conclusion:
I think it’s mainly that he didn’t provide them a handy alternative to Black-Scholes. I can’t pretend to fully understand the practical implications of his fractal view of markets, but it does seem more useful as a critique than as a positive model of market behavior. You can’t haul in big consulting fees or create giant new securitization markets with a critique. So the natural tendency of both scholars and bankers has been to hold on for dear life to the Black-Scholes approach to modeling market risk.
I think, sadly, that this is largely correct. Mandelbrot was unable to provide a concise alternative formula for pricing and risk measurement -- that much should be obvious from his argument that models which make assumptions about the measurability (and predictability) of volatility are doomed.
But as easy as it is to follow that line of reasoning, just as it's easy to hate VaR and copula pricing once all the cool bloggers are doing it, we need to breath. The world isn't black and white, and neither are risk models. Black-Scholes may be an imperfect pricing model, but is it better than nothing? Absolutely. Same goes for VaR. As soon as we dismiss models like these for "failing to predict risk", we have already failed the test. These models aren't used -- in fact, can't be used -- to predict risk. Anyone with the patience to examine them can see that. I've written it countless times: models are just the tools. A given model can no more predict, much less avoid, a financial crisis than a hammer can build (or destroy) a house.
So Black-Scholes: bad for predicting risk? Maybe. Good for pricing options? Maybe. Better at pricing options than the alternative, which is guessing? You bet.
Var: bad for predicting risk? Maybe. Good for measuring risk? Maybe. Good for defining a key risk level for a given distribution? Yes (in fact, that's the only thing it's good for. It's actually the only thing it does!).
As much as I agree with Mandelbrot's every word on the topic of finance (and many of my beliefs spring directly from his well), I can not jump on the bandwagon of I-told-you-so-ers who would like us to believe that we are better off with no models than with imperfect ones. A lot more damage has been wrought by people foolish enough to think their models conveyed information which they actually didn't, than by any equation. You want to price an option with Black-Scholes? Go right ahead. Just keep your volatility forecasts to yourself.