“a flaw in the model that I perceived as the critical functioning structure that defines how the world works.” It’s worth dwelling on that phrase: “the critical functioning structure that defines how the world works.” That’s a hell of a big thing to find a flaw in.Anyway, I'll probably quote a lot of Lanchester in the coming period, maybe automatically since I will be at a bankers' convention in Mallorca. To start off with, something on the way models supposed to model risk only work in unrisky situations. The Black Monday crash of 1987 was a ten-sigma event, meaning it is ten standard deviations from the modelled norm. This means, as Roger Lowenstein wrote, that
on the basis of the market's historical volatility, had the markets been open every day since the creation of the universe, the odds we still have been against its falling that much in a single day. In fact, had the lift of the Universe been repeated one billion times, such a crash would still have been theoretically 'unlikely'.The 1998 Russian bond default (I don't remember it either) was a seven-sigma event. As Lanchester writes:
it wasn't the only one. The last decades have seen numerous five-, six- and seven-sigma events. Those are supposed to happy, respectively, one day in every 13,932 years, one day in every 4,039,906 years, and one day in every 3,105,395,906 years. And yet no one concluded from this that the statistical models in use were wrong.