Stewarts’ Banks crash

Ian Stewart The mathematical equation that caused the banks to crash The Observer 12 Feb 2012

The Black-Scholes equation was the mathematical justification for the trading that plunged the world’s banks into catastrophe

…companies hired mathematically talented analysts [as distinct from ‘proper mathematicians, but] forgot (sic) to ask how reliable the answers would be if market conditions changed.

The idea behind many financial models goes back to Louis Bachelier in 1900, who suggested that fluctuations of the stock market can be modelled by a random process known as Brownian motion.

… on 19 October 1987, Black Monday, the world’s stock markets lost more than 20% of their value within a few hours. An event this extreme is virtually impossible under the model’s assumptions. In his bestseller The Black Swan, Nassim Nicholas Taleb, an expert in mathematical finance, calls extreme events of this kind black swans. … the phrase now refers to an assumption that appears to be grounded in fact, but might at any moment turn out to be wildly mistaken.

… usually the model performed very well, so as time passed and confidence grew, many bankers and traders forgot the model had limitations. They used the equation as a kind of talisman, a bit of mathematical magic to protect them against criticism if anything went wrong.

Virtually every financial crisis in the last century has been pushed over the edge by the herd instinct.

The world economy desperately needs a radical overhaul and that requires more mathematics, not less. It may be rocket science, but magic it’s not.

My comments

From a narrowly mathematical perspective, this is a good rejoinder to those who blame mathematicians for the crash. But in terms of presentation I have some remarks:

  1. My reading of Taleb is that black swans are ‘low probability’ events. Ian’s characterisation seems very much more insightful.
  2. Before the crash, Ian had published a highly relevant manifesto (as below) but this seemed to fall short, both in scope and depth.
  3. Surely a key point is that the assumption that data series such as those for stock markets are stochastic in the sense that Bachelier thought is unjustifiable and almost certainly wrong for anything influenced by ‘life’.

My own view is that statistical analysis of the kind that Stewart critiques is useful, just so long as one understands that any conclusions beyond that properly justified by the underlying mathematics are not valid. What seems needed is surely something like the ‘modern Bayesian’ approach of Keynes, Turing and Good, uncorrupted by metaphysical error.

See Also

Ian Stewarts’ maths manifesto.

Dave Marsay.

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