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The uses and abuses of mathematical models

I will remember that I didn’t make the world, and it doesn’t satisfy my equations

According to this economist article companies are now looking at how their models were wrong and what to do. Society’s desire to model the future is not going away. As these models are updated and stress-tested companies will once again come to rely on them – that is until they break again. This is worth reading for anyone interested in models, feedback loops, or investing.

Moreover, heavy use of models may have changed the markets they were supposed to map, thus undermining the validity of their own predictions, says Donald MacKenzie, an economic sociologist at the University of Edinburgh. This feedback process is known as counter-performativity and had been noted before, for instance with Black-Scholes. With CDOs the models’ popularity boosted demand, which lowered the quality of the asset-backed securities that formed the pools’ raw material and widened the gap between expected and actual defaults.

A related problem was the similarity of risk models. Banks thought they were diversified, only to find that many others held comparable positions, based on similar models that had been built to comply with the Basel 2 standards, and everyone was trying to unwind the same positions at the same time. The breakdown of the models, which had been the only basis for pricing the more exotic types of security, turned risk into full-blown uncertainty (and thus extreme volatility).

The way forward is not to reject high-tech finance but to be honest about its limitations, says Emanuel Derman, a professor at New York’s Columbia University and a former quant at Goldman Sachs. Models should be seen as metaphors that can enlighten but do not describe the world perfectly. Messrs Derman and Wilmott have drawn up a modeller’s Hippocratic oath which pledges, among other things: “I will remember that I didn’t make the world, and it doesn’t satisfy my equations,” and “I will never sacrifice reality for elegance without explaining why I have done so.” Often the problem is not complex finance but the people who practise it, says Mr Wilmott. Because of their love of puzzles, quants lean towards technically brilliant rather than sensible solutions and tend to over-engineer: “You may need a plumber but you get a professor of fluid dynamics.”

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