Lecture focuses on financial models behaving badly

12 July 2013

Mathematical models are useful in the world of finance but treating them like the laws of physics can be disastrous, according to financial expert and former physicist Prof. Emmanuel Derman.

Speaking to a lecture audience at the IOP’s centre in London, he said: “The solution to our financial crises will not lie in mathematics. Remember that at some point a model will break down.”

Prof. Derman started out as a theoretical physicist and later moved into finance, becoming a managing director at Goldman Sachs. He is now an academic at Columbia University and head of risk at Prima Capital Partners. Although he has developed financial models that have become industry standards, he cautioned against regarding such constructs as if they were of the same nature as Kepler’s laws of planetary motion or Maxwell’s equations. “The equations of physics and finance resemble each other from a syntatical point of view, but their semantics is very different,” he said. “They are always idealisations and they sweep the dirt under the rug.”

Drawing a distinction between theories and models, he referred to the biblical story of God saying to Moses in the desert “I am what I am”. Prof. Derman said: “In a sense what he’s saying is ‘you can’t compare me to anything else that you know about’. For me, that’s the quality of theories in that they are an absolute form of attempted knowledge, not of relative knowledge. Theories say ‘this is the way the world behaves’, or ‘this is the way I think the world behaves’, without referencing anything else.”

Models, however, worked like metaphors, such as comparing the nucleus to a liquid drop. “It’s useful and picturesque, but not true in the same sense as Newton’s laws or the Dirac equation,” he said. “The Black-Scholes Financial Option Model compares the uncertain movement of stock prices to the diffusion of smoke from a cigarette. It’s useful up to a point, but it’s not fact. Models are really images of reality but they are not reality itself. If you forget that, you’re becoming an idolator. A little hubris is a good thing but catastrophes strike when hubris evolves into idolatory.”

Physicists understood this, and while physics had theories and models, finance would never have anything but models, he said, and it was better to think of these models as thought experiments. Many people had blamed financial engineers for the recent crash, a little unfairly, he said, when other factors such as keeping interest rates low when there was a crisis or ceaselessly stimulating the market were implicated.

In a question and answer session, Prof. Derman agreed that there might be some merit in comparing the financial world with nonlinear systems, such as the climate, and said that some people were looking at models that incorporated phase transitions.

You can watch the lecture in full below.