DerivaQuote: Science, Mathematics, Finance and its People

Science and mathematics are playing an increasing role in understanding derivatives. Specialists need to understand how scientists think.

Mathematics is being applied to finance because the big money is no longer using computers as fast calculators, but as machines to create new trading opportunities.

The intellect has little to do on the road to discovery. There comes a leap in consciousness, call it intuition or what you will, and the solution comes to you and you don't know how or why.

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

The early inventors of the first derivatives, working late at night next to those particle-physics laboratories, apparently had few friends when they went to cocktail parties.

If you can call a currency swing five seconds earlier than someone else, that's an advantage. There's so much money at stake and so little margin spread between profit and no profit. that's why we have all these Russian mathematicians sitting around in the corners of major London and New York brokers.

From Wall Street's viewpoint, a professor with a scholarly paper is "like a two-year old coming with something he drew."

All in all, risk management has a great deal of art versus science, although we certainly see more science coming in all the time.

Unbundling products is like particle physics - breaking down the whole into its fundamental building blocks which determine and explain its characteristics.

If all it took to beat the markets was a Ph.D. in mathematics, there'd be a hell of a lot of rich mathematicians out there.

I hold that, in economics and the social sciences, engineering has been the science of misplaced and misdirected concreteness.

People continue to believe that it's a science. That's rubbish: marking over-the-counter products is an art.

[O]nce a model has been developed, we are able to improve the realism of its assumptions step by step. But unlike physics, which is a science with constant (if poorly understood laws), the "laws" of economics and finance change constantly, even as we discover them. Sometimes they change because we have discovered them.

Charles Sanford, Chmn of the Board, Bankers Trust
"The Risk Management Revolution"
Proceedings of Symposia in Pure Mathematics, 1997, p. 325.

The tape was no different from Einstein's unified field, although you could make a hell of a better case for it. The truth, all truth, was in the print. In the numbers up there on the tape, APL 24 1/2, X 83, BR 7, COM 14 3/8, IBM 112 1/4. Symbols followed by integers followed by fractions. Like the equations of physics or calculus, the expressed the sum total of complex situations; they embraced knowledge, opinion, expectation; time past, present, and future; people, places, and things; abstraction and essence, universal and particular, comparative and specific. With a reach and scope and diversity of application and effect greater than any scientific formulation.

... at that time, the notion of partial differential equations was very, very strange on Wall Street.

I remember when I was at Goldman Sachs, and we produced these wonderful models for portfolio immunization. I had people asking me for the numbers down to the last cent. And they were really serious about this. There were numbers that involved billions of dollars, and by the time you got to the last cent, you have the most perfect random number generator imaginable.

Too large a proportion of recent "mathematical" economics are more concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

Ownershp of an obscure formula is not enough to demand a million dollars a year in salary in any other industry and I don't see why it should be in this one.

I needed income because I had a wife and a baby. So I started sending resumes. People sid: "Why physics?" I said I could apply those skills to finance. In one interview with JP Morgan, after many unsuccessful attempts, I said: "I don't know what you do and how you do it, but I've done a lot of projects, learn quickly and I think you should give me the opportunity." And they did.

Mathematical risk quantification has become a pseudo religion that pacifies our insecurity. Models have become sacred pagan gods, but God's wrath can change.

The best we can do with modeling is create resemblances of behaviour. But we cannot determine the reality of behavior.

What attracted me to the options business more than anything else was the mathematics of it. I liked the Black-Scholes model and was more comfortable with it than I should have been at the time.

There is a tempting and fatal fascination in mathematics. Albert Einstein warned against it. He said elegance is for tailors, don't believe in something because it's a beautiful formula. There will always be room for judgment.

Paul Samuelson
Trillion Dollar Bet
NOVA, PBS, February 8, 2000

Math doesn't drive financial markets, people drive financial markets, and people are not predictable. We do not yet have a universal theory of human behavior or human motivation. Given that that's so, we're not likely to have robust models of financial market behavior that will always work, and I think the hubris of the mathematician is to ignore that fact.

Peter Fisher
Trillion Dollar Bet
NOVA, PBS, February 8, 2000

Just as the engineering of digital bits would eventually lead to the Internet, the mathematically driven engineering of stocks, bonds and other securities would create the modern multi-trillion dollar financial system.

Financial modeling is never going to provide eight-decimal place forecasting. You shouldn't really expect it to. In physics, you're playing against God, and God doesn't change the laws very often. You're trying to describe the created world with a combination of intuition and experiment and mathematics. You use parameters like mass and charge, which are time-independent and not obviously of human origin. In finance you're playing against God's creatures, agents who value assets according to their feelings about the future in general and their future in particular; these feelings are ephemeral or at best unstable and fresh news on which they are based keeps streaming in. Finance uses parameters like future risk and future return, which not only refer to the future rather than today, but also are opinions rather than facts. Expected value in finance clearly derives from human beings who are doing the expecting, which mass and charge and electromagnetic force apparently don't or at least not in an obvious way.

'You can't overintellectualize these Greek letters, ' Pflug reflected, referring to the alphas, betas, and gammas in the option trader's argot. 'One Greek word that ought to be in there is hubris.'

Roger Lowenstein
When Genius Failed: The Rise and Fall of Long-Term Capital Management
New York: Random House, 2000, p. 89

Quantitative finance isn't mathematics or chess; it's not a field for brilliant idiot savants.

I am sorry that people lose their jobs, their homes and their retirement savings, but only in the same general way I'm sorry people get sick or lose friends. A trade or model of mine might have caused some economic disasters, just as a sneeze of mine might have transmitted a virus that caused someone to get sick, or an article I wrote might have caused two friends to have an argument that caused a rift between them. If you worry about the unknowable consequences of your activities you can never do anything.

Let us not forget there were plenty of financial disasters before quants showed up on Wall Street, and the subsequent disasters (including the current one) had plenty of help from the non-quants.

Think of quantitative finance as gardening; we need sturdy tools for it, but not surgical instruments.