Several years ago, my son, who did a PhD thesis on the reception history of Max Weber, the founding father of sociology, introduced me to two influential essays by Weber, entitled respectively Science as a Vocation and Politics as a Vocation. In them Weber discusses what problems you have to face, and what personality and character you have to own, if you decide to make these fields your calling, and he’s surprisingly thoughtful and yet practical about it.
I thought it would be interesting to begin to think about the same questions with respect to entering the field of Quantitative Finance, particularly from a practitioner’s point of view.
According to Zvi Bodie, financial engineering is the application of science-based mathematical models to decisions about saving, investing, borrowing, lending, and managing risk. I think that’s a reasonable definition.
Science – mechanics, electrodynamics, molecular biology, etc., – seeks to discover the fundamental principles that describe the world, and is usually reductive and analytic. Engineering is about using those principles, constructively and synthetically, for a purpose. Thus, mechanical engineering is concerned with building devices based on Newton’s laws, suitably combined with heuristic or empirical rules about more complex forces (friction, for example) that are too difficult to derive from first principles. Electrical engineering is the study of how to create useful electrical devices based on Maxwell’s equations and solid-state physics, combined with similar heuristics. Similarly, bio-engineering is the art of building prosthetics and other biologically active devices based on the principles of biochemistry, physiology and molecular biology.
So what is financial engineering? In a logically consistent world, financial engineering should be layered above a solid base of financial science. Financial engineering would be the study of how to create functional financial devices – convertible bonds, warrants, synthetic CDOs, etc. – that perform in desired ways, not just at expiration, but throughout their lifetime. That’s what Black-Scholes does – it tells you, under certain assumptions, how to engineer a perfect option from stock and bonds.
But what exactly is financial science?
Canonical financial engineering or quantitative finance rests upon the science of Brownian motion and other idealizations that, while they capture some of the essential features of uncertainty, are not finally very accurate descriptions of the characteristic behavior of financial objects. (You should perhaps even object to my use of the word ‘characteristic’ since it’s not clear that financial markets even have time-invariant characteristics.) Markets are filled with anomalies that disagree with standard theories. Stock evolution, to take just one of many examples, isn’t Brownian. We don’t really know what describes its motion. Maybe we never will. And when we try to model stochastic volatility, it’s an order of magnitude vaguer.
So, the point I want to make, for those people who consider coming into the field from one of the hard sciences, is that financial engineering rests on a shaky basis. That’s not to say that it isn’t worth doing. In one sense it makes it more interesting. If you’re going to work in this field, you have to understand that you’re not doing classical science at all, and that the classical scientific approach doesn’t have the unimpeachable value it has in the hard sciences. You have to ask yourself if you can live with that.