Financial Engineering, Behaviorial Economics and Praxeology
My initial bias is to be skeptical of the value of such an approach. Mathematical futures/options forecasting seems similar to Max Cohen's grandiose attempt to predict the mathematical patterns in the stock market in the movie Pi (an excellent film); an illusory objective, like perpetual motion or attempts to square the circle. Mapping the current state of the economy is one thing, but making toy models of previous markets and simulating them based on the future seems a blind bet on intelligence to model what is not amenable to insightful modeling: human actions and behavior in the future.
Thinking about it, I realized my bias against such modeling came back to Mises' illustration of two approaches to economics. Murray Rothbard writes, 'One example that Mises liked to use in his class to demonstrate the difference between two fundamental ways of approaching human behavior was in looking at Grand Central Station behavior during rush hour. The " objective" or " truly scientific" behaviorist, he pointed out, would observe the empirical events: e.g., people rushing back and forth, aimlessly at certain predictable times of day. And that is all he would know. But the true student of human action would start from the fact that all human behavior is purposive, and he would see the purpose is to get from home to the train to work in the morning, the opposite at night, etc. It is obvious which one would discover and know more about human behavior, and therefore which one would be the genuine "scientist."'
Certainly this example illustrates a natural division of approaches, and to my mind makes a succinct and convincing case for praxeology, but the behaviorist may not be down for the count.
Before picking up the thread, it should be noted of course that financial engineers and quants are not (generally, anyway) trying to derive scientific truths or general principles. On the contrary, they are concerned with modeling many particular truths, especially particular generalized patterns that underlie particular phenomena. Everything is contingent and models are always susceptible to review.
It is less obvious, then, what particular, if any, contingent patterns or principles a financial engineer may uncover. The reason to hire a financial engineer, of course, is to help traders make money by exploiting inefficiencies in the market. Hayek's explanation for apparent "inefficiencies" in a given market is that since knowledge is dispersed asymmetrically, it is expected for there to be a kinked array of market prices within a short interval, there is no perfect knowledge. Behaviorial economists formulate much the same principle, but assert that modeling such inefficiencies may provide tangible insight into the patterns of knowledge distribution, or more precisely, the patterns of it's output given certain inputs.
In essence, one might say that a financial engineer is creating a telescope that allows traders to obliquely understand what tends to happen given a relatively stable(but disparate) distribution of knowledge. This is an empirical question, but I think there may a basis in this example, for a weak (but sound) case that even behavioral economists have some contribution to the development of an applied economic science, potentially aiding praxeologists in much the same way telescopy has aided astronomy and physics and computers have aided number theorists.
Addendum: It's come to my attention that Gene has already written about this topic in depth here, thoroughly discussing the philosophical importance of financial modeling, but most interestingly (to me, anyway), providing some key insights into the practical significance of modeling. I liked this analogy:
"Mathematical equations can be useful for modeling the result of people following through on previously made plans, for capturing "equilibrium-like" phases of markets.
"Analogously, we could say that once a player in a basketball game decides to shoot jumper, we could use an equation that, based on the initial force vector that the shooter chooses to apply to the ball, then predicts the progress of the shot. Such an equation will be of little use, however, in predicting whether the player will change his mind and pass instead."