I was thinking some more about what makes a good theory.
In the natural sciences, a good theory is one that makes accurate predictions. There, the aim of all theory is to predict the future. (If there were no time dimension, there would be no future, and you’d need no theories at all.)
In finance, a good theory is something different. A good theory is something that gives you insight and a way of thinking about phenomena, even if it’s not a wonderful predictor. A good theory starts from something intuitive about markets, or something qualitative, and then quantifies it, which leads to new concepts, which one then develops intuition about through the theory, which then becomes the subject of newer theories.
So, to go back to options theory: one guesses that options prices are related to volatility. Black-Scholes quantifies that in terms of GBM and volatility. Volatility then becomes something one gets intuition about. Ultimately one gets theories of volatility itself.
I’m being a bit simplistic, but this is very different from physics or applied math. Options theory does make some predictions — e.g. if volatility doesn’t change, then, given the price of a 100-strike option, you can calculate the price of a 90-strike option one week from today. That is predictive, but not on the same scale as predicting where an antiballistic missile aimed at a Taepodong will be in three minutes. But it is still useful.
Another difference: models in physics or chemistry or applied math start from the present and predict variables in the FUTURE; models in finance start from known future events — e.g. cash flows –and then imply/calibrate the volatility, say, that makes the value of that cash flow in the PRESENT match the price in the market. Physics models move forwards in time; financial models often move backwards in time.
Note 1. Normally, in physics, present causes propagate their effects into the future. Many of the equations of physics are symmetric between past and future, and one imposes causality on the solutions, choosing only the waves that propagate from past to future. But, there’s a Feynman-Wheeler theory of electrodynamics from the late 1940s in which every object in the future sends a wave back to the past and every object in the present also sends a wave into the future, and the sum of these somehow, I don’t remember how, still ends up behaving causally.
Note 2. We always say the future is in front of us and the past behind, conflating time with spatial location. Recently there was an article in the New York Times Science section in which they reported on some tribe in South America that referred to the future being behind and the past in front. The reason was that you can see the past, hence, like things you can see, it’s in front, but you cannot see the future, hence, like things you cannot see without turning, it’s behind us.