I know it’s splitting hairs, but technically Black-Scholes is a model. It does fit under “option pricing theory” which says that the value of an option is determined by the value of a replicating portfolio. And Black-Scholes pioneered the idea that you can use stochastic calculus to determine the value of a replicating portfolio for an option.

Theories are basically groups of ideas and justifications that hang together in a coherent framework for solving a set of problems. Models are a particular instance of those theories used to solve a more concrete specification of those problems. It’s true that there is a grey area where it’s hard to tell where the model ends and the theory begins, but the basic idea is that a model is justified by a theory (set of principles).

Ultimately, it’s not all that important, but it can help you keep track of things because theories can spawn many types of models, whereas models don’t tend to have submodels (other than “special cases” of a model).

So behavioral finance is a proto-theory (I don’t feel the principles hang together firmly enough to be a fully developed theory, but it’s starting to get there.

APT is a theory because the equation is justified by the idea that arbitragers will buy and sell risky assets to push prices up and down, until risk is priced linearly according to the equation. What makes APT a theory is not the equation, but the description of the process that makes the equation work. To make an APT model, you need to further specify what the risk factors actually are.

That’s why CAPM is a different theory. CAPM and a 1-factor APT model that uses market returns as the only risk factor will actually produce the exact same equation, but they are different theories about why that equation is justified. One talks about how all investors are rational and therefore come to the same conclusions based on the same information; the other talks about how only some investors need to be rational, and if they engage in arbitrage behavior, they’ll bring prices in line to what the equation asserts.

Modern portfolio theory uses the idea that the correlation of assets is relevant to portfolio risk and concludes that optimization can generate higher sharpe ratios (efficiency) simply by changing the balance of assets in a portfolio.

There was a time when Discounted Cash Flow was a new theory… the idea that the value of a risky asset is the present value of future cash flows. This is such a fundamental part of finance today that we think of it as a model or a law, even, but there was a time in the early 20th century when that idea was new.

If this goes in your paper… cite me.