In CFA books, we have five theories concerning term structures of interest rates
The co-existence of 5 theories means that they all are useful and each one can explain something that others can not do.
Each theory is defended by whom? (Quants? Asset Managers? Economists? Scientists?.. )
Working as quantitative analyst, I really don’t know on which theory my stochastic calculus, my pricing models,… base.
Depends on the goals of the company. A Insurer may have a maturity that corresponds to its policies. A bank with its mortgages. A trader trying to make money. Not everyone follows the same theory.
If you have to use interest rates projections rather than current market interest rates, then know well all those theories and know when to apply one or more of them.
I think now that the stochastic calculus (and Quantitative Finance in general) bases on the “Local Expectation Theory”.
The Unbiased Expectation Theory is use for people in Finance who need only simple models easy to use.
The three others, I don’t know, maybe for economists (I have read an example in Curriculum 5 about Quantitative Easing, they try to explain the change in volume of assets of US Treasury by Preferred Habitat Theory )