Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has dropped below zero), which are the most striking applications for the models in financial economics/quant finance field?
By that I mean which of the so called "stylized facts" and standard models of modern finance are becoming highly controversial or just plain useless? As a couple of examples which spring to mind are the following (do not necessarily have to do with sovereign bond yields, but the concept of negative (nominal) interest rates as such):
- The CIR interest rates model completely breaks down due to the square root term
- The proof that an American call option written on a non-dividend paying underlying will not be exercised before the maturity is false
- Markowitz selection obviously encounters difficulties incorporating negative yields
What are the other consequences, on let us say, CAPM, APT, M&M or any other model in finance? Which long held beliefs are hurt the most by negative yields?