How can you develop your own interest rate model? What must be take cautiously before making one? Also what is the regulation that one mustfollow? Also what is some common properties that models would be satisfying?
There is a lot of different kind of IR models. You can modelize short rates, forward rates or more complex rates like Swap rates. Once you chose a rate and a model that fit your needs (some are easier to use for a given application or asset class, some models are incompatible with some hypothesis or other models). The model will usually take the form of a Stochastic differential equation, wich give the dynamic of your rate(s). The SDE will contain some parameters. You then have to find the parameters that represent the real life (calibration process). This is probably the hardest part as it require both theoretical and practical computations.
There is no regulation on that, just properties that your model should respect or not based on what you need. But this is not written in stone. For exemple some models were heavily criticised because they could become negative, people preferred positive models wich would be more reallistic because everybody know rates could not be negative. Some rates recently become negative...
This is a very broad answer as I can't sum up decades of works of thousands people in one post. You should really read a courses on IR models. Look for the slides of Brigo and/or Mercurio courses.