I'm studying interest rates theory and in the rates world are quite a few diffusion models, Hull-White 1factor, Hull-White 2factor, Ho-Lee, Vasicek, CIR, Derman-Toy, Black-Karasinski , Chen, etc etc. Other asset classes don't have nearly as many models.
I) which of these are used by banks in production to price and risk manage (ie Greeks calc) rates exotics products ?
II) do banks tend to use short rate models for pricing and risk management or HJM models ?
III) Also, in terms of calibrating these models, in the rates world, which derivative instruments are treated as 'priced by the market' & are used to calibrate the diffusion equation parameters (is it ie swaptions, caps, floors?) which will in turn be used to price exotics. e.g. in equities, vanilla options are used to extract the vol surface that is used to price more complex instruments, there's no pricing for vanillas, they're the instrument that's used to extract the volatility surface.