I have a few questions regarding hull white calibration, specificly for the trinomial tree model.
1.I am wondering what are the ideal instruments could be used for hull white model calibration? Cap, Floor or Swaptions? Also for swaptions, what strikes should be used, ATM?
2.Also, if I want to calibrate a 30 year hull white trinomial tree, ideally, how many and what expiries and tenors should be used to construct an optimal tree? As granular as possible?
3.Lastly, can I use the tree calibrated from the above instruments to price other instruments (or solve OAS), for example, bermuda callable bonds. Or, I have to calibrate a specific tree for every instrument I want to price?