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?
Answer
I assume you are asking for the popular Hull/White one-factor model.
You could eiter calibrate them to Cap/Floor Volas or to swaption volas. Don't try to fit a model to both at the same time. You should decide this by the products you want to price. If you want to price caps/floors with the model, calibrate it to cap/floor volas and vice versa.
Calibrate it to ATM. There are models that could handle the smile effect (volas away from ATM). But the plain vanilla Hull/White can not. If you are interested in the modeling of smile effects, you should read about the SABR model maybe.
- 2.
The answer might depend on the products you want to price. If you want the model to fit one area of the market better than others, you could think about mainly calibrating it to those. However, in general situations, you should take all volas that you have up to 30 years maturity.
You could (theoretically) use such a calibrated model to price other products. But it is not a good idea. Your prices would not be in line with 'the market'
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