fixed income - How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market.

I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to calibrate the model to the zero curve.

1. Will this produce a sensible calibration of the model in respect of derivatives?


2. If not, how does one proceed in this case?