I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought about implementing simple methodologies, like one factor short-rate models (in my sight the BDT model) for discounting the future cash flows that I could receive if the options are exercised.
So I would like to know if it's a good a idea to start pricing with this kind of models. How good or bad could this end up being? (compared to more sophisticated models). Should I spend time trying to calculate more complete models like the LMM or so? If so, which instruments should I use to get the right parameters?
Many models start assuming that there is an observable swaption/cap/floor market, but if there isn't such a market, how should parameters be estimated? For example, I could get the zero yield from the swap market, but what about the vol? How do I benchmark my models?