sabre

Lets see if I can think my way through this. In both cases you are short optionality before you begin hedging.

The option you are short is the option to the homeowner, or their right to refinance. You hedge the duration drift and convexity by buying options.

In case one, you assume all borrowers have the same "strike" price, ie if rates go lower all borrowers will have equal incentive to prepay but different times they will do the prepay, maybe with some sort of distribution.

In this base case, since all borrowers have the same strike, and before rates go down none have prepay incentive, you could hedge with ATM options.

In case two, you assume some borrowers behave like case 1, but some are long OTM options, ie they need more of a move in rates to be ITM. You would hedge these borrowers using OTM options.

At least thats my logic by just thinking through it. Hope that makes sense?