I'm not sure I fully understand your question. Are you looking for a construction loan or is the house being built and you are responsible for the permanent loan? If you are needing permanent financing, then you need to find a conventional or FHA loan where you can essentially float the interest rate until whatever time you are nearing the end of the build. There are many lenders that require you to lock your loan at the time you take the application/send it to underwriting thereby giving yourself 2 months time where rates could improve but you are set.
At Flagstar, we float the loan through the entire underwriting process, so you could techinically be floating your loan for up to 6 months while you wait for you home to be finished. You can lock your loan at anytuime between when you apply and the time your loan is clear to close.
If you'd like, you can call me to discuss your options and what it is you are looking to do. I am in North Carolina but can originate loans in all 50 states. Thanks for your time.