Interest rate on a refinance jumbo loan

I am looking to refinance my Jumbo Loan at $1,040,000.00) with credit score between 760-800 , current house value is at 1,600,000.00 , what kind of rate can I expect ? Please advise .

Thank You ,
Nate

It'll be hard finding someone to do the refinance. Most of the shops you hear about on TI aren't doing jumbo refi's. If you can find a lender to do it - my guess is rate would be in the mid-3's.

About 2 months ago where refi rates for high conforming was 2.5 for 30 years (0 pts) with Owning and Lenderfi, Jumbo (> $1m) was low 3?s (3.125 was what I quoted thru my contacts at that time, 30 yrs 0 pts). 

But this was before that new refi 0.5 pt fee that?ll ultimately go to the consumer (now pushed back to Dec?)?, so it could be in the low-ish to mid 3?s as best potsticker mentioned

Talked to BOFA loan officer last week about getting a loan new home. He said jumbo loan offer cheaper rate than nonconforming loan for my case since wife and I both have 760+ credit score and our LTV is between 40-50%.

I have not looked into loan for a while since i bought my last house 12 years ago. I was under the impression that FHLMC or Fannie Mae loans should have lower rate than jumbo loan. Isnt this not the case anymore?

BOFA website shows bigger loan amount, cheaper rate. For example 300k is 3.1% but $1 million is only 2.8% for 30 years fixed. What is main reason behind this? I thought current rate was at least 3%  regardless of the loan amount.

If i were to go jumbo option, what are the reasonable fees nowadays like origination, title, appraisal for new construction nowadays?

TIA

Generally speaking jumbo rates have been lower than conventional loans recently.