I finally finished my refinancing and thought I could make an update here. The bank is Citi Mortgage. The rate is 5.875%.
It should be 0 cost. But I still end up to pay some locking fee about $2800 because the lender required us to have 6 months payment history. When I got the rate we had only made 5 mortgage payments. Comparing with today’s rate (about 6.35%), we feel it still makes sense to pay the fee to lock the rate.
Finally it is done. It took a bit long.