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What is the incentive for a bank to refinance a mortgage at a lower rate?
Banks make money on load origination fees. The "points" you pay or closing costs are the primary benefit to the banks. A vast majority of the time risks associated with the mortgage are sold to another party. FYI, the same is true with investment banks. In general, the transaction costs (which are ignored by modern finance theory) are the main thing running the incentives for the industry.