[Correction: Last week F&I magazine incorrectly reported that Chase had informed dealers last Monday that it would begin requesting higher down payments from borrowers. A company spokesman said the policy had been in place for some time now and that the company had not communicated any new policies in recent weeks.]

With questions of which lender will bow out next, Chase points to its recent deal with Mazda as proof of its stability.

"We signed Mazda as a client," said Mary Kay Bean, spokesperson for Chase Auto Finance, which officially became Mazda's finance source for dealers on OCt. 16. "I think that’s a signal of our capability."

Compared to the same period a year ago, Chase did report a 27 percent drop in underwriting for auto loans in the third quarter. And compared to the second quarter, the $3.8 billion in auto loans it originated was down 32 percent from the second quarter.

"We were booking deals … but there may not be as many loans to make. Obviously, sales are down," Bean said in response to the decline in originations. "I think, in essence, what we're trying to do is what’s right for our business, what's right for the dealer and their customers."

The company's net revenue was $506 million, up $59 million, or 13 percent, driven high loan balances and increase automobile operating lease revenue. The company also increased its provision for credit losses by $28 million, reflecting higher estimated losses.

"I think we've looked at quality rather than volume for a long time," said Bean. "One of the tenets of our business is to do deals that are affordable to customer, made sense for our dealers and made sense for our business."