Bank of America Corp and JPMorgan Chase & Co have started modifying tens of thousands of mortgages where the banks deem the loans especially risky, even if the borrowers have not asked, the New York Times reported on Sunday.

In some cases, the paper said, the banks are slashing the amount borrowers owe, citing one case in Florida where a woman's principal balance was cut in half.

The paper said the banks are targeting holders of pay option adjustable-rate mortgages, a type of loan where borrowers have the option of skipping some principal and interest payments and having the amount added back onto the loan.

Such option ARM loans were seen as especially high risk in the wake of the financial crisis; the two banks collectively still have tens of billions of dollars of such loans in their portfolios.

One law professor quoted by the Times said the banks were behaving in contradictory ways, modifying some loans that should not be and not modifying some loans that should be.

Spokespeople for the two banks were not immediately available to comment.

(Reporting by Ben Berkowitz. Editing by Maureen Bavdek)