On Monday, May 4th 2020, The F.D.A. has announced that companies who are selling CONVID-19 coronavirus antibody tests must submit data to the F.D.A.  Existing companies with test on the market must prove accuracy within the next ten days or face removal from the market.  Companies with new test must submit their data and an application within 10 days of their plans to marketing their product.

Below are 2 Weblinks to major news site articles with more details and a third Weblink to a continually updating F.D.A. site that lists the companies and their data that have Emergency Use Authorized for their Serology Test with included is some Performance data.

Washington Post - F.D.A. steps up scrutiny of coronavirus antibody tests to ensure accuracy

https://www.washingtonpost.com/health/2020/05/04/fda-steps-up-scrutiny-coronavirus-antibody-tests-ensure-accuracy/

New York Times - F.D.A. Orders Companies to Submit Antibody Test Data 

https://www.nytimes.com/2020/05/04/health/fda-antibody-tests-coronavirus.html

F.D.A. - E.U.A. Authorized Serology Test Performance

https://www.fda.gov/medical-devices/emergency-situations-medical-devices/eua-authorized-serology-test-performance

An important fact to keep in mind is, even though one has the Antibody it is not yet known, if that provides immunity from Coronavirus. Conclusions about immunity have yet to have been verified, due to it being a new virus strain.