Exhibit 31.1

Certification Pursuant to

Rules 13a-14(a) or 15d-14(a) under the Securities Exchange Act of 1934, as Amended

I, Richard M. McVey, certify that:

1. I have reviewed this Amendment No. 1 to Form 10-K of MarketAxess Holdings Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report.

/s/ RICHARD M. MCVEY

Richard M. McVey

Chief Executive Officer

(principal executive officer)

Dated: March 18, 2019