Verified Certificate

Supported by the following organizations

This is to certify that Ralph Silva successfully completed and received a passing grade in 15.435x: Derivatives Markets: Advanced Modeling and Strategies a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Deborah Lucas

Deborah Lucas

Sloan Distinguished Professor of Finance MIT Sloan School of Management

Egor Matveyev

Egor Matveyev

Executive Director of Micromasters Program in Finance MIT Sloan School of Management

Dimitris Bertsimas

Dimitris Bertsimas

Vice Provost for Open Learning Massachusetts Institute of Technology

Chris Capozzola

Chris Capozzola

Senior Associate Dean for Open Learning; Professor of History Massachusetts Institute of Technology

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.