Verified Certificate

Supported by the following organizations

This is to certify that ALFREDO JOSE VELASQUEZ TUBILLAS 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

Sanjay Sarma

Sanjay Sarma

Vice President for Open Learning Massachusetts Institute of Technology

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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.