Verified Certificate

Supported by the following organizations

This is to certify that Michael Murphy successfully completed and received a passing grade in BEM1105x: Pricing Options with Mathematical Models a course of study offered by CaltechX, an online learning initiative of Caltech.

Noted by

Jaksa Cvitanic

Jaksa Cvitanic

Richard N. Merkin Professor of Mathematical Finance California 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.