Pension Stability Act This bill requires the Department of Labor to establish user fees for qualified professional asset managers (QPAMs) who have been convicted of a crime and apply for an individual exemption (known as a QPAM waiver) to the prohibited transaction rules under requirements for certain private benefit plans. The fees apply to large regulated banks, savings and loan associations, insurance companies, and federally registered investment advisors who are QPAMs; must be at least $1 million per application for an individual exemption; and increase based on the severity of the crime and the number of prior applications for individual exemptions. Labor must transfer the amounts collected from the user fees to the Pension Benefit Guaranty Corporation to assist in guaranteeing benefits under pension plans.