Stop Health Premium Spikes Act of 2020 This bill establishes a temporary risk corridor program to reimburse health insurers for medical costs that are greater than expected. Specifically, the program requires the Department of Health and Human Services to pay insurers 75% of the cost of providing benefits under a plan that exceeds 105% of the total annual premiums for the plan, reduced by administrative expenses. The program applies to plan years 2020 and 2021.