Get to grips with assumption agreements. This simple guide explains their purpose, key elements, and how they affect your business dealings.An Assumption Agreement is a legal document through which one party transfers its obligations or duties under a contract to another party. It allows one party to "assume" the rights and responsibilities of the other party. An assignment and assumption agreement is a contract that allows one of the parties to transfer their contractual rights and duties to another party. DEPOSIT INSURANCE CORPORATION, RECEIVER of FIRST REPUBLIC BANK,. The first step in creating an assignment and assumption agreement is to clearly identify the parties involved and their respective roles.