The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. Bank services of MoneyGram on money transfer are available only to individuals. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account. The benefits of money transfers by MoneyGram: simplicity in making up.