In article questions of the analysis of the financial risks connected with activity of financial institutions and first of all exchange structure are considered. The problem of increase of financial stability of the exchange is analyzed, potential and real risks are considered. On the basis of the analysis which is carried out in work the most important risks are revealed. Various classifications of risks are presented and sub classifications of each of groups are established. During the analysis the role of inflation and inflationary risks, and also their influences on financial stability of financial institutions and the exchange is studied. Also deflationary risks, currency risks and risks of an investment of the capitals are considered. Manifestation of risks at portfolio and real investments are analyzed. The separate group of risks connected with the organization of activity of the company is allocated reverse, settlement and commercial risks Are considered. The technique of risks of Global Association of Risk Professionals is considered. In work the main coefficients defining financial stability of the company are calculated. In some cases the behavior of various risks as a result of application of a technique of IFRS is analyzed. The financial condition of the Moscow Exchange for the last five years with identification of key parameters of development is in detail analyzed. As conclusions on work the most essential risks in activity of the exchange are specified.