Financial crises appear throughout human history. While there are many schools of thought on what the actual causes of such crises are, it has been suggested that the creation of credit money might be a source of financial instability. We discuss how the credit mechanism in a system of fractional reserve banking leads to non-local transfers of purchasing power that also affect non-involved agents. To overcome this issue, we impose the local symmetry of time homogeneity on the monetary system. A bi-currency system of non-bank assets (money) and bank assets (antimoney) is considered. A payment is either made by passing on money or by receiving antimoney. As a result, a free floating exchange rate between non-bank assets and bank assets is established. Credit creation is replaced by the simultaneous transfer of money and antimoney at a negotiated exchange rate. This is in contrast to traditional discussions of full reserve banking, which stalls creditary lending. With money and antimoney, the problem of credit crunches is mitigated while a full time symmetry of the monetary system is maintained. As a test environment for such a monetary system, we discuss an economy of random transfers. Random transfers are a strong criterion to probe the stability of monetary systems. The analysis using statistical physics provides analytical solutions and confirms that a money-antimoney system could be functional. Equally important to the probing of the stability of such a monetary system is the question of how to implement the credit default dynamics. This issue remains open.