The monetary system will certainly become more sophisticated, but more stable and resilient at the same time. The financial sector is one of the least regulated and one of the most innovative parts of the economy, and is continually becoming more efficient. The development of futures contracts and other derivatives has enabled investors to protect themselves from and to benefit from unexpected fluctuations in prices, interest rates and exchange rates. While this can be seen as one cost of inflation, it also neutralises inflationist policies and reduces the incentive for pursuing them. Most financial markets will grow in size and will become more integrated into international markets.
Size adds stability because it means that one shock can be absorbed by many more participants.
This also means that government economic policies have less effect because markets are better able to anticipate the effects and to avoid them where necessary. Controls on credit, for example, would now prove almost useless in any developed economy because funds can simply be moved across borders or packaged in different ways. We will never arrive at a cashless economy, as some have predicted. Many people prefer to make transactions with anonymity and cash is the form of money that allows this. And as long as we have taxes, there will be people who want to evade them through using cash in the underground economy.