Its not possible to argue definitively whether Central Bank policies have or have not made currencies stable. I welcome you to argue they have not succeeded. But the mechanism is there for them to try. Economies go from stability to instability as a natural cycle. Without a counter cyclical mechanism in place you are at the mercy of economic forces.
The "stability of a currency" is in fact very problematic. Of course, a currency that is used a lot gains stability, because of the "stickyness of prices". People get used to prices, and if prices are suddenly very different, they tend to adapt their buying habits as a function of this differential, rather than doing an updated full market study each time.
That is, if you think a bread should cost about $1.-, and you suddenly see a bread at $5.-, you will probably not buy it (and you will think of the bakery as a thief). If you think that a modest car should cost about $ 15 000.-, then if one presents you a modest car for $ 50 000.- you will not buy it. On the other hand, if you see an "opportunity" to buy a modest car for $ 6000.-, you may "jump on the occasion" even though you were not considering buying a new car any soon.
The more people have prices in mind, the less daily volatility is possible, because people would buy more at lower prices, and buy less at higher prices. Wages are also such a thing. They are contractually established. Your boss cannot just walk in and tell you that this month, he will only pay half of your usual salary. He won't walk in, and you will not get nervous, because next month, he's not paying the double.
So usage, and psychological stickyness of prices, stabilise money on the short term.
On the longer term, central banks try to stabilise (well, to inflate slightly) the *consumer price index*. However, in doing so, these central banks forget that prices are market signals. There can very well be market forces that would change the consumer price index basket value with respect to other assets. By trying to stabilise/inflate the consumer price index, central banks are sometimes obliged to inflate LARGELY other assets, like stock, housing prices, and other things.
Moreover, as increased economic productivity should normally DEFLATE the consumer price index, the slight inflation that central banks want to establish can be hugely inflationary without people noticing.
It is interesting to see that
http://en.wikipedia.org/wiki/Inflation#mediaviewer/File:US_Historical_Inflation_Ancient.svg average inflation was compensated with deflation historically, as long as there was a sound money principle (essentially a precious metal standard). When central banks really kicked in, we only got inflation.
As central banks, just like any other human endeavour, is ill informed, based upon human action, and must guess what will happen, in fact, central banks are usually *just as wrong* as any other economic agent in knowing where the economy is heading. By giving them more power, they are then just as well causing cycles. They are causing OTHER cycles than the "free running dynamics", but they cause cycles by their misconceptions just as well as the "natural" business cycles.