Now, where do the rates of exchange arise from?
In a way, it is a way of keeping track of the relative strengths of the economies. We need to go down to the basics: We have a pool of labour of fixed size in the short term (months time horizon), with a productivity given by their industriousness, by the capital tools they have and by the efficiency of their system of economic governance. To this we have a certain number of "drawing rights", a certain number of future contracts on the pool of labour, or "money", as we decided to call them.
If any of these parameters change, the rate of exchange with other economies will also change. If the number of money changes, the pool of labour is unchanged, making each contract less valuable.
And so on for the other parameters - if the capital tools are all washed to sea by a tsunami, the value of the currency relative to others will drop, for the new situation will not allow for the same productivity.