I was discussing exchange rates with a friend and realized we have a different understanding of how they work. We both understand that floating exchange rates are dictated by market forces (supply/demand) and can fluctuate from day to day.
However, we disagreed about how "the" exchange rate is set and whether there is a single universal exchange rate between two given currencies at any time. We both acknowledged that different currency exchange services will offer different rates depending on how much of a margin they take. We disagreed on whether there is a universal rate that an exchange service would use if not operated for profit (e.g. a free currency exchange service provided by one's bank).
My friend seems to think that there is a single universal "trading price" between two currencies at any given time, and that this is the rate a not-for-profit exchange of currency would take place. I think he believes this is the number you get if you just Google the exchange rate between two currencies.
My understanding is that there is no universal rate at any given time, and "the" exchange rate you see when you do a web search is just an average of recent trading prices. This would mean that a bank or other service performing a not-for-profit exchange would not necessarily follow the same exchange rate you get when you look up the current rate.
Which conception is more accurate? If my friend's conception is more accurate, is there some agency responsible for setting "the" current exchange rate between floating currencies?