Of course, money exchange has been used since Biblical times because countries could use coins with different quantities of metal, depending on size (fair enough) or content (problems for clueless merchants). However, as long as everyone knows for sure the value of that coin, you should be able to use it in Orlais as well as in Ferelden.
Classical and medieval coinages generally had values associated with the ratio of various precious metals in their alloy; higher percentages of gold by weight, for example, would be more valuable. When different rulers coined on different alloy ratios, the rulers who could afford to put more precious metal in their coins were regarded as more powerful and more solvent, and the metals themselves had their own high value as commodities. It's a somewhat bizarre mixture of the fiat and commodity concepts.
Trade was easier when multiple rulers coined on the same standard of weights and measures, insuring that, say, a Korinthian silver
stater (a term indicating not merely the denomination of the coin, but its weight) had the same composition as an Aiginatan silver
stater. This reduced uncertainty and eliminated the necessity of intensively checking the weight of each coin exchanged in a given transaction. In Hellenistic times, the Attic standard, after Athenian systems of weights and measures, was the most commonly used coinage; most of the great monarchies of the East made use of it (save the Ptolemaic empire, which as usual had its own special way of doing things).
This is relevant because
the states of Thedas also employ a near-universal standard of weights and measures, imposed and maintained by the Dwarven Merchants' Guild. An Orlesian sovereign is equivalent to a Fereldan royal; they weigh the same, and they are composed of the same proportion of metal. This effectively eliminates any need for exchange rates. One wonders, however, whether the usual practices of shaving or debasing wouldn't show up again in times of fiscal extremity. Loghain, for example, was in such dire financial straits that he was literally selling off his own citizens for Tevinter gold at the end of his time in power; if he did not abandon the dwarven standard as well, the power of the Merchants' Guild's retribution must be terrifying indeed.