Latinum has value because everyone agrees
to pretend it has value. It's the same idea behind modern currency. Do you think the pieces of paper with numbers printed on them that we use as currency are inherently valuable? No - it's just a representation of one
way to track value. The currency in your pocket doesn't even represent the sum total of all "money" in circulation. Most money exists only as data in computers. And every kind of currency can be counterfeited or hacked. The fact that it can
be counterfeited doesn't mean it loses value, it just means it's important to make doing so illegal and/or incredibly difficult. Latinum can be replicated, but doing it may be illegal (and send a red flag to the authorities) or so incredibly difficult to do that it's not worth the effort (except for a few smart, ambitious or stubborn individuals).
Latinum probably functions the exact
same way, and perhaps in a more complex way, too. This is the currency of an interstellar society with access to technologies we lack. The value of latinum may be present as "molecular serial numbers", or something. I don't know. BUT, I do know that assuming a culture as complex as the Ferengi, specialized in financial and business systems, shouldn't be thought of as engaging in mere barter
with pieces of ore
. On the other hand, they may prefer to be thought of as simplistic barbarians using baubles as currency, to make their opponents (both military and business) underestimate them - and allow them to gain the upper hand!