I think C is the best choice, but A is not obviously wrong. Neither are perfect fits, so I think the question is poorly written.
The phrase "specifying fixed exchange rates" refers to the banks' practice of choosing an exact value for an exchange rate, rather than allowing the exchange rate to fluctuate based on a formula that takes other economic indicators into account. "Fixed" refers to the fact that the exchange rate is not allowed to fluctuate - it is chosen as a constant number.
The transitive verb "to stabilize" is defined by Merriam-Webster as:
2 : to hold steady: such as
a : to maintain the stability of (something, such as an airplane) by means of
b : to limit fluctuations of stabilize prices
c : to establish a minimum price for
Meaning b is the closest fit, but only means that "fluctuations have been limited." When the value doesn't fluctuate at all because it has been set to a constant, words like "locked" or "pinned" become closer fits. "Fastened" is a rough synonym for these words, but I think a native speaker would be much more likely to use either of them instead of "fastened" in this context.
This is unrelated to your question, but it's worth mentioning that "convinient" is a typo for "convenient".
This is also unrelated, but I think most speakers would use "precision" in place of "preciseness" (discussion).