a. Given three currencies, a currency cross-rate is the implied exchange rate of a third country pair given the exchange rates of two pairs of three currencies that have a common currency.
b. For example, suppose we have the following exchange rates for three currencies:
A/B = 10 and B/C = 5
If we have to find the exchange rate between A and C, then we can do so as follows:
A/B × B/C = A/C = 10 × 5 = 50
c. Taking another example, suppose we have another currency quotes:
P/Q = 50 and R/Q = 10
And if we have to find the quote for P/R, we can do so as follows:
P/Q × Q/R = P/R = 50 × 1/10 = 5
d. If the relationship does not hold between the three currencies, as discussed above, it would be possible to arbitrage these three currencies to earn profits.