Cross Rates Part 1

Cross rates refer to currency exchange rates where neither currency is the USD. In other words, neither the base nor the counter currency is the dollar in a cross rate.
Why this omission of the US Dollar?
The derivation of a cross rate requires the exchange of each respective currency in relation to the USD. Trading through the dollar, and the dollars (by design) cancel out, leaving us with only two terminal currencies.
Why this method?
Firstly due to the dominance of the USD in international trade, the exchange of each currency to the dollar provides the best indicator of the price and
Secondly, by emulating a trade through the dollar, a fair market price is determined. The assumption here is that market prices will enforce convergence to this price. Why? Because deviations from this price will be open to arbitrage. For instance, if the available market price is lower than the price calculated, it will be possible for an astute market practitioner to purchase the relatively cheaper currency in exchange for the currency priced relatively higher and vice versa. Doing so will result in a risk-free profit to the market practitioner.
Non-arbitrage pricing means that we assume market forces have already been at play and no arbitrage opportunities exist for the price.
Put differently, a market participant, no matter how smart, should not be able to guarantee a profit from any trade that does not involve risk.
The method in words
By trading currencies ‘through the dollar’ and, the dollar serving an intermediary role, the dollar exchanges cancel out and we end up with the terminal cash flows which relates the rate of exchange of one base non-USD currency for a variable rate of a non-USD counter currency.
Cross rates include currency pairs classified as both ‘majors’ and ‘minor’ pairs and provide a method to calculate the two-way prices in any currency pairs, irrespective of how liquid (or illiquid) a particular market is. The only requirement being that both currencies are tradeable to the USD.
In the next video we investigate the exact method used to calculate cross rates with an example.