cross rate derivation illustrated

There’s confusion over the term “cross”. I believe it means the pair is not “native” to the broker/dealer you are using, so they have to synthesize 2 “native” trades. If your broker/dealer offers only USD/XXX , then a lot of non-USD currency pairs will be crosses.

If you are a big dealer bank using EBS and Reuters, then you can combine those 2 brokers’ offerings together and present a consolidated list of “native” pairs. Anything not in the list is considered a cross currency pair. Note EBS/Reuters “native” spreads are very tight. This is a defining feature of “native” pairs.

Since a cross is always synthesized using 2 pairs, transaction cost (and bid/ask spread) is higher.
——————-
In the context of “cross rate”, this term means “an exchange rate between 2 non-USD currencies”. That’s a USD cross. There are also Euro crosses — any non-Eur currency pair whose rate is computed from 2 Eur rates.

If USD/AAA has a bid/offer and USD/BBB has a bid/offer, and CCC/USD has a bid/offer. When computing the cross rates between A B and C, just remember to always take the worse prices, which are the safest prices for the market-maker.
– Offer of the cross pair is worse joining worse
– Bid of the cross pair is worse joining worse too

One principal, but many scenarios. Here’s one scenario.Given
1) USD/CHF = 0.9648/52
2) USD/JPY = 82.64/69
CHF/JPY offer must be computed as USDJPY / USDCHF, but which number by which number? Worst offer quote is the highest, so 82.69 / 0.9648 = 85.71.

Here’s the math explained in English. As a market maker who is publishing the 4 quotes of 1) and 2), at what price am i willing to convert my CHF into JPY? Well, I would convert to USD then JPY, using the safest/greediest conversion rates among my outgoing quotes. I would safely convert from CHF to USD at 0.9648, then safely convert from USD to JPY at 82.69.

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