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# Cross Rate Calculation – Using Mid-Rates

A cross rate is a rate when neither currency has a major currency such as USD, EUR, GBP, AUD etc as one of the currencies in the pair. Usually these currency pairs are not directly traded in the market but derived from other currencies.

### Cross Rate – Example

JPYINR is not a directly traded currency so the JPYINR rate is derived from the USDJPY and the USDINR rate.

To derive a cross rate

For the sake of illustrating how to derive a cross rate lets take the example of EURCAD

To derive EURCAD we need the 2 pairs – EURUSD and USDCAD

the EUR rate is 1.0987-89

The CAD rate is 1.3630-32

One way to do this is to simply take the mid rate of EURUSD and USDCAD and derive the EURCAD midrate. Once we have the mid rate we could construct a spread around it. e.g. the migrate for

1 EUR is 1.0988 USD

and the mid rate for 1 USD is 1.3631 CAD

Therefore 1 EUR is 1.0988 x 1.3631 CAD = 1.4978

Depending on market conditions you could trend, decide your spread accordingly and quote say 1.4977-80

## Cross Rate Calculation – Using Bid-Ask Rates

When you look at the currency pairs quoted in the market you see they are quoted using the bid and ask. As we have already mentioned bid is the rate the dealer buys and ask is the rate the dealer sells. Another way would be to construct the Bid/ask rate of a cross currency is by using the bid/ask spreads quoted for each pair in the market and derive the rate for EURCAD

Lets begin with the BID rate ie the rate the price maker buys EURCAD

In order to BUY EUR and SELL CAD at an X rate we would need to know at what rate we can SELL EUR BUY CAD to square our position in the FX market. To work out this cross rate we need to break it into 2 steps

1. SELL EUR BUY USD – we can do this at the market Bid rate for EUR/USD 1.0987
2. SELL USD BUY CAD – we can do this at the market Bid rate for USD/CAD 1.3630

In effect we get 1.0987 x 1.3630 = 1.4975

This becomes the ceiling for our bid price. If we bid anything higher than this we would make a loss at the current market rates

To derive the ASK rate – the rate at which we can sell EUR/CAD we can break this down into similar two step process. If we SELL EUR and BUY CAD, we would need to cover the EUR short position and the CAD long position. We could do that at the market rates

1. Buy EUR and SELL USD at 1.0989
2. Buy 1 USD and Sell CAD at 1.3632

We can therefore BUY 1.0989 USD at 1.0989 x 1.3632 to give us the rate 1.4980

This becomes our ASK floor rate. If we sell below this rate it would be difficult for us to make any money from the deal.

So the bid rate would be lower than the rate at which you can construct a sale ie 1.4975

and your ask rate would be higher than the rate at which you can construct your buy ie 1.4980

you could quote anywhere between 1.4973-82 for a cross rate.

This is only an illustration on how you could quote a cross rate. In reality no one would hit a price maker on a 9 pip spread. We will look at how price makers actually quote in the FX markets and how that forms the price ticks you see in your charts in later session. Here we focus only on the basic math for you to get familiar with bid, ask, and bid-ask spreads.

### Recap

Now we know a little more of FX math, some really basic calculations. We have seen how rates are quoted, direct/indirect rates quotations, bid ask spreads, PIPs, cross rates. A few more concepts such as forward rates, FX swaps, calls trades and we should be pretty much done with the majority of the FX math.

As an exercise calculate the current cross rates for JPYINR, CADCNY, THBINR or any cross rate that would be relevant for you, maybe related to your countryÂ

Next we look at tenors in the FX markets

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