FX Rate Calculation

When you see a rate like EUR/USD of 1.6 / 1.61, it means this:

  • Bid: 1.6; Quoter buys EUR and sells USD at 1.6
  • Ask: 1.61; Quoter sells EUR and sells USD at 1.61

If you are on the receiving end, you always end up paying more or getting less! Note Bid <= Ask always.

  • If you want to sell your 1 EUR, you will get 1.6 USD
  • If you want to sell your USD, you will have to fork 1.61 USD for 1 EUR

Currency Cross Rate Calculation

A Cross Rate is sometimes calculated based on 2 other FX Rates going through a common currency, referred to as the Cross Currency. Given that the rates are following some market conventions whereby the USD is not always the main currency, the calculation is a bit more complex. Note the differences:

  • EUR/USD: 1.2; 1 Euro gives you 1.2 USD
  • USD/CAD: 1.1; 1 USD gives you 1.1 CAD
  • GBP/USD: 1.6; 1 GBP gives you 1.6 USD

So what should the calculation be for EUR/GBP? or GBP/CAD? Furthermore the calculation becomes more confusing if you consider Bid and Ask...To put it simply in the words of "Mastering Financial Calculations":

  • Given two exchange rates A/B and A/C, the cross rate are:
  • B/C = A/C divided by A/B
  • and C/B = A/B divided by A/C
  • But you need to use the opposite side when calculating bid/ask, e.g.
    • B.C Bid = A.C.bid / A.B.ask
    • B.C Ask = A.C.ask / A.B.bid
  • Given two exchange rates B/A and A/C, the cross rate are:
  • B/C = B/A multiplied by A/C
  • and C/B = 1 divided by (B/A multiplied by A/C)
  • And you need to use the same side when calculating bid/ask, e.g.
    • B.C Bid = A.C.bid * A.B.bid
    • B.C Ask = A.C.ask * A.B.ask

Examples

The rates may be a bit old but they provide a non trivial set. Assuming, the calculator first checks for GBP cross ccy and then USD and the BASE rates below:

Currency Pair Bid Ask
EUR/USD 1.30 1.11
GBP/CHF 1.51589 1.5156
EUR/GBP 0.79 0.796
USD/CAD 103.931 103.94
USD/JPY 1.089 1.090

And now the calculation examples

Currency Pair Cross Ccy Bid Ask Description
CAD/JPY USD 95.349541 [ bid(USD/JPY) / ask(USD/CAD) ]
calc = 103.931 / 1.090 = 95.349541 (rounded)		 95.445363 [ ask(USD/JPY) x ask(USD/CAD) ]
calc = 103.94 / 1.089 = 95.445363 (rounded)		 
CAD.JPY Mkt Convention:true Cross Ccy:USD
Quoter buys  CAD and sells JPY at 95.349541
Quoter sells CAD and buys  JPY at 95.445363
EUR/CHF GBP 1.197553 [ CHF/EUR = bid(GBP/CHF) / ask(GBP/EUR) ]
Note bid(GBP/CHF) = 1.51589
Note ask(GBP/EUR) = 1 / bid(EUR/GBP) = 1 / 0.79 = 1.265822785
calc = 1.51589 / 1.265822785 = 1.197553 		1.206418 [ ask(GBP/CHF) / bid(GBP/EUR) ]
calc = 1.5156 / 1.256281407035 = 1.206418 (rounded to 6 dp) 
EUR.CHF Mkt Convention:true Cross Ccy:GBP
Quoter buys  EUR and sells CHF at 1.197553
Quoter sells EUR and buys  CHF at 1.206418

Once you have an FXRate, you can call:

  • getBid: bid (amount the quoter would buy Ccy1 for a given amount of Ccy2).
  • getAsk: ask (amount the quoter would sell Ccy1 for a given amount of Ccy2).
  • getMid: (bid+ask)/2
  • convertAmountUsingBidOrAsk: Given a monetary amount in the original currency, calculate the resulting amount in the other currency, using BID or ASK.
  • getPaymentAmountForBuying: to get the amount you would get by buying a currency amount.
  • getReceiptAmountForSelling: to get the amount you would get by selling a currency amount.

The code is available here: