Skip to content
All library documents

Finding FX Triangular Arbitrage and Accounting for Execution Risks

Article Quant Q&A · Author: idknuttin
Read the original

Summary

The document presents a textbook triangular arbitrage using quoted buy and sell rates from two FX dealers. The example cycles borrowed pounds through euros and dollars before converting back to pounds, producing a small surplus under the stated quotes. It illustrates how inconsistent cross rates can reveal a potential arbitrage path across currencies and dealers.

Key ideas

  • A triangular currency cycle can reveal an arbitrage when quoted conversion rates are inconsistent.
  • The example starts with borrowed pounds, converts through euros and dollars, and returns to pounds.
  • Displayed prices may change before an order is filled, so a theoretical gain may disappear during execution.
  • Wide spreads can signal poor liquidity and limit the amount available at the quoted price.
  • Different currency settlement dates and holiday calendars can create interest-rate costs that affect profitability.

Tags

ForexArbitrageExecution
Full text
# Is there an efficient method or technique to find an arbitrage between two FX dealers?


# Is there an efficient method or technique to find an arbitrage between two FX dealers?












Crossposted on Mathematics SE

I was able to solve the following problem and find the arbitrage but only after spending a long time on it and trying out different possibilites. Is there a method or technique that can help me find the arbitrage faster and in a more efficient way rather than just trying out different possibilites?

> Dealers $A$ and $B$ use the following exchange rates: $$ \begin{array}{l|l|l} \text{dealer } A & \text{Buy} & \text{Sell} \\\hline \text{EUR } 1 & \text{USD } 1.018 & \text{USD } 1.0284 \\ \text{GBP } 1 & \text{USD } 1.5718 & \text{USD } 1.5944 \\ \end{array} $$ $$ \begin{array}{l|l|l} \text{dealer } B & \text{Buy} & \text{Sell} \\\hline \text{EUR } 1 & \text{GBP } 0.6354 & \text{GBP } 0.6401 \\ \text{USD } 1 & \text{GBP } 0.6309 & \text{GBP } 0.6375 \\ \end{array} $$ Find an arbitrage opportunity.

My answer:

- Borrow 1 British pound (GBP)

- Go to dealer B and exchange your pounds for euros (1.5623 euros)

- Go to dealer A and exchange euros for dollars (1.5904)

- Go to dealer B and exchange dollars to pounds (1.0034 pounds)

- Return the 1 pound you borrowed and you just made 0.0034 pounds

There is an arbitrage of 0.0034 pounds.

## Answer by Ariel Silahian (score 1)

https://quant.stackexchange.com/a/23151

Can't wait to see you implement it in real life... You will experience so many uncontrolled variables and scenarios...

One common scenario is: you see what you think is a good price... Then you aggress on it... By the time you are filled, your entire great arbitrage formula is gone. (It is not enough for you to be fast - in nanoseconds - you would also have to interact with all the players)

## Answer by Will Gu (score 1)

https://quant.stackexchange.com/a/31346

As far as I know, the answer is yes and people do it all the time. There's something to add to the textbook example though. First the bid/ask spread on FX spot market is usually much tighter, meaning the room for taking advantage of the such arbitrage is smaller than you think (or you would need huge capital to leverage this kind of trade). For some currency pairs with wider spread, it usually means the liquidity is poorer, and you probably won't be able to execute large trade at the displayed best price. Secondly the spot date of the currency pairs may not be the same (depending on the holiday schedule of different countries), so you'd have to take the real interest rate into consideration.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.