Question

What are the no-arbitrage conditions for:

Two –point arbitrage

Three-point arbitrage

Answer 1

Arbitrage is the purchase of foreign currency on one market for immediate resale on another market (in a different country) in order to profit from a price discrepancy. Hence, arbitrage may be defined as an operation that consists in deriving a profit without risk from a differential existing between different quoted rates. It may result from two currencies (also known as geographical arbitrage) or from three currencies (also known as triangular arbitrage).

• Inverse quotes and 2-point arbitrage: The arbitrage transaction that involve buying a currency in one market and selling it at a higher price in another market is called Two – point Arbitrage. Foreign exchange markets quickly eliminate two – point arbitrage opportunities if and when they arise.

• Cross rates and 3-point arbitrage: The term three – point arbitrage refers to the kind of transaction where one starts with currency A, sell it for B, sell B for C and finally sell C back for A ending up with more A than one began with. Efficient foreign exchange markets do not permit risk – less arbitrage profit of this kind.
• Two point arbitrate is basically buying a security in one market and simultaneously selling it in another market at a higher price, thereby profiting from the temporary difference in prices. This is considered a risk-free profit for the investor/trader.
• Triangular arbitrage is the result of a discrepancy between three foreign currencies that occurs when the currency's exchange rates do not exactly match up. These opportunities are rare and traders who take advantage of them usually have advanced computer equipment and/or programs to automate the process. The trader would exchange an amount at one rate (EUR/USD), convert it again (EUR/GBP) and then convert it finally back to the original (USD/GBP), and assuming low transaction costs, net a profit.

• As an example, suppose you have $1 million and you are provided with the following exchange rates: EUR/USD = 0.8631, EUR/GBP = 1.4600 and USD/GBP = 1.6939.

  With these exchange rates there is an arbitrage opportunity:

• Sell dollars for euros: $1 million x 0.8631 = €863,100
• Sell euros for pounds: €863,100/1.4600 = £591,164.40
• Sell pounds for dollars: £591,164.40 x 1.6939 = $1,001,373
• Subtract the initial investment from the final amount: $1,001,373 - $1,000,000 = $1,373

• From these transactions, you would receive an arbitrage profit of $1,373 (assuming no transaction costs or taxes).