Triangular Arbitrage with Bitcoin

Abstract

Bitcoins are bought and sold with most major currencies, and the resulting prices are ‘exchange rates’ of currencies per Bitcoin. The price of Bitcoins in national currencies have been quite volatile over the brief period of Bitcoin’s existence. Among national currencies, the possibility of triangular arbitrage leads to near equality of bilateral exchange rates and exchange rates obtained via triangular trade. We explore the relationship between a bilateral exchange rate of two major national currencies and the exchange rate that can be obtained via triangular trade through Bitcoins. Features of the Bitcoin exchanges make it difficult to meet conditions necessary for strict (risk-free) arbitrage, but market pressures from the threat of arbitrage constrain the national currency prices of Bitcoins to adjust toward the bilateral foreign exchange rate obtained in the traditional foreign exchange market. In this paper, we compare the Bitcoin implied exchange rate between the US Dollar and the Chinese Renminbi to the market US Dollar/Renminbi exchange rate, and show that the Bitcoin implied rate adjusts toward the FOREX market rate due to market pressures from the threat of triangular arbitrage. One implication is that the bilateral rate and the triangular trade rate obtained from trade in Bitcoins are cointegrated, and we study the adjustment process when these exchange rates are misaligned.