A Study on the Nonlinearity in the Arbitrage Transactions of Cryptocurrency: Using the Bitcoin Prices in Several Countries

The relative price of a cryptocurrency, denominated in different currencies implies a multilateral exchange rate. If the multilateral exchange rate differs from the bilateral one, then there exists an opportunity for arbitrage, and hence the multilateral and bilateral rate would not diverge much from each other. However, the pressure to return to the equilibrium is likely to depend on the level of the discrepancy, because cryptocurrency market is typically shallow and there are transaction costs for arbitrage. This study analyzes the nonlinearity in the convergence of the two exchange rates and finds that the two exchange rates are cointegrated and the cointegration relation is not linear.