The law of one bitcoin price?

Bitcoin, a digital currency, constitutes a textbook example where the law of one price should be satisfied as, unlike asset pairs previously studied in the literature, it is a fully fungible asset with identical payoffs. Despite this, we show the existence of persistent, statistically significant differences between U.S. dollar-denominated bitcoin prices in multiple bitcoin exchanges. We argue that the price difference has two components: One, microstructure frictions such as the bid-ask spread, order book depth and volatility and negatively related to volume; and market segmentation. Two, an “illegality premium” due to the use of bitcoin to avoid foreign exchange restrictions, money laundering, etc. We find evidence that microstructure frictions explain part, but not all, of the price differences. For example, the absolute values of price differences are positively related to the bid-ask spread, order book depth and volatility and are negatively related to volume. Price differences are also higher on exchanges with smaller trade sizes, consistent with clientele effects from greater institutional trading. Moreover, impulse responses indicate that shocks to illiquidity and volatility have more persistent effects on absolute price differences between exchange pairs with more retail trading and greater counterparty risk. Finally, the speed of arbitrage and the amount of price discovery is related to the arbitrage frictions. Thus, limits to arbitrage remain relevant even in the context of a homogeneous asset class where many of the frictions in more traditional asset markets are absent. In ongoing work, we quantify this illegality premium using a number of innovative measures of illegality.

Keywords: bitcoin exchanges, limits to arbitrage, digital currency