When arbitrage related prices share the same underlying asset, there are multiple channels to incorporate new information on the fundamental value of the asset. In this paper, we present an empirical microstructure model to characterize each channel’s price discovery speed. We identify the information sources of price adjustments to separate price discovery from the market responses to liquidity shocks. We assess market efficiency of price discovery visually, by the time paths of price convergence toward the new fundamental value, and numerically, by the magnitude of pricing errors during the price discovery process. We also use our price discovery model to illustrate the structural determinants of two often used price discovery measures: the information share and component share. We show that two measures are static and unable to reveal the underlying price discovery dynamics between markets. Applying our new measures to quotes from spot foreign exchange rates, we find that substantial price discovery of the yen/euro exchange rate occurs through the US dollar. The dollar’s price discovery contribution is positively related to the relative liquidity of the dollar markets versus the cross rate market, and reaches a minimum during the European business hours.