We develop a theoretical model of international trade pricing in which individual exporters and importers bargain over the transaction price and exposure to exchange rate fluctuations. We find that the choice of price and invoicing currency reflects the full market structure, including the extent of fragmentation and the degree of heterogeneity across importers and across exporters. Our study shows that a party has a higher effective bargaining weight when it is large or more risk tolerant. A higher effective bargaining weight of importers relative to exporters in turn translates into lower import prices and greater exchange rate pass-through into import prices. We show the range of price and invoicing outcomes that arise under alternative market structures. Such structures matter not only for the outcome of specific exporter-importer transactions, but also for aggregate variables such as the average price, the average choice of invoicing currency, and the correlation between invoicing currency and the size of trade transactions.