Interest rates parity and no arbitrage as equivalent equilibrium conditions in the international financial assets and goods markets

• We provide conditions for the existence of equilibrium in both international financial assets and goods markets.
• We introduce a weaker notion of Uncovered Interest (rate) Parity (UIP) and we show its equivalence to the no-arbitrage condition in the international financial markets.
• We introduce the concept of common no arbitrage and we show its equivalence to the UIP.
• These results bridge concepts of no arbitrage in general equilibrium theory and financial microeconomics, and interest parity in international financial macroeconomics.
• The UIP is required for the existence of equilibrium in both international financial assets and goods markets and for the existence of the Law of One Price.

In this paper, we consider a two-period consumption model with many financial assets. In the spirit of Hart (1974), consumers purchase financial assets in period 00 and consume in period 11. We differ from Hart by considering that each agent is a country. We provide conditions for the existence of an equilibrium in both international financial assets and goods markets.First, we introduce a weaker notion of Uncovered Interest (rate) Parity (UIP) called Weak Uncovered Interest (rate) Parity (WUIP), and we show its equivalence to the no-arbitrage condition in the international financial markets.Second, we introduce the concept of common no arbitrage and we show its equivalence to the UIP.These results bridge concepts of no arbitrage in general equilibrium theory and financial microeconomics, and of interest parity in international financial macroeconomics. In a multi-country model with many currencies and only one good, we introduce a country-specific conversion rate which transforms the returns on assets valued in local currency into units of physical good. We define also the exchange rates between currencies of different countries. The UIP is required for the existence of an equilibrium in both international financial assets and goods markets and for the existence of the Law of One Price.