We develop a monetary model that incorporates over-the-counter (OTC) asset trade. After agents have made their money holding decisions, they receive an idiosyncratic shock that affects their valuation for consumption and, hence, for the unique liquid asset, namely money. Subsequently, agents can choose whether they want to enter the OTC market in order to sell assets and thus boost their liquidity or to buy assets and thus provide liquidity to other agents. In our model, inflation affects not only the money holding decisions of agents, as is standard in monetary theory, but also the entry decision of these agents in the financial market. We use our framework to study the effect of inflation on welfare, asset prices and OTC trade volume. In contrast to most monetary models, which predict a negative relationship between inflation and welfare, we find that inflation can be welfare improving within a certain range, because it mitigates a search externality that agents impose on one another when they make their OTC market entry decision. Also, an increase in the holding cost of money will lead to a decrease in asset prices, a regularity that is well documented in the data and often considered anomalous.