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The description of the empirical structure of interbank networks constitutes an important field of study since network theory can be used as a powerful tool to assess the resilience of financial systems and their robustness against failures. On the other hand, the development of reliable models of interbank market structure is relevant as they can be used to analyze systemic risk in the absence of transaction data or to test statistical hypotheses regarding network properties. Based on a detailed data-driven analysis of bank positions (assets and liabilities) taken from the Bankscope database, we here develop a minimal, stochastic, agent-based network model that accounts for the basic topology of interbank networks reported in the literature. The main assumption of our model is that loans between banks attempt to compensate assets and liabilities at each time step, and the quarterly aggregation of daily networks yields structures comparable with those observed in empirical studies. In particular, our model is able to qualitatively reproduce degree distributions, the distributions of transactions by value and transactions by volume, the distribution of exposures (link weights), the correlations with nearest-neighbor averages, and the local structure (clustering coefficient). As our simple model captures the overall structure of empirical networks, it can thus be used as a null model for testing hypotheses relative to other specific properties of interbank networks.