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In this paper, we introduce a model of interbank trading with memory. The memory mechanism is used to introduce a proxy of trust in the model. The key idea is that a lender, having lent many times to a borrower in the past, is more likely to lend to that borrower again in the future than to other borrowers, with which the lender has never (or has infrequently) interacted. The core of the model depends on only two parameters, which are common to all lenders: one is w and it is representing the attractiveness of borrowers, the other one is Q and it represents the memory of lenders in their assessment of counter parties. The stronger the w parameter, the more random the matching results between lenders and borrowers. The stronger the Q parameter, the more stable the trading relationships become. Model outcomes and real money market data are compared through a variety of measures that describe the structure and …