What is the Price for Lending in Financial Networks?

Béni Egressy, Andreas Plesner, Roger Wattenhofer

Abstract: We explore the impact of the network structure on lending in financial networks. Specifically, we ask what price agents should charge when lending to each other and how much this price should depend on the network topology. We begin with a simple model that incorporates debts and external assets. We then extend this model to account for default costs as well. In the simplest model, all agents have an identical break-even price and all agents offering this price is a Nash equilibrium. This price is \(\frac{1}{r_b}\) per unit of money, where \(r_b\) is the recovery rate of the borrower. In the extended model, with default costs, agents can have different break-even prices. Yet surprisingly, we find that a Nash equilibrium is for all agents to bid the same price of \(\frac{L_b}{r_b L_b - (1 - \alpha ) d}\), where \(L_b\) is the total debt of the borrower, \((1 - \alpha )\) is the default loss rate, and d is the amount being borrowed. Our study shows that network location does not impact debt pricing. However, the overall network topology plays a crucial role in the stability of the network regarding new debt contracts. We show that a single debt contract can push almost every agent in a network into default. Moreover, requiring agents to hold a fixed fraction of their liabilities in liquid assets does not rule out such scenarios.