A Repo Model of Fire Sales with VWAP and LOB Pricing Mechanisms

Abstract: We consider a network of banks that optimally choose a strategy of asset liquidations and borrowing in order to cover short term obligations. The borrowing is done in the form of collateralized repurchase agreements, the haircut level of which depends on the total liquidations of all the banks. Similarly the fire-sale price of the asset obtained by each of the banks depends on the amount of assets liquidated by the bank itself and by other banks. By nature of this setup, banks' behavior is considered as a Nash equilibrium. This paper provides two forms for market clearing to occur: through a common closing price and through an application of the limit order book. The main results of this work are providing the existence of maximal and minimal clearing solutions (i.e., liquidations, borrowing, fire sale prices, and haircut levels) as well as sufficient conditions for uniqueness of the clearing solutions.