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We develop a framework for price-mediated contagion in financial systemswhere banks are forced to liquidate assets to satisfy a risk-weight basedcapital adequacy requirement. In constructing this modeling framework, weintroduce a two-tier pricing structure: the volume weighted average price thatis obtained by any bank liquidating assets and the terminal mark-to-marketprice used to account for all assets held at the end of the clearing process.We consider the case of multiple illiquid assets and develop conditions for theexistence and uniqueness of clearing prices. We provide a closed-formrepresentation for the sensitivity of these clearing prices to the systemparameters, and use this result to quantify: (1) the cost of regulation, instress scenarios, faced by the system as a whole and the individual banks, and(2) the value of providing bailouts to consider when such notions arefinancially advisable. Numerical case studies are provided to study theapplication of this model to data.

Price mediated contagion through capital ratio requirements with VWAP liquidation prices