  We develop a framework for price-mediated contagion in financial systems
where banks are forced to liquidate assets to satisfy a risk-weight based
capital adequacy requirement. In constructing this modeling framework, we
introduce a two-tier pricing structure: the volume weighted average price that
is obtained by any bank liquidating assets and the terminal mark-to-market
price 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 the
existence and uniqueness of clearing prices. We provide a closed-form
representation for the sensitivity of these clearing prices to the system
parameters, and use this result to quantify: (1) the cost of regulation, in
stress scenarios, faced by the system as a whole and the individual banks, and
(2) the value of providing bailouts to consider when such notions are
financially advisable. Numerical case studies are provided to study the
application of this model to data.
