# Decentralized Clearing in Financial Networks

Working paper

Issue number:

RM/16/005

Series:

GSBE Research Memoranda

Publisher:

Maastricht University School of Business and Economics

Year:

2016

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents’ assets might be insufficient to satisfy their
liabilities leading to defaults. We assume the primitives to be denoted in some unit
of account. In case of default, bankruptcy rules are used to specify the way agents are
going to be rationed. We present a convenient representation of bankruptcy rules.
A clearing payment matrix is a payment matrix consistent with the prevailing
bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing
payment matrices and the corresponding values of equity are not uniquely determined.
We provide bounds on the possible levels equity can take. We analyze
decentralized clearing processes and show the convergence of any such process in
finitely many steps to the least clearing payment matrix. When the unit of account
is sufficiently small, all decentralized clearing processes lead essentially to the same
value of equity as a centralized clearing procedure. As a policy implication, it is not
necessary to collect and process all the sensitive data of all the agents simultaneously
and run a centralized clearing procedure.