Decentralized Clearing in Financial Networks

Abstract

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. Abstract 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.

An Axiomatization of the Proportional Rule in Financial Networks

“…As discussed in Example 2.4, the use of the proportional rule implicitly takes a long-run perspective by assuming that the entire endowments of a defaulting bank can be used to make payments to its creditors. This assumption is less restrictive than it may seem at first sight as it follows from the analysis in Csóka and Herings (2018) that the final payment matrix is not sensitive to the exact timing of the payments. It is therefore not needed that the liquidation of a bankrupt bank takes place immediately and the model is consistent with the case where the unwinding of a defaulting bank's assets can take a substantial amount of time.…”

“…The fact that a greatest solution exists follows from an extension of arguments in Eisenberg and Noe (2001) and Csóka and Herings (2018) that are based on an application of Tarski's fixed point theorem. The bankruptcy rule b 6 obviously satisfies claims boundedness, limited liability, priority of creditors, and impartiality.…”

A Note on Uniqueness of Clearing Prices in Financial Systems

“…Crucial assumption in Eisenberg and Noe (2001) is the principle of proportionality; in case of a defaulting node, the corresponding clearing price is shared proportional to the liabilities of the node to the others. Groote- Schaarsberg et al (2018) and Csóka and Herings (2018) show in a continuous and discrete setting, respectively, that the assumption of proportionality in solving defaulting situations is not crucial at all, as the idea of clearing prices is still meaningful for other bankruptcy rules. In accordance with Eisenberg and Noe (2001) both aforemen-tioned works stress the fact that clearing prices may not be unique -but the resulting allocation is.…”

The Triangle of ICOs, Bitcoin and Ethereum: A Time Series Analysis

“…Our study contributes to research on cryptocurrencies (e.g., Boehme et al 2015;Cheah and Fry 2015; Urquhart 2018), ICOs (Adhami et al, 2018), and how these transformative innovations are used to finance blockchain-based ventures (Csóka and Herings 2017;Iansiti and Lakhani 2017).…”