Fractional Claims Trades and Donations in Financial Networks

TL;DR

This paper investigates fractional claims trading and donations in financial networks, demonstrating polynomial-time algorithms for optimal creditor-positive trades and highlighting computational hardness in more complex scenarios with default costs.

Contribution

It introduces a framework for fractional claims trading and donations, providing polynomial-time algorithms for optimal trades and analyzing computational hardness in networks with default costs.

Findings

Optimal creditor-positive trades can be computed in polynomial time.

In networks with default costs, trades that improve assets are NP-hard to compute.

Efficient algorithms exist for optimal donations to multiple banks in networks without default costs.

Abstract

Exploring measures to improve financial networks and mitigate systemic risks is an ongoing challenge. We study claims trading, a notion defined in Chapter 11 of the U.S. Bankruptcy Code. For a bank $v$ in distress and a trading partner $w$, the latter is taking over some claims of $v$ and in return giving liquidity to $v$. The idea is to rescue $v$ (or mitigate contagion effects from $v$'s insolvency). We focus on the impact of trading claims fractionally, when $v$ and $w$ can agree to trade only part of a claim. In addition, we study donations, in which $w$ only provides liquidity to $v$. They can be seen as special claims trades. When trading a single claim or making a single donation in networks without default cost, we show that it is impossible to strictly improve the assets of both banks $v$ and $w$. Since the goal is to rescue $v$ in distress, we study creditor-positive trades, in which $v$ improves and $w$ remains indifferent. We show that an optimal creditor-positive trade that maximizes the assets of $v$ can be computed in polynomial time. It also yields a (weak) Pareto-improvement for all banks in the entire network. In networks with default cost, we obtain a trade in polynomial time that weakly Pareto-improves all assets over the ones resulting from the optimal creditor-positive trade. We generalize these results to trading multiple claims for which $v$ is the creditor. Instead, when trading claims with a common debtor $u$, we obtain NP-hardness results for computing trades in networks with default cost that maximize the assets of the creditors and Pareto-improve the assets in the network. Similar results apply when $w$ donates to multiple banks in networks with default costs. For networks without default cost, we give an efficient algorithm to compute optimal donations to multiple banks.