Network Valuation in Financial Systems

In this work we introduce an interbank network with stochastic dynamics subject to an endogenous notion of distress contagion that accounts for worries about future defaults within the network. Specifically, this entails a forward-backward approach to the equilibrium dynamics, enforced by a mark-to-market valuation adjustment for interbank claims, whereby the conditional probabilities of future defaults are required to determine today's balance sheets. Distinct from static mo...

This paper investigates whether a financial system can be made more stable if financial institutions share risk by exchanging contingent convertible (CoCo) debt obligations. The question is framed in a financial network model of debt and equity interlinkages with the addition of a variant of the CoCo that converts continuously when a bank's equity-debt ratio drops to a trigger level. The main theoretical result is a complete characterization of the clearing problem for the in...

We consider networks of banks with assets and liabilities. Some banks may be insolvent, and a central bank can decide which insolvent banks, if any, to bail out. We view bailouts as an optimization problem where the central bank has given resources at its disposal and an objective it wants to maximize. We show that under various assumptions and for various natural objectives this optimization problem is NP-hard, and in some cases even hard to approximate. Furthermore, we also...

We report a study of a stylized banking cascade model investigating systemic risk caused by counter party failure using liabilities and assets to define banks' balance sheet. In our stylized system, banks can be in two states: normally operating or distressed and the state of a bank changes from normally operating to distressed whenever its liabilities are larger than the banks' assets. The banks are connected through an interbank lending network and, whenever a bank is distr...

A minimal stochastic dynamical model of the interbank network is introduced, with linear interactions mediated by an integral of recent variations. Defining stress as the variance over the banks' states, the interaction correction to the stress expectation is derived and studied on the short-medium timescale in an expansion. It is shown that, while different interaction matrices can amplify or absorb fluctuations, on average interactions increase the stress expectation. More ...

Since the latest financial crisis, the idea of systemic risk has received considerable interest. In particular, contagion effects arising from cross-holdings between interconnected financial firms have been studied extensively. Drawing inspiration from the field of complex networks, these attempts are largely unaware of models and theories for credit risk of individual firms. Here, we note that recent network valuation models extend the seminal structural risk model of Merton...

This paper provides a general framework for modeling financial contagion in a system with obligations in multiple illiquid assets (e.g., currencies). In so doing, we develop a multi-layered financial network that extends the single network of Eisenberg and Noe (2001). In particular, we develop a financial contagion model with fire sales that allows institutions to both buy and sell assets to cover their liabilities in the different assets and act as utility maximizers. We p...

The question of how to stabilize financial systems has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beale et al. ("Individual versus systemic risk and the regulator's dilemma", Proc Natl Acad Sci USA 108: 12647-12652, 2011) demonstrated that higher portfolio diversity among banks would reduce systemic risk by decreasing the risk of simultaneous defaults at the expense of a higher likelihood of individual defaults. In practice, how...

We study the incentives of banks in a financial network, where the network consists of debt contracts and credit default swaps (CDSs) between banks. One of the most important questions in such a system is the problem of deciding which of the banks are in default, and how much of their liabilities these banks can pay. We study the payoff and preferences of the banks in the different solutions to this problem. We also introduce a more refined model which allows assigning priori...

This work proposes an augmented variant of DebtRank with uncertainty intervals as a method to investigate and assess systemic risk in financial networks, in a context of incomplete data. The algorithm is tested against a default contagion algorithm on three ensembles of networks with increasing density, estimated from real-world banking data related to the largest 227 EU15 financial institutions indexed in a stock market. Results suggest that DebtRank is capable of capturing ...