An integrated model for fire sales and default contagion

Abstract

Fire sales and default contagion are two of the main drivers of systemic risk in financial networks. While default contagion spreads via direct balance sheet exposures between institutions, fire sales describe iterated distressed selling of assets and their associated decline in price which impacts all institutions invested in these assets. That is, institutions are indirectly linked if they have overlapping asset portfolios. In this paper, we develop a model that helps us understand the joint effect of the two contagion channels and investigate structures of financial systems that promote or hinder the spread of an initial local shock. We first consider the contagion process for an explicitly given system and then derive our main results for random ensembles of systems whose macroscopic statistical characteristics of defining parameters are close to each other. In particular, we model direct exposures by means of a random graph. Our approach ensures robustness to local uncertainties and changes in the system. We characterize resilient and non-resilient system structures by criteria that can be used by regulators to assess system stability. Moreover, we provide explicit capital requirements that secure the financial system against the joint impact of fire sales and default contagion. Keywords Systemic risk • Financial contagion • Asset fire sales • Price-mediated contagion • Default contagion • Capital requirements JEL Classification C02 • E61 • G01 B Thilo Meyer-Brandis

Fire Sales, Default Cascades and Complex Financial Networks

“…We refer to e.g., [27,30,53] for a more detailed review of the literature on fire sales. Our work complements a number of recent papers that integrate the fire sales loss into the cascades of insolvencies in interbank networks, see e.g., [7,16,20,23,26,34,38,42,50,56]. In particular, [34] uses and extends the methods developed in [5,8] to provide a resilience condition for the financial network in an integrated model of fire sales and default contagion, in the context of inhomogeneous random graphs.…”

“…Namely, in the notations above, starting from a small fraction of institutions representing the fundamental defaults, the financial network is said to be resilient if lim Ñ0 z ‹ ppq " 0. We refer to [3,5,34] for the resilience conditions.…”

“…Now combine (34), (35) and (36) and by Remark 3.9, we conclude that φ n pp ‹ n q " φ n pp ‹ n q ´φn pp n q " p ‹ n ´p n ´pgpf Γ pz ‹ ppq; pq `op1qqrpf 1 Γ pz ‹ ppq; pq `op1qq p´pf 1 W pz ‹ ppq; pq ´1f 2 W pz ‹ ppq; pq `op1qq `pf 2 Γ pz ‹ ppq; pq `op1qqspp ‹ n ´p n q " pρ `op1qqpp ‹ n ´p n q.…”

When do you Stop Supporting your Bankrupt Subsidiary? A Systemic Risk Perspective

“…Specification of financial shock: Following previous literature on contagion in financial networks Amini et al (2016a); Detering et al ( , 2021Detering et al ( , 2020a we now consider a network that has a-priory no defaults, meaning P((C 1 , C 2 ) ∈ D J,1 ∪D J,2 ) = 0. We then apply a small shock to the system.…”

“…Another stream of literature considers contagion effects in random networks (Gai and Kapadia (2010b); Amini et al (2016a); Detering et al ( , 2020b, and Detering et al (2021) for an extension incorporating fire sales). In these papers, asymptotic results (as the number of banks increases to infinity) are facilitated to determine the final damage to the system after some initial shock hits some vertices.…”