An Optimization View of Financial Systemic Risk Modeling: Network Effect and Market Liquidity Effect

Abstract

Financial institutions are interconnected directly by holding debt claims against each other (the network channel), and they are also bound by the market when selling assets to raise cash in distressful circumstances (the liquidity channel). The goal of our study is to investigate how these two channels of risk interact to propagate individual defaults to a systemwide catastrophe. We formulate a constrained optimization problem that incorporates both channels of risk, and exploit the problem structure to generate the solution (to the clearing payment vector) via a partition algorithm. Through sensitivity analysis, we are able to identify two key contributors to financial systemic risk, the network multiplier and the liquidity amplifier, and to discern the qualitative difference between the two, confirming that the market liquidity effect has a great potential to cause systemwide contagion. We illustrate the network and market liquidity effects-in particular, the significance of the latter-in the formation of systemic risk with data from the European banking system. Our results contribute to a better understanding of the effectiveness of certain policy interventions. In addition, our algorithm can be used to pin down the changes of the net worth (marked to market) of each bank in the system as the spillover effect spreads, so as to estimate the extent of contagion, and to provide a metric of financial resilience as well. Our framework can also be easily extended to incorporate the effect of bankruptcy costs.

A Bayesian Methodology for Systemic Risk Assessment in Financial Networks

“…Parts of the problem can be overcome by using different input matrices for the KL method, see e.g. Chen et al (2014). Mastromatteo et al (2012) have proposed a message-passing algorithm for estimating interbank exposures.…”

Sensitivity of the Eisenberg-Noe Clearing Vector to Individual Interbank Liabilities

“…We use the same dataset from 2011 of European banks from the European Banking Authority that has been used in previous studies relying on the Eisenberg-Noe framework (Gandy and Veraart (2016), Chen et al (2016)). As in these papers, given the heuristic approach to the dataset, our exercise should be considered to be an illustration of our results and methodology, rather than a realistic full-fledged empirical analysis.…”

“…To populate the remaining key variables of the Eisenberg-Noe model, we therefore first assume, as in Chen et al (2016), that for each bank the interbank liabilities are equal to the interbank assets. Furthermore, we assume that all non-interbank assets are external assets, and the non-interbank liabilities are liabilities to a society sink-node.…”

“…Moreover, extensions of this model have been developed to include effects such as fire sales (e.g. Cifuentes et al (2005), Nier et al (2007), Gai and Kapadia (2010), Chen et al (2016), Amini et al (2016a,b), Weber and Weske (2017), Feinstein (2017a), Feinstein and El-Masri (2017), Feinstein (2017b), Di Gangi et al (2015)), cross-ownership (e.g. Elsinger (2009), Elliott et al (2014), Weber and Weske (2017)), bankruptcy costs (e.g.…”

The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks

“…While we investigate their joint impact, up to now the literature has only been studying these factors separately: Bankruptcy costs are, for example, considered by Elsinger (2009), Elliott et al (2014), Rogers and Veraart (2013), and Glasserman and Young (2015); cross-holdings, e.g., by Elsinger (2009), Elliott et al (2014), Fischer (2014), Suzuki (2002), and Karl and Fischer (2014). Cifuentes et al (2005) incorporate fire sales into the setting of Eisenberg and Noe (2001); their approach is further extended by Amini et al (2013), Chen et al (2016), Gai and Kapadia (2010), Nier et al (2007), and Feinstein (2017). Most of these papers consider only one extension of the basic framework.…”