Risk In Financial Networks Research Articles

Quantum computing reduces systemic risk in financial networks

In highly connected financial networks, the failure of a single institution can cascade into additional bank failures. This systemic risk can be mitigated by adjusting the loans, holding shares, and other liabilities connecting institutions in a way that prevents cascading of failures. We are approaching the systemic risk problem by attempting to optimize the connections between the institutions. In order to provide a more realistic simulation environment, we have incorporated nonlinear/discontinuous losses in the value of the banks. To address scalability challenges, we have developed a two-stage algorithm where the networks are partitioned into modules of highly interconnected banks and then the modules are individually optimized. We developed a new algorithms for classical and quantum partitioning for directed and weighed graphs (first stage) and a new methodology for solving Mixed Integer Linear Programming problems with constraints for the systemic risk context (second stage). We compare classical and quantum algorithms for the partitioning problem. Experimental results demonstrate that our two-stage optimization with quantum partitioning is more resilient to financial shocks, delays the cascade failure phase transition, and reduces the total number of failures at convergence under systemic risks with reduced time complexity.

The drivers of systemic risk in financial networks: a data-driven machine learning analysis

The purpose of this paper is to assess the role of financial variables and network topology as determinants of systemic risk (SR). The SR, for different levels of the initial shock, is computed for institutions in the Brazilian interbank market by applying the differential DebtRank methodology. The financial institution(FI)-specific determinants of SR are evaluated through two machine learning techniques: XGBoost and random forest. Shapley values analysis provided a better interpretability for our results. Furthermore, we performed this analysis separately for banks and credit unions. We have found the importance of a given feature in driving SR varies with i) the level of the initial shock, ii) the type of FI, and iii) the dimension of the risk which is being assessed – i.e., potential loss caused by (systemic impact) or imputed to (systemic vulnerability) the FI. Systemic impact is mainly driven by topological features for both types of FIs. However, while the importance of topological features to the prediction of systemic impact of banks increases with the level of the initial shock, it decreases for credit unions. Concerning systemic vulnerability, this is mainly determined by financial features, whose importance increases with the initial shock level for both types of FIs.

Solvency contagion risk in the Chinese commercial banks’ network

We study a model for solvency contagion risk in financial networks, which allows the spread of contagion to occur before the point of default. This model can quantify systemic contagion loss through stress testing. In the usual case, only the total liabilities and total assets in such a network can be observed. To overcome this problem, we adopt a Gibbs sampling method to generate samples of the interbank liabilities matrix conditioning on the edges. This methodological approach is applied to a Chinese commercial bank network. Our results show that the systemic contagion losses of this network are highly dependent on the perceived exogenous recovery rate, especially when the external shock is strong. In the stress testing, we also analyze solvency contagion losses due to equity and exposure by decomposing the changes in contagion losses from 2008 to 2018 into several individual parts. We find that the contagion losses of the network exhibit a downward trend, indicating a more robust and stable network.

Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk

The damage of the novel Coronavirus disease (COVID-19) is reaching an unprecedented scale. There are numerous classical epidemiology models trying to quantify epidemiology metrics. To forecast epidemics, classical approaches usually need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the emergence of a pandemic state by studying the Forman–Ricci and Ollivier–Ricci network curvatures. Discrete Ollivier–Ricci curvature has been used successfully to forecast risk in financial networks and we suggest that those results can provide analogous results for COVID-19 epidemic time-series. We first compute both curvatures in a toy-model of epidemic time-series with delays, which allows us to create epidemic networks. We also compared our results to classical network metrics. By doing so, we are able to verify that the Ollivier–Ricci and Forman–Ricci curvatures can be a parameter-free estimate for identifying a pandemic state in the simulated epidemic. On this basis, we then compute both Forman–Ricci and Ollivier–Ricci curvatures for real epidemic networks built from COVID-19 epidemic time-series available at the World Health Organization (WHO). This approach allows us to detect early warning signs of the emergence of the pandemic. The advantage of our method lies in providing an early geometrical data marker for the pandemic state, regardless of parameter estimation and stochastic modelling. This work opens the possibility of using discrete geometry to study epidemic networks.

Systemic Risk in Financial Networks: A Survey

We provide an overview of the relationship between financial networks and systemic risk. We present a taxonomy of different types of systemic risk, differentiating between direct externalities between financial organizations (e.g., defaults, correlated portfolios, fire sales), and perceptions and feedback effects (e.g., bank runs, credit freezes). We also discuss optimal regulation and bailouts, measurements of systemic risk and financial centrality, choices by banks regarding their portfolios and partnerships, and the changing nature of financial networks.

Systemic Risk in Financial Networks: A Survey

We provide an overview of the relationship between financial networks and systemic risk. We present a taxonomy of different types of systemic risk, differentiating between direct externalities between financial organizations (e.g., defaults, correlated portfolios and firesales), and perceptions and feedback effects (e.g., bank runs, credit freezes). We also discuss optimal regulation and bailouts, measurements of systemic risk and financial centrality, choices by banks' regarding their portfolios and partnerships, and the changing nature of financial networks.

An integrated model for fire sales and default contagion

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.

Compound Poisson models for weighted networks with applications in finance

We develop a modelling framework for estimating and predicting weighted network data. The edge weights in weighted networks often arise from aggregating some individual relationships between the nodes. Motivated by this, we introduce a modelling framework for weighted networks based on the compound Poisson distribution. To allow for heterogeneity between the nodes, we use a regression approach for the model parameters. We test the new modelling framework on two types of financial networks: a network of financial institutions in which the edge weights represent exposures from trading Credit Default Swaps and a network of countries in which the edge weights represent cross-border lending. The compound Poisson Gamma distributions with regression fit the data well in both situations. We illustrate how this modelling framework can be used for predicting unobserved edges and their weights in an only partially observed network. This is for example relevant for assessing systemic risk in financial networks.

Compound Poisson Models for Financial Networks

We develop a modelling framework for estimating and predicting weighted network data. The edge weights in weighted networks often arise from aggregating some individual relationships between the nodes. Motivated by this, we introduce a modelling framework for weighted networks based on the compound Poisson distribution. To allow for heterogeneity between the nodes, we use a regression approach for the model parameters. We test the new modelling framework on two types of financial networks: a network of financial institutions in which the edge weights represent exposures from trading Credit Default Swaps and a network of countries in which the edge weights represent cross-border lending. The compound Poisson Gamma distributions with regression fit the data well in both situations. We illustrate how this modelling framework can be used for predicting unobserved edges and their weights in an only partially observed network. This is for example relevant for assessing systemic risk in financial networks.

Non-Performing Loans and Systemic Risk in Financial Networks

In this paper we study the implications of non-performing loans (NPLs) for financial stability using a network-based approach. We start by combining loan-level data from DealScan and firm-level data from Orbis to reconstruct the empirical global financial network in the period 1991-2016 and identify a series of stylized facts. Based on these findings, we develop a model in which two types of agents, banks and firms, are linked in a network by their reciprocal claims and analyze how an increase in NPLs affects the stability of the system. We study the model analytically and with numerical simulations, deriving a synthetic measure of systemic risk and quantifying the threshold level of NPLs that triggers a systemic crisis. Our model shows that there exist a level of connectivity that maximizes the fragility of the financial system and that small changes in the initial NPLs shock can have very different consequences at the aggregate level.

Impact of contingent payments on systemic risk in financial networks

In this paper we study the implications of contingent payments on the clearing wealth in a network model of financial contagion. We consider an extension of the Eisenberg–Noe financial contagion model in which the nominal interbank obligations depend on the wealth of the firms in the network. We first consider the problem in a static framework and develop conditions for existence and uniqueness of solutions as long as no firm is speculating on the failure of other firms. In order to achieve existence and uniqueness under more general conditions, we introduce a dynamic framework. We demonstrate how this dynamic framework can be applied to problems that were ill-defined in the static framework.

A dynamic approach merging network theory and credit risk techniques to assess systemic risk in financial networks

The interconnectedness of financial institutions affects instability and credit crises. To quantify systemic risk we introduce here the PD model, a dynamic model that combines credit risk techniques with a contagion mechanism on the network of exposures among banks. A potential loss distribution is obtained through a multi-period Monte Carlo simulation that considers the probability of default (PD) of the banks and their tendency of defaulting in the same time interval. A contagion process increases the PD of banks exposed toward distressed counterparties. The systemic risk is measured by statistics of the loss distribution, while the contribution of each node is quantified by the new measures PDRank and PDImpact. We illustrate how the model works on the network of the European Global Systemically Important Banks. For a certain range of the banks’ capital and of their assets volatility, our results reveal the emergence of a strong contagion regime where lower default correlation between banks corresponds to higher losses. This is the opposite of the diversification benefits postulated by standard credit risk models used by banks and regulators who could therefore underestimate the capital needed to overcome a period of crisis, thereby contributing to the financial system instability.

Systemic Centrality and Systemic Communities in Financial Networks

A systemically important firm could be too-connected-to-fail and/or too-important-to-fail, two properties which centrality measures and community detection methods can capture respectively. This paper examines the performance of these measures in a variance decomposition global financial network. Too-connected-to-fail risk and vulnerability rankings are quite robust to the choice of centrality measure. The PageRank centrality measure, however, does not seem as suitable for assessing vulnerabilities. Two community identification methods, edge betweenness and the map equation (Infomap) were used to identify systemic communities, which in turn capture the too-important-to-fail dimension of systemic risk. The first method appears more robust to different weighting schemes but tends to isolate too many firms. The second method exhibits the opposite characteristics. Overall, the analysis suggests that centrality measures and community identification methods complement each other for assessing systemic risk in financial networks.

Systemic centrality and systemic communities in financial networks

A systemically important firm could be too-connected-to-fail and/or too-important-to-fail, two properties which centrality measures and community detection methods can capture respectively. This paper examines the performance of these measures in a variance decomposition global financial network. Too-connected-to-fail risk and vulnerability rankings are quite robust to the choice of centrality measure. The PageRank centrality measure, however, does not seem as suitable for assessing vulnerabilities. Two community identification methods, edge betweenness and the map equation (Infomap) were used to identify systemic communities, which in turn capture the too-important-tofail dimension of systemic risk. The first method appears more robust to di erent weighting schemes but tends to isolate too many firms. The second method exhibits the opposite characteristics. Overall, the analysis suggests that centrality measures and community identification methods complement each other for assessing systemic risk in financial networks.

Centralized netting in financial networks

Abstract We consider how the introduction of centralized netting in financial networks affects total netted exposures between counterparties. In some cases there is a trade-off: centralized netting increases the expectation of net exposures, but reduces the variance. We show that the set of networks for which expected net exposures decreases is a strict subset of those for which the variance decreases, so the trade-off can only be in one direction. For some network structures, introducing centralized netting is never beneficial to dealers unless sufficient weight is placed on reductions in variance. This may explain why, in the absence of regulation, traders in a derivatives network do not develop central clearing. Our results can be used to estimate margin requirements and counterparty risk in financial networks. We also provide techniques to evaluate the robustness of our results to behavioral responses to the introduction of centralized netting.

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

The paper presents a comprehensive model of a banking system that integrates network effects, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium. The number of defaults corresponding to the greatest price-payment equilibrium is analyzed in several comparative case studies. These illustrate the individual and joint impact of interbank liabilities, bankruptcy costs, fire sales and cross-holdings on systemic risk. We study policy implications and regulatory instruments, including central bank guarantees and quantitative easing, the significance of last wills of financial institutions, and capital requirements.

Optimal Monitoring and Mitigation of Systemic Risk in Financial Networks

This paper studies the problem of optimally allocating a cash injection into a financial system in distress. Given a one-period borrower-lender network in which all debts are due at the same time and have the same seniority, we address the problem of allocating a fixed amount of cash among the nodes to minimize the weighted sum of unpaid liabilities. Assuming all the loan amounts and asset values are fixed and that there are no bankruptcy costs, we show that this problem is equivalent to a linear program. We develop a duality-based distributed algorithm to solve it which is useful for applications where it is desirable to avoid centralized data gathering and computation. Since some applications require forecasting and planning for a wide variety of different contingencies, we also consider the problem of minimizing the expectation of the weighted sum of unpaid liabilities under the assumption that the net external asset holdings of all institutions are stochastic. We show that this problem is a two-stage stochastic linear program. To solve it, we develop two algorithms based on Monte Carlo sampling: Benders decomposition algorithm and projected stochastic gradient descent. We show that if the defaulting nodes never pay anything, the deterministic optimal cash injection allocation problem is an NP-hard mixed-integer linear program. However, modern optimization software enables the computation of very accurate solutions to this problem on a personal computer in a few seconds for network sizes comparable with the size of the US banking system. In addition, we address the problem of allocating the cash injection amount so as to minimize the number of nodes in default. For this problem, we develop two heuristic algorithms: a reweighed l1 minimization algorithm and a greedy algorithm. We illustrate these two algorithms using three synthetic network structures for which the optimal solution can be calculated exactly. We also compare these two algorithms on three types random networks which are more complex.

Systemic Risk and the Dynamics of Financial Networks

This paper has two main objectives: first, to provide a formal definition of endogenous systemic risk that is firmly grounded in equilibrium dynamics of financial networks; and second, to construct a discounted stochastic game (DSG) model of the emergence of equilibrium network dynamics that fully takes into account the feedback between network structure, strategic behavior, and risk. Based on our definition of systemic risk we also propose a formal definition of tipping points. Using these tools we then provide a strategic approach to making global assessments of systemic risk in financial networks. Our approach is based on three key facts: (1) the equilibrium dynamics which emerge from the game of network formation generate finitely many disjoint basins of attraction as well as finitely many ergodic measures (implying that, starting from any financial network, in finite time with probability one, the dynamic sequence of financial networks arrives at one of these basins and once there stays there), (2) each basin of attraction is homogenous with respect to its default characteristics (meaning that if a basin contains states having a particular set of defaulted players, then all states contained in this basin have the same set of defaulted players), and (3) the unique profile of basins generated by the equilibrium dynamics carries with it a unique set of tipping points (special states) - and these tipping points provide an early warning of network failure.

Elimination of systemic risk in financial networks by means of a systemic risk transaction tax

Financial markets are exposed to systemic risk (SR), the risk that a major fraction of the system ceases to function, and collapses. It has recently become possible to quantify SR in terms of underlying financial networks where nodes represent financial institutions, and links capture the size and maturity of assets (loans), liabilities and other obligations, such as derivatives. We demonstrate that it is possible to quantify the share of SR that individual liabilities within a financial network contribute to the overall SR. We use empirical data of nationwide interbank liabilities to show that the marginal contribution to overall SR of liabilities for a given size varies by a factor of a thousand. We propose a tax on individual transactions that is proportional to their marginal contribution to overall SR. If a transaction does not increase SR, it is tax-free. With an agent-based model (ABM) (CRISIS macro-financial model), we demonstrate that the proposed ‘Systemic Risk Tax’ (SRT) leads to a self-organized restructuring of financial networks that are practically free of SR. The SRT can be seen as an insurance for the public against costs arising from cascading failure. ABM predictions are shown to be in remarkable agreement with the empirical data and can be used to understand the relation of credit risk and SR.

Evolutionary systemic risk: Fisher information flow metric in financial network dynamics

Recently the topic of financial network dynamics has gained renewed interest from researchers in the field of empirical systemic risk measurements. We refer to this type of network analysis as information flow networks analysis (IFNA). This paper proposes a new method that applies Fisher information metric to the evolutionary dynamics of financial networks using IFNA. Our paper is the first to apply the Fisher information metric to a set of financial time series. We introduce Evolution Index (EI) as a measure of systemic risk in financial networks. It is shown, for concrete networks with actual data of several stock markets, that the EI can be implemented as a measure of fitness of the stock market and as a leading indicator of systemic risk.