Optimal Intervention in Economic Networks using Influence Maximization Methods

We consider optimal intervention in the Elliott-Golub-Jackson network model and show that it can be transformed into an influence maximization problem, interpreted as the reverse of a default cascade. Our analysis of the optimal intervention problem extends well-established targeting results to the economic network setting, which requires additional theoretical steps. We prove several results about optimal intervention: it is NP-hard and additionally hard to approximate to a constant factor in polynomial time. In turn, we show that randomizing failure thresholds leads to a version of the problem which is monotone submodular, for which existing powerful approximations in polynomial time can be applied. In addition to optimal intervention, we also show practical consequences of our analysis to other economic network problems: (1) it is computationally hard to calculate expected values in the economic network, and (2) influence maximization algorithms can enable efficient importance sampling and stress testing of large failure scenarios. We illustrate our results on a network of firms connected through input-output linkages inferred from the World Input Output Database

Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often estimate this matrix because complete information on bilateral liabilities is rarely available. As a result, the clearing vector may suffer from estimation errors in the liabilities matrix. We quantify the clearing vector's sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. This allows us to compute upper bounds for the worst case perturbations of the clearing vector in our simple setting. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix. Applying our methodology to a dataset of European banks, we find that perturbations to the relative liabilities can result in economically sizeable differences that could lead to an underestimation of the risk of contagion. Our results are a first step towards allowing regulators to quantify errors in their simulations.Comment: 37 page

Computing the impact of central clearing on systemic risk

The paper uses a graph model to examine the effects of financial market regulations on systemic risk. Focusing on central clearing, we model the financial system as a multigraph of trade and risk relations among banks. We then study the impact of central clearing by a priori estimates in the model, stylized case studies, and a simulation case study. These case studies identify the drivers of regulatory policies on risk reduction at the firm and systemic levels. The analysis shows that the effect of central clearing on systemic risk is ambiguous, with potential positive and negative outcomes, depending on the credit quality of the clearing house, netting benefits and losses, and concentration risks. These computational findings align with empirical studies, yet do not require intensive collection of proprietary data. In addition, our approach enables us to disentangle various competing effects. The approach thus provides policymakers and market practitioners with tools to study the impact of a regulation at each level, enabling decision-makers to anticipate and evaluate the potential impact of regulatory interventions in various scenarios before their implementation

Systemic Risk in Financial Networks

In this dissertation, I have used the network model based approach to study systemic risk in financial networks. In particular, I have worked on generalized extensions of the Eisenberg--Noe [2001] framework to account for realistic financial situations viz. pricing of corporate debt while accounting for network effects, asset liquidation mechanisms during fire sales, dynamic clearing and impact of contingent payments such as insurance and credit default swaps. First, I present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. I demonstrate that the comonotonic setting provides a lower bound to the price of debt under Eisenberg-Noe financial networks with consistent marginal endowments. Special consideration is given to the setting in which firms only invest in a risk-free bond and a common risky asset following a geometric Brownian motion. Next, I develop a framework for price-mediated contagion in financial systems where banks are forced to liquidate assets to satisfy a risk-weight based capital ratio requirement. I consider the case of multiple illiquid assets and develop conditions for the existence and uniqueness of equilibrium prices. I show that the sensitivity analysis of these prices with respect to the system parameters can be written as a fixed point problem and prove the existence and uniqueness of this problem. I also develop a methodology to quantify the cost of regulation faced by different banks in this setting. Numerical case studies are provided to study the application of this model to data. Furthermore, I extend the network model of financial contagion to allow for time dynamics in both discrete and continuous time. Emphasis is placed on the continuous-time framework and its formulation as a differential equation driven by the operating cash flows. I provide results on existence and uniqueness of firm wealths under the discrete and continuous-time models and discuss the financial implications of time dynamics. In particular, I focus on how the dynamic clearing solutions differ from those of the static Eisenberg--Noe model. Finally, I study the implications of contingent payments on the clearing wealth in a network model of financial contagion. I 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, I introduce a dynamic framework and demonstrate how this setting can be applied to problems that were ill-defined in the static framework