Network Valuation Model: a general framework for systemic risk in financial networks
The literature on systemic risk in financial networks has grown extensively in the recent years leading to many developments. However, an important gap has emerged between the stream of works based on Eisenberg-Noe, in which the evaluation of claims is carried out ex-post, and the practical necessity to take into account the ex-ante uncertainty on the external assets of financial institutions. Another gap has also emerged between the predictions of the counterfactual exercises based on the Eisenberg-Noe approach and the experience from policy makers and practitioners about the role of mark-to-market evaluation of claims. We report on a series of very recent results that contribute to fill in these gaps. In particular, we show analytically why in the exercises based on Eisenberg-Noe the estimation of second round effects are typically very small and why, contrary to the common understanding, most network effects are actually ruled out by construction. Further, we describe a novel framework for network valuation (NEVA) that combines the endogenous calculation of recovery rates with an ex-ante valuation of expected values of claims. Remarkably, both the Eisenberg-Noe approach and the DebtRank approach appear as special cases of the general framework. We characterize the existence and uniqueness of the solutions of the valuation problem and we provide sufficient conditions for the convergence of the algorithm to compute the maximal solution. As an application, we report on ongoing work on ECB supervisory data of the largest Euro Area banks. the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution. As an application we results the results of ongoing analysis of exposure of largest Euro Area banks