Physica A 442 (2016) 329–342 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Systemic risk measures ✩ Solange Maria Guerra a , Thiago Christiano Silva a , Benjamin Miranda Tabak b,∗ , Rodrigo Andrés de Souza Penaloza c , Rodrigo César de Castro Miranda d,c a Research Department, Banco Central do Brasil, Brazil b Universidade Católica de Brasília, Brazil c Universidade de Brasília, Brazil d Banco Central do Brasil, Brazil highlights • We construct systemic risk measures. • We use a Contingent Claims and a complex networks Approach. • Our indicators capture the stress dependency structure. • The method helps identify Systemically Important Banks. • We can track the evolution of systemic risk over time. article info Article history: Received 23 February 2015 Received in revised form 13 July 2015 Available online 24 September 2015 Keywords: Systemic risk Joint default indicator Clusters abstract In this paper we present systemic risk measures based on contingent claims approach and banking sector multivariate density. We also apply network measures to analyze bank common risk exposure. The proposed measures aim to capture credit risk stress and its potential to become systemic. These indicators capture not only individual bank vulnerability, but also the stress dependency structure between them. Furthermore, these measures can be quite useful for identifying systemically important banks. The empirical results show that these indicators capture with considerable fidelity the moments of increasing systemic risk in the Brazilian banking sector in recent years. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Since the early 19th century it is well known that one bank may jeopardize the soundness and/or confidence of the whole financial sector [1]. The advances in information technology and computing sectors, among other factors, have paved the way for financial innovation and strong and continuous integration between global and local financial markets. As a consequence, the complexity and systemic consequences of risk materialization have largely increased over time. Unlike other types of risk to which financial institutions are exposed, systemic risk is much more recognized for its effects rather than its causes. Systemic risk generally occurs in many distinct forms and is the result of the interconnection ✩ The views expressed in the paper are those of the authors and not necessarily reflect those of the Banco Central do Brasil. We wish to thank Editor H. Stanley and the anonymous referees for the constructive comments, which have helped in improving the paper. ∗ Corresponding author. E-mail addresses: solange.guerra@bcb.gov.br (S.M. Guerra), thiago.silva@bcb.gov.br (T.C. Silva), Benjaminm.tabak@gmail.com (B.M. Tabak), penaloza@unb.br (R.A. de Souza Penaloza), rodrigo.c.miranda@gmail.com (R.C. de Castro Miranda). http://dx.doi.org/10.1016/j.physa.2015.09.013 0378-4371/© 2015 Elsevier B.V. All rights reserved.