We propose a novel approach based on the Marshall–Olkin (MO) copula to estimate the impact of systematic and idiosyncratic components on cross-border systemic risk. To use the data on non-failed banks in the suggested method, we consider the time to bank failure as a censored variable. Therefore, we propose a pseudo-maximum likelihood estimation procedure for the MO copula for a Type I censored sample. We derive the log-likelihood function, the copula parameter estimator and the bootstrap confidence intervals. Empirical data on the banking system of three European countries (Germany, Italy and the UK) shows that the proposed censored model can accurately estimate the systematic component of cross-border systemic risk.

Introduction

The 2007–۲۰۰۸ financial crisis has shown how a shock that originates in one country or asset class can quickly propagate to other markets and across borders. A key aspect of financial contagion is given by the linkages among banks. In the Euro area, the cross-border exposures arose as a prominent issue with the European sovereign debt crisis in 2011 and 2012, where large exposure of many EU banks to stressed sovereigns were revealed by the European Banking Authority (EBA, 2013). In a broader perspective, correlated exposures have recently been shown to be a major source of systemic risk. Given the importance of this research field, this paper is focused on systemic risk in the European banking sector. By definition, systemic risk involves a collection of interconnected institutions that have mutually beneficial business relationships through which insolvency can quickly propagate during periods of financial distress Billio, Getmansky, Lo, and Pelizzon (2012). Systemic risk is mainly due to idiosyncratic and systematic shocks (see De Bandt, Hartmann, & Peydró, ۲۰۰۹ and European Central Bank, 2010). The former affects only the health of a single financial institution, while the latter affects the whole economy, e.g. all financial institutions together at the same time. The component of systemic risk due to idiosyncratic shocks is also known as contagion risk in the literature (De Bandt et al., 2009). One of the the main aims of this paper is to propose a new methodological approach for the analysis of systemic risk to jointly model idiosyncratic and systematic shocks. We propose to apply the copula approach to measure systemic risk between the banking sectors of two countries. To our knowledge, the only papers that previously applied copulae to assess banking system stability are Baglioni and Cherubini (2013a), Baglioni and Cherubini (2013b), Straetmans (2010) and Weiss (2012). In other words, the approach is quite novel to the area of banking and systemic risk. The contributions of this paper are twofold. The first of these is to apply the Marshall and Olkin (MO) copula for modelling systemic risk between two countries. The second innovative aspect is how time to failure is considered for non-failed banks as rightcensored.