The joint credit risk of UK global‐systemically important banks

• DOI: http://doi.org/10.1002/fut.21855
• Date: 01 October 2017
• Author: Mario Cerrato,John Crosby,Yang Zhao,Minjoo Kim
• Published date: 01 October 2017

Received: 29 January 2017

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Accepted: 15 March 2017

DOI: 10.1002/fut.21855

RESEARCH ARTICLE

The joint credit risk of UK global-systemically important banks

Mario Cerrato

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John Crosby

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Minjoo Kim

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Yang Zhao

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1

Adam Smith Business School/Economics,

University of Glasgow, Glasgow, Scotland,

UK

2

Business School, University of

Technology Sydney, Sydney, New South

Wales, Australia

3

International Institute for Financial Studies

and RCFMRP, Jiangxi University of

Finance and Economics, Nanchang, China

Correspondence

Yang Zhao, International Institute for

Financial Studies and RCFMRP, Jiangxi

University of Finance and Economics,

No.169, East Shuanggang Road, Nanchang

330013, China.

Email: zhaoyang8@jxufe.edu.cn

We study the joint credit risk in the UK banking sector using the weekly CDS spreads

of global systemically important banks over 2007–2015. We show that the time-

varying and asymmetric dependence structure of the CDS spread changes is closely

related to the joint default probability that two or more banks simultaneously default.

We are able to flexibly measure the joint credit risk at the high-frequency level by

applying the combination of the reduced-form model and the GAS-based dynamic

asymmetric copula model to the CDS spreads. We also verify that much of the

dependence structure of the CDS spread changes are driven by the market factors.

Overall, our study demonstrates that the market factors are key inputs for the effective

management of the systemic credit risk in the banking sector.

JEL CLASSIFICATION

C32, G32

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INTRODUCTION

The financial crisis of 2007–2008 and EU sovereign debt crisis have caused great concern about the credit risk of large financial

institutions and sovereign entities. Both central banks and financial authorities have paid much more attention to the supervision

of the credit risk in the large financial institutions since then (see the series of reports by Bank of England, 2013, 2015; Basel

Committee on Banking Supervision, 2011, 2012) and several studies have recently focused on the credit risk of banks in the US,

EU, and Asia (see Acharya, Drechsler, & Schnabl, 2014; Dieckmann & Plank, 2012; Huang, Zhou, & Zhu, 2012, among others).

Moreover, the UK voted for Brexit in 2016, which amplified uncertainty about the UK financial market as well as the global

financial market. Since the UK has significant trade and financial linkages with the Euro-zone countries and London is one of

World finance centres, banking activities in the UK and their default probabilities are not only important for the regional

financial markets but also for the international financial markets. Therefore, studying the systemic credit risk in the UK banking

sector at this point will provide important implications for policy makers and investors to decide how to cope with the coming

financial shock from a hard Brexit.

Recent empirical studies show that estimating the joint default probability plays an important role in banking supervision (see

Erlenmaier & Gersbach, 2014; Pianeti, Giacometti, & Acerbis, 2012). This is because it can be viewed as an efficient measure of

systemic risk, as the systemic default arises from the simultaneous defaults of multiple large banks. From the perspective of

practitioners, modeling the joint default probability is also of great interest for credit risk management. For these reasons, it is

essential to study how the credit risk of banks are contemporaneously correlated each other and how their correlations are

varying over time. It will help the risk managers of banks to get a deeper understanding of the credit risk in the banking sector and

properly model it by considering various market scenarios such as joint or conditional default.

In this study, we employ a reduced-form model taking advantage of the CDS spread among several methods for estimating

the default probability (see Hull & White, 2000; O’Kane & Turnbull, 2003). This is because the CDS spread is a good proxy for

the credit risk of bank and contains market information which plays an important role in predicting future credit quality (see Bank

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of England, 2007; European Central Bank, 2007). Therefore, all our analyses are performed using the CDS spreads. What we

intend in this study are as follows: First, we introduce a method of modeling the joint credit risk of banks using the CDS spreads

of the UK G-SIBs. The most important part here is the dependence structure between the CDS spreads of banks. Thus we conduct

intensive research on this part. Second, we propose a time-varying asymmetric copula to model the dependence structure of the

CDS spreads.

1

This copula combines the generalized hyperbolic skewed tcopula (hereafter GHST) with the generalized

autoregressive score (hereafter GAS) model. The GHST copula is popular in many empirical finance studies for modeling the

asymmetric dependence (see Christoffersen, Errunza, Jacobs, & Langlois, 2012; Demarta & McNeil, 2005; Smith, Gan, & Kohn,

2012), and the GAS model has recently been developed to model the time-varying dependence, which is increasingly popular in

many empirical finance studies due to its attractive econometric properties (see Creal, Koopman, & Lucas, 2013; Creal,

Schwaab, Koopman, & Lucas, 2014; Janus, Koopman, & Lucas, 2014; Lucas, Schwaab, & Zhang, 2014; Salvatierra & Patton,

2015). Third, we attempt an economic analysis of what drives the dynamics of the joint credit risk in the banking sector. We will

focus on identifying the drivers of the CDS spreads comovement, motivated by the fact that the dynamics of the joint credit risk

are closely related to the comovement of the CDS spreads. In particular, we use an economic factor model incorporating market

factors to conduct further analysis on the drivers of the CDS spreads comovement.

We make two notable contributions to the literature on credit risk in the banking sector: First, we find the dependence

structure of the CDS spread changes of UK G-SIBs is asymmetric and time-varying over time. This is closely related to

measuring the systemic credit risk of banks such as the joint default probability. In particular, we demonstrate that the

combination of the reduced-form model and the time-varying asymmetric copula can simply and flexibly measure the systemic

credit risk using banks’CDS spreads. Unlike many other methods, our proposed method can not only incorporate market

information properly but also more accurately model the dynamics of joint credit risk in the high-frequency level. Second,

through a factor model based analysis of the comovement of the CDS spreads, we identify economic channels that generate the

dependence structure of the CDS spread changes. So far, there have been many studies on the market factors as the determinants

of individual CDS spreads (e.g., Collin-Dufresne, Goldstein, & Martin, 2001; Cooper & Priestley, 2011; Ericsson, Jacobs, &

Oviedo, 2009; Galil, Shapir, Amiram, & Ben-Zion, 2014; Liu & Zhang, 2008; Longstaff & Schwartz, 1995), but there are few

studies on how the market factors are related to the joint credit risk of banks. Our analysis shows that the market factors can

account for more than 60% of the correlation of the CDS spread changes; thereby, they are closely related to the joint credit risk.

Another important finding is that the time-varying and asymmetric dependence of the CDS spread changes is mostly driven by

the market factors.

The empirical results for the joint credit risk of the UK G-SIBs found in our study provide important policy

implications for the Bank of England (hereafter BoE) to supervise the systemic credit risk in the banking sector. First, our

study suggests that the stability of the systemic credit risk should be secured by reducing the exposure of bank’screditrisk

to market. Second, the asymmetric dependence structure between banks’CDS spread changes suggests that the systemic

credit risk becomes even more serious in the regime of market downturn. Therefore, the central bank should keep

monitoring the comovement between the CDS spreads of banks and the market factors for the effective credit risk

management.

The remainder of this study is organized as follows. Section 2 details the way how we compute the joint default probability of

the UK G-SIBs. Section 3 presents the empirical study on the joint credit risk of the UK G-SIBs using the dataset of weekly

corporate CDS spreads. Section 4 further studies on the drivers of the joint credit risk based on a factor model analysis with

various market factors. Section 5 concludes.

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MODELING JOINT CREDIT RISK

In this section, yewe detail how we compute the joint default probability. First, we calibrate a marginal default probability for an

individual bank. We then find a corresponding value of the CDS spread change to the calibrated default probability from its

marginal probability distribution.

2

Hence, it is a threshold to determine the default of the individual bank. Second, we model the

marginal probability distribution of the CDS spread change for each bank considering its distributional characteristics. Third, we

model a dependence structure of banks’CDS spread changes which is a key input for constructing a joint probability distribution.

Finally, we apply a Monte Carlo simulation to computing the joint default probability.

1

See Oh and Patton (2017), they have recently studied the dependence structure of corporate CDS spreads using the factor copula model.

2

We measure the CDS spread change by the first-difference of the log CDS spread. It is not an asset return but the change of credit risk in the bank.

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