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조건부 도산확률을 이용한 은행부문의 시스템리스크 측정

  • Seung Hwan Lee Senior Economist, Economic Research Institute, The Bank of Korea
본 연구는 한 금융기관의 도산이 다른 금융기관의 도산에 미치는 영향을 나타내는 조 건부 도산확률(conditional probability of default; CoPD)을 추정하고 이를 이용하 여 시스템리스크를 측정하는 방법을 제안하였다. 모의실험 결과 CoPD를 이용한 시 스템리스크 측정은 Adrian and Brunnermeier(2009)의 CoVaR의 문제점인 극단의 존성에 대한 측정오류를 해결할 수 있을 뿐만 아니라 금융기관의 재무건전성 정보를 반영하는 장점이 있는 것으로 나타났다. 6개 국내 은행을 대상으로 CoPD를 이용한 시스템리스크 측정 방법을 적용하여 시스템리스크 지표를 시산하였다. 시산 결과 시 스템리스크 지표는 2003년 신용카드 사태 이후 상당기간 안정세를 보이다가 글로벌 금융위기가 진행되었던 2007∼2009년 중에는 크게 상승하는 모습을 보였다. 또한 BIS자기자본비율과 외화유동성 비율이 시스템리스크 지표와 반대방향으로 2∼3분기 선행하여 변동하는 것으로 나타나 시스템리스크에 영향을 미치는 주요 요인으로 분 석되었다.
시스템리스크; 조건부도산확률; 결합확률분포; 극단의존성; 은행시스템; Systemic Risk; Conditional Probability of Default; Joint Probability Distribution; Tail Dependence; Banking System

Measuring Systemic Risk in the Banking Sector Using the Conditional Probability of Default

  • Seung Hwan Lee
The 2007~2009 global financial crisis has highlighted the danger of systemic risk, largely caused by interconnectedness and externality among financial institutions. Generally, systemic risk is a difficult concept to define and measure accuately, making it even more challenging for policy makers to effectively address the issue. Although no clear consensus has been established on a formal definition of systemic risk, it usually denotes the risk related to all the potential results followed by the collapse of a whole financial system, consisting of many interacting financial institutions. In order to effectively prevent such systemic risk, it is necessary to first develop a reliable method to measure such risk. The previous studies on the systemic risk can be divided into two structural approaches: using contingent claims analysis (Lehar, 2005, Gray, Merton, and Bodie, 2008, and Gray and Jobst, 2009) and reduced- form approaches focusing on the statistical tail behavior of financial institutions’ asset returns (Adrian and Brunnermeier, 2009, and Chan-Lau, 2010). In this paper, we propose a new method to gauge systemic risk: the conditional probability of default (CoPD), which is derived from the joint probability distributions of banks’ asset returns. In order to obtain CoPD, we first estimate the joint probability distributions of asset returns and the default points of banks in the system. Since the market values of bank assets are unobservable, we estimate asset returns using stock prices and debt maturity structures following Merton (1974) and Crosbie and Bohn (2003). To maximize the consistency between asset values and asset volatilities, we estimate them using the recursive exponentially weighted moving average algorithm developed by Lee (2010). In doing so, we assume that a bank is in default if the market value of its assets is less than the default point, which is estimated based on the debt maturity structure of banks. We define CoPD as a default probability of a bank, conditional on other banks being in default. The difference between CoPD and unconditional PD, CoPD, contains useful information on systemic risk.CoPD?? denotes the change in default probability of bank i when bank j goes bankrupt. The stronger the interdependence between bank i and bank j gets, the higher CoPD?? becomes. This method allows us to develop systemic risk indicators which measure how much the default possibility of banks increases when other banks in the system go bankrupt. The systemic risk indicator (SRI) can be calculated based on the n×n CoPD matrix, whose element CoPD?? denotes the difference between CoPD?? and unconditional PD ? . The overall systemic risk may be captured by the mean value of all off-diagonal elements in the matrix. SRI measures the increase in default probability of a bank on average when a bank in the system falls default. If there are no direct and indirect connections between banks, SRI approaches 0. The stronger the interdependence within the banking system gets, the higher SRI will be. In order to measure how much the default probabilities of other banks increase when the bank goes bankrupt, we also develop the systemic importance indicator (SII) of each individual bank as well as the systemic vulnerability indicator (SVI), which are supplementary information of the systemic risk indicator. We may calculate SII as the column mean of the CoPD matrix. On the other hand, the systemic vulnerability indicator of an individual bank measures how much the default probability of the bank increases when other banks go bankrupt. Thus, SVI can be calculated as the row mean of the CoPD matrix. Meanwhile, Adrian and Brunnermeier (2009) have proposed a popular systemic risk measure: CoVaR, which may evaluate the systemic risk contribution of an individual bank. However, this method entails some serious measurement errors on tail dependence. The concept of tail dependence generates a measure for extreme co-movements in the lower and upper tail of asset return distributions, respectively. A reliable systemic risk measure must correctly capture the lower tail dependence among the involved banks. Simulation results suggest that CoVaR underestimates the systemic risk if lower tail dependence is significant, whereas it overestimates the systemic risk if upper tail dependence is strong. The Monte-Carlo experiments show that CoPD can accurately address the problem with CoVaR on tail dependence. The CoPD may also reflect the information about the financial strength of banks. In this study, we calculate the systemic risk indicators for six Korean domestic banks by applying our method. The empirical results show that the systemic risk indicator of the Korean banking system had remained stable for a long period of time after the 2003 credit card crisis until the sub-prime mortgage crisis broke out (2007~2009). Since then the systemic risk of the Korean banking system has dramatically increased again. Secondly, large banks’ systemic importance is considerably high, while low-capital banks are systemically vulnerable. Finally, the BIS capital ratio and the FX liquidity ratio have changed in the opposite direction of the systemic risk indicator with a lead of two or three quarters.