Abstract:
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We propose a new estimation method of Adrian and Brunnermeier (2014)'s and Giradi and Ergun (2013)'s CoVaR and Delta CoVaR, financial system risk measures conditional on an institution in a financial distress. The new method is based on a three regime bivariate normal (3RN) distribution which is composed of three bivariate normal distributions with asymmetric variance matrices for the right-tail, left-tail and mid-part corresponding to the return of an institution. The distribution captures explicitly the asymmetric correlation of system return and institution return: usually stronger for bad times than for good times. The 3RN distribution allows simple evaluations of the CoVaR and Delta CoVaR taking full advantage of asymmetric correlation. An implementation for the quasi maximum likelihood estimator (QMLE) is provided, for which large sample normality is established. The proposed estimation method is applied to stock price data sets. The data analysis shows that the proposed method is better than existing methods in terms of conditional violation. In a Monte-Carlo study, finite sample validity of the QMLE is demonstrated by studying size for a significance test of Delta CoVaR.
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