The Application Of Copula-based Methods In Systemic Risk Measurement

Research on systemic risk started early but achieved little progress.Since the global financial crisis of 2007-2009,systemic risk has received wild attention and has become a critical research topic in financial risk management.Due to the contagion of systemic risk,the characterization of the dependent structure of risk factors plays a significant role in measuring systemic risk.As one of the most important theoretical tools in dependence research,copulas offer a flexible way to describe the dependence structure,and dynamic copulas capture the dynamics of the dependence.Moreover,copulas express dependence on a quantile scale which is helpful in the field of extreme risk.Hence,this thesis proposes new dynamic copula-based methods to estimate the widely-used systemic risk measures,CoVaR and SRISK,respectively.The proposed method to estimate CoVaR is based on the theory of the limiting threshold copula.Given the practical application and tractable parametric form,the Clayton copula is chosen as the limiting lower threshold copula.It turns out that such copula can be used directly to model the dependence structure,making CoVaR estimation straightforward.The outcome owes to the particular form of the Clayton copula.The finding thus suggests that to model the dependence structure for estimating CoVaR,the copula can be selected based on a sound statistical theory rather than overall fitting results.The study also shows that the Clayton copula cannot be selected from a standard comparison of information criteria.The complete model includes the GAS model capturing the time-varying tail dependence and the AR(1)-GJR-GARCH(1,1)-Skew model describing the marginal behavior.Several competing models are considered for comparison.The methods are tested in an application to 62 publicly traded institutions in the financial sector of the US stock market.The backtesting results show that the predictive performance of the proposed method is superior to the alternatives.Hence,the work provides a simple and effective way of estimating both CoVaR and Va R.So far,the limiting threshold copula is first introduced to estimate CoVaR,and thus the study contributes to the literature on the application of multivariate extreme value theory.The thesis also develops a dynamic copula-based simulation method to estimate LRMES,the critical component of SRISK.Specifically,firstly select a proper dynamic GARCH-Copula model,construct model innovations based on Rosenblatt’s transformation,then simulate independent and identically distributed noises by resampling from the innovations,and finally estimate LRMES via Monte Carlo approximation.Several dynamic copulas are adopted to describe the dependence structure of financial returns with a given marginal distribution,AR(1)-GJR-GARCH(1,1)-Skew .Model selection is performed by comparing the mean squared errors of MES predictions.Information criteria are not adopted because they are relevant to model fit,and the best model fit is not necessarily suitable for investigating tail risks,as shown in the case of CoVaR.The study on SRISK shows that a standard comparison using information criteria comes to a contrary conclusion.The GARCH-DCC model is considered a benchmark model in comparison.Focusing on extreme returns,five scenarios of market distress are adopted to investigate the sensitivity of the MES predictions to the different dependence specifications.The empirical application is based on 60 publicly traded institutions in the financial sector of the US stock market for the period January 1,2007,to December 31,2019.The results show that the dynamic Clayton and rotated Gumbel copulas can provide satisfactory performance,especially the former,which has a better performance in a higher level of market distress and outstanding computational efficiency in calculating model innovations.