Construction And Generalization Of Some Systemic Importance Risk Measures: A Study Based On The Copula Approach

This thesis focuses on the study of systemic importance risk measure for financial systems.Considering financial systems composed of interconnected institutions,three kinds of systemic importance risk measure have been proposed in the literature,which are(1)The probability that at least one bank is under stress,given that another specific bank is under stress(PAO);(2)The expected number of bank failures in the system given that one bank has bankrupted(SII);(3)The probability that a particular bank will bankrupt,given that there exists at least one another bankruptcy in the system(VI).In this thesis,by employing copula theory,we reformulate the probability representations of these three systematic importance risk measures,and discuss the influence of multivariate dependence and tail dependence on them.Furthermore,we construct three corresponding general systemic importance risk measures based on PAO,SII and VI,respectively.They are:(1)The probability that at least N banks are under stress,given that another specific bank is under stress(GPAO);(2)The expected number of bank failures in the banking system given that N banks have bankrupted(GSII);(3)The probability that N particular banks will fail,given that there exists at least one another bankruptcy in the system(GVI).For the three generalized systemic importance risk measures,we further discuss the influence of the dependence structure among financial institutions on them.Specifically,different from the extreme-value-theory approach used in the literature,we reformulate the probability representations of traditional PAO,SII and VI by using Copula theory.Compared with the extreme value theory,by characterizing the tail behavior of the underlined risk distribution with the help of Copula theory,one can obtain a variant characterization on the tail dependence structure,and can model the scenario where different risk contributions go to tail at different rates.Based on the Copula approach,it is found that for some popular Copula families,such as the Farlie–Gumbel–Morgenstern Copula family and the Archimedean Copula family,when dependence parameters are ordered in some ways,these system importance risk measures will also exhibit corresponding ordering relations.Furthermore,for the proposed generalized systemic importance risk measures,such as GPAO,GSII and GVI,similar ordering relations can be found.In addition,it can be found that the influence of tail dependence of risks among financial institutions on the systemic importance risk measure cannot be ignored.It has become clear that when the dependence structure among financial institutions can be described by Copula family whose upper tail dependence parameter is positive,the characteristics of its systemic importance risk measure will be significantly different from those in the scenario where the dependence structure can be described by Copula family whose upper tail dependence parameter is 0.Finally,we find that multivariate dependence has no consistent influence on systemic importance risk measures.