The Research On Coherent Measures Of Credit Portfolio Risk With Default Contagion

Under the double background of the third revolutions in finance and the intensifying competition in Chinese banking industry, based on the theoretic need with the existing credit risk models being defective and the practical demand with a series of default contagion process by Enron Event, Worldcom Scandal, Parmalat Fraud and current Subprime Lending Crisis in US, this paper systemically study coherent measures of credit portfolio risk with default contagion.Default contagion is when a firm defaults, credit crisis will propagate to its affiliated enterprise in manner of contagion, as a result, and increase the default probability of all firm, even bankruptcy.Firstly, based on analyzing default contagion mechanisms and discussing the limitation of conditionally independent models, this paper establishes interacting intensities default contagion model which synthetically take into account cyclical correlations and default contagion among affiliated enterprise, and study calculating every default state probability of credit portfolio, ascertaining new models parameters and effect of default contagion on default correlation. The result of the instance show: the local interaction of firms with their business partners increases their default correlation, therefore default contagion in nature is default correlation, and the default correlation by default contagion is larger than the one by cyclical correlation.Secondly, utilizing the mixed method of Saddlepoint approximation and continuous-time Markov Chains'Kolmogorov differential equation, this paper also research the calculation of coherent measures of simple default contagion portfolio. This method divides the credit portfolio into two parts: the sub-portfolio of the interactional firms and the one of conditionally independent ones, then under the condition of fixing macro-economy factor, uses respectively Saddlepoint approximation and continuous-time Markov Chains'Kolmogorov differential equation to compute the two parts'conditional loss distribution, and combines organically their into an integer, at last calculates the whole conditional loss distribution'integral on the systemic risk, therewith gets the credit portfolio loss distribution and computes its risk measures. The result of the instance show: default contagion increases the probability of extremely small and large credit portfolio loss, that is the tail loss distribution turn"fat", thereby enhances the risk measures"VaR"and"ES". ES refers to conditional expectation of the tail loss distribution beyond"VaR", consequently for conditionally independent models the underestimate of"ES"is larger than the one of"VaR".Finally, because it is difficult to calculate the default state transition Kolmogorov differential equation for the large and complex credit portfolio, this paper establishes mean-field default contagion model. On the assumption that the same credit rate asset is homogeneity, this method divides credit portfolio into some sub-portfolios, and supposes the default intensity of every firm in the same sub-portfolio's is the same, and is function of the macro-economy factor and the proportion of defaulted firms in the portfolio. Thereby the default state space's dimensionality of credit portfolio is evidently diminished so that it is convenient to calculate the large and complex default contagion portfolio's loss distribution. The result of the instance show: when the proportion of defaulted firms is increased, default contagion produces a feedback on no-defaulted firm and makes its default intensity jump upwards, therefore increases the fluctuation of the number of defaulted firms in the portfolio by the movement of macro-economy, makes credit portfolio tail loss distribution"fat"and enhances risk measures"VaR"and"ES".In conclusion, for credit risk management, it is theoretically and practically significative to study default contagion theory, and this paper just aims at promoting the development of the international credit risk management theory, supplies a gap of the domestic research on default contagion and instructs Chinese commercial bank risk measurement and management.The research is sponsored by the National Natural Science Foundation of China (Grant No.70573076) and Research Foundation of the Doctoral Program of Higher Education (Grant No.20050056057).