Multivariate Dynamic Stochastic Models of Credit Risk

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This project develops stochastic models of credit risk. Credit risk is the risk that a financial counterparty will default on its financial obligation. The research objective of the project is to develop models describing multivariate stochastic dynamics of credit risk and analytical and computational tools to help implement the models in industrial practice and public policy. The mathematical modeling framework for arrivals of defaults of multiple counterparties (obligors) will be based on multivariate random time changes of Markov processes. The key features of the proposed modeling framework important in applications are that they can achieve any desired level of correlation among default (failure) times of multiple obligors and that the simultaneous defaults (failures) are possible (have positive probability), thus enabling the researcher to model default clustering phenomena. The project will develop an analytical methodology for this class of models based on the spectral theory. This will allow explicit analytical calculations for multivariate default (failure) time distributions by explicitly computing spectral expansions in problems of moderate size. The project will also develop a simulation methodology to deal with large problems with many obligors that cannot be efficiently solved by the analytical spectral method. If successful, stochastic models and analytical and computational tools developed in this project will help better understand and model credit risk in the financial industry and will aid in the development of public policy to regulate financial institutions. In addition to applications in finance, the mathematical modeling framework and analytical and computational tools developed in the project will advance general stochastic modeling methodology that is applicable to a wide range of reliability and failure applications, including computer and communications networks, electric power grid, manufacturing, and biological systems.