| This paper mainly research Copula theory and its using in credit risk management. On the basis of Copula theory, this paper put up credit default risk model. The paper's main work and research are as following:Firstly, explains and describes the first sort credit risk model, that is the structural model. Discuss the model's influential factor and deduce the analytical expression of default probability, default distance and default spread. The in-depth models of structural model including First-passage-approach and Excursion-approach. The former involved the barrier clause in a contract and the latter involved the cost of default, so the latter model demands a recovery period.Secondly, this paper expatiates on another influential credit risk model, that is reduced model. Its difference from structural model lie in no answer the question why the corporation default. But it more agree with the real world's abrupt default phenomenon. A real transition matrix comes from Standard&Poor explains the use of reduced model in credit risk management. Particularly, the markov theory of random process has been used in reduced model.Thirdly, this paper explains the meaning of incomplete information by occurrences and writes the mathematical expression of incomplete information and defines the information filtration. Because of the information's incomplete, so we construct a distribution of default probability in advance. This distribution take advantage of the so called Copula theory. Copula is a joint default probability essentially, but it including the non-lined factors, so it more suitable to the real world. Under different market circumstance we can use the corresponding Copula because different Copula has different distribution character.Especially, there is an important thought lie in the incomplete information credit risk model, that is the model's parameters should be updated in time according to the current information filtration. We can get different default probability under different circumstance by Copula, such as both two corporations default, or one default and the other no default, or both two corporations no default. And the default time point can be choosed arbitrarily. In fact, it is a typical quantificational model. The model answer how much the probability when the default occur, so it can be used in credit risk management. |
