Copula Based Simulation Procedures For Pricing Credit Default Swaps

As U.S. subprime mortgage crisis in the 2008 slowly evolved into a global financial crisis. Credit derivatives play a primary role in the current financial crisis such as CDS. Therefore, the pricing CDS become a hot issue. For pricing CDS, it is very important how to define the correlation between the assets. Recently it is very popular using copula function to describe the dependent structure between the assets since copula function has some advantages. For example, the joint distribution of assets can be decomposed into the marginal distribution function and the copula function, which greatly facilitates the modeling, parameter estimation and numerical simulation.In this paper, we study the basic theory of pricing basket default swaps. First, we introduce the concept of default intensity to describe a default time distribution of assets, and then use copula functions to describe the nonlinear dependent structure among the assets. Monte Carlo simulation is widely used to measure the default risk in basket credit swap. The main contribution of this paper in theory is that a dynamic copula function is introduced to capture the change of dependent structure of the underlying assets. The time-varying characteristics of the dynamic copula model improve the accuracy of pricing credit default swaps.Subsequently, in the empirical application, we choose the optimal copula function by AIC statistical indicators for the static model. The results show that the best fitting copula is different for different the sample data. Then we extend the static copula to the dynamic case, thus allowing us to use copula theory in the analysis of time-varying dependence structure. We examine daily log-return of the index in china over a long period, and find the dependent structure described by dynamic copula can capture the change of of external economic environment, which cannot be caught by the static copula model. This is meaning the time-varying copula model can remedy the static copula model's defect and the pricing of credit default swap is more accurate.Finally, this paper deals with the comparison of procedures for credit default times'simulation on the pricing of nth to default swap. We simulate the data of the return of the underlying assets under dynamic copula, and then estimate the static correlation matrix using these data. Based on the comparison, when the maturity is approaching, the number of underlying assets is larger or the number of default assets in basket is smaller, the volatility of CDS's contract value is relatively large and dynamic copula copula function's advantage is more obvious for this case. Thus, the dependent structure described by dynamic copula model is more valuable on pricing of nth to default swaps.