The Study Of Financial Risk Theory Based On Coupla Methods

With the gradual opening and amalgamation of the world economic system, the quantitative analysis and management of the financial risk have been attracting quite a lot of attention. Among the kinds of proposed credit risk models, the reduced form credit risk model is a very important kind of credit risk measurement model, which has been widely used in financial industry. In the reduced form credit risk models, the default survival probability and the modeling of the default dependence structure are always two key research subjects of some domestic and overseas scholars. In this dissertation, based on some copula approaches, we investigate the pricing of some credit derivatives and make some quantitative analysis of the correlated default risk under the framework of the reduced form credit risk models and jump-diffusion CIR (Cox-Ingersoll-Ross) models. The expectation and variance of the discounted aggregate claims and the actuarial premium calculations are also discussed. The main results obtained in this dissertation are as follow.Firstly, we discuss the distributions of the jump-diffusion CIR models and their applications in credit risk. By means of the piecewise deterministic Markov process theory and martingale theory, we first obtain the close forms of the Laplace transforms for the distribution of jump-diffusion CIR model and its integrated process. Based on the obtained Laplace transforms, we derive the pricing of the defaultable zero-coupon bond and the fair premium of a risk-free CDS (Credit Default Swap). We also study the pricing of the default-free zero-coupon bond and the European put option on the zero-coupon bond. In addition, we also discuss the pricing of the premium of CDS at the discrete-time case.Secondly, we investigate the default correlation between two firms and the pricing of CDS rate. We first introduce a concept of two-dimensional jump-diffusion CIR model and obtain the joint Laplace transforms for the distribution of the two-dimensional model. On this basis we apply Copula method to study the joint survival probability of two firms, and then analyze their correlated default risk. We also discuss the pricing of CDS rate with bilateral counterparty risk in the reduced form credit risk model.Finally, we study the moments of the discounted aggregate claim amounts and the premium calculation in actuarial science. The interest rate is assumed to be a jump-diffusion CIR process, and the jump sizes in the model are assumed to obey the mixed-exponential distribution. We apply Laplace method to derive the expectation and variance of the discounted aggregate claims in a continuous-time compound renewal risk model. In this case, we employ FGM (Farlie-Gumbel-Morgenstern) Copula with two parameters to describe the dependence structure between the claim interval and the subsequent claim size. We also provide the actuarial premium calculations on the base of the standard deviation premium principle.