Jacobi Model And Mortgage-backed Securities Pricing Research Under The Cir Model

The securitization of mortgages is a major innovation in the world financial market. However there are a lot of problems in the process of its development. Nowadays, it is one of the most important financial engineering and financial mathematics subjects that how to do risk measurement and monitor risk while developing financial innovation, and how to establish a reasonable mathematical model to quantify the risk.In this paper, we first give a brief introduction about the content, basic principles, the major risks and different types of mortgage-backed securities. By analyzing prepayment risk in the framework of reduced form model, we establish a dynamic prepayment model through the ration of the actual remaining principal and remaining principal in the pool of loans. Factors that affect prepayment behavior are extremely complex, and the market interest rate is one of the most important factors. We assume that the market risk-free rate satisfies a Jacobi process, and the impact of other factors that affect prepayment follows a CIR process. Under this assumption, we derive the covering pricing equation for MBS, and obtain the analytical solution for pass-thorough securities through fundamental solutions for Jacobi process and CIR process.