"Mortgage-related hit worse than expected" has been a frequently cited phrase in recent months, and is usually followed by a list of victims consisting of banks and hedge funds. Although the current mortgage mess was caused by the subprime mortgage or bad credit mortgage, the broad impact of this subprime crisis promotes more concern in the loan lenders, the borrowers and mortgage-related products like mortgage backed securities. Since credit market is one of the successful application areas of statistics, we think a better understanding of MBS and its related risk and a more accurate credit risk assessment due to the application of more advanced statistics would contribute to the rebuilding of the credit market.

Nonparametric methods have proven to be useful in terms of capturing the flexible relationship between economic variables, while fewer assumptions about the economics constraint are made than in the traditional structural approach. This thesis follows the nonparametric trend and applies a new practical method, penalized splines, to investigate the issues on mortgage-backed securities (MBSs) and credit risk. The first application is to investigate the impacts of different interest rates on the prices of MBSs and show the hedging strategy based on the estimated smoothing functions. The second application concerns the stability of the impact of burnout effect on the prices of MBSs and its indication to the prepayment modelling. Finally, a credit risk model with varying coefficients is provided to explore the credit risk of small and medium-sized enterprises (SMEs) in China.