Static Research On Mathematical Models And Algorithms For Term Structure Of Interest Rate

The term structure model of interest rate is defined as the relations between the interest rates and their maturities at the same risk level. It is extensively applied to asset pricing, design of financial goods, hedging, arbitraging and investment decision. In the background of domestic stock market, we do theory and empirical analysis research of the linear programming method, the method of fitting based on polynomial spline function, the method of fitting based on genetic algorithms and the fitting based on GCV penalty function.In models, the result obtained from linear programming model is discrete, so we use cubic polynomial interpolation method to make it continuous and smooth. The model based on genetic algorithm has solved the problem that the polynomial pieces are fixed by man, and we also analyzes the various parameters of the models. The model based on GCV penalty function balances the precision and smoothness. Besides, the paper also introduces genetic algorithms into the model of fitting based on GCV polynomial spline function and use ergodic method to find the best penalty parameter first time. At last, the paper makes a comparative study among four models through four aspects such as the precision analysis, image analysis, smooth analysis and velocity of calculate analysis. And the results display that the model of fitting based on GCV polynomial spline function fit the term structure of interest rates best when it meets the four requirements above.