The Random Polynomial Model Of The Term Structure Of Interest Rates

With the development of the global financial market innovation and the theory ofcapital market, at the same time, with the deeply of the interest rate marketization andmulti-level capital market gradually established. The theory of the term structure ofinterest rate has received more and more attentions in the financial field. This thesis willexamine the term structure model of interest rates with polynomial coefficients by usingqualitative methods.In this thesis, the author firstly reviews the background and significance of the termstructure of interest rates. Secondly, the author respectively introduces the developmentof the two stages of the term structure theory of interest rate. Then the author outlines thetwo classes of term structure model of interest rate, and puts forward the main content onthe basis of the extended model. In this thesis, the author analyses and reviews thetraditional term structure theory of interest rate from four mainly aspects. Then, As forthe modern term structure theory of interest rate, This thesis examines the static anddynamic models, single-factor models and multi-factor models, domestic and foreign andso on, and it is studied by dividing it into several cases.In this thesis, the author mainly introduces the random polynomial model of the termstructure of interest rates. The author firstly introduces the non-parameters model workedby Ait-Sahalia and the general parameters model. Based on these two classes of models,the author introduces the main content. The forms of these models that named for randompolynomial model of the term structure of interest rates are relatively complex. Toestablish model to analyze and forecast changes of the interest rates, it is important tochoose an appropriate model with "good" properties. These "good" properties should beheld by the controlled stochastic differential equations, for example, the existence anduniqueness of the global nonnegative solutions, boundedness of the moment, and the convergence of numerical solution and so on. In general, these equations have no explicitsolutions, so it becomes to examine their numerical solutions and approximate their exactsolutions. By the new method developed by theory of the stochastic differential equations,this thesis establishes the existence-and-uniqueness theory of the global nonnegativesolutions of the controlled equation with probability one and examines the momentboundedness of this solution. Finally, this thesis also proves that the numerical solutioncan be used to compute the expected payoffs.