The Extended CIR-CKLS Interest Rate Model

This thesis gives a framework on the term structure theory of interest rate, including the basic theory of term structure of interest rates, the importance of research, development process. Some important results are introduced on continuous-time models of interest rate term structure. This thesis also attaches importance to the'good'properties of the stochastic differential equations managing the classical CIR model and CKLS model, which are desired for interest rate models, for example, reverting property, existence and uniqueness of the nonnegative solution, the moment boundedness and so on. When the equation has no explicit solution, this thesis also examines whether its numerical scheme may converge its exact solution.Based on the CIR model and CKLS model, this thesis investigates an extended model named as the CIR-CKLS model, which includes the CIR model and CKLS model as special cases. This model holds the advantages of these two classes of models, so it can simulate and predict changes of the interest rates model precisely.By the knowledge of stochastic differential equations, this thesis examines this CIR-CKLS model and this model admits a unique global nonnegative solution with probability one and reveals the moment boundedness of this nonnegative solution. This thesis also examines convergence of the Euler- -Maruyama scheme of this model. Finally, as an example, this thesis examines the bond and shows that the numerical solution can compute the expected payoffs.