Test Analysis Of Several Typical One-dimensional Diffusion Models

The continuous time diffusion models are a good tool for asset price, interest rate and other financial quantity modeling. Researchers often use the specific diffusion models to carry out pricing, hedging and risk management of derivatives.The research on the setting of the diffusion models have been developed and perfected.In this paper, the method of testing the specific one dimensional diffusion models was intensive studied, and improved combine bootstrap and goodness fit test to test Vasicek model, CIR model and CKLS model. The test result is better than Hong and Li.Firstly, we provided the conditions of the null hypothesis and alternative hypothesis for the specific one dimensional diffusion models; An effective method for calculating the transfer probability density of diffusion models were proposed, the method was based on Hermite polynomials. Then gave the calculation of generalized residual error sequence of the diffusion models;The test method of Hong and Li was reviewed and the defects of the method were pointed out, then proposed an improved test method and calculated a new test statistics. At the same time, the critical value was calculated by bootstrap method.Secondly, we introduce three kinds of typical one-dimensional diffusion models:Vasicek model, CIR model and CKLS model. Then provided the parameter estimation methods and the calculation of transfer probability density of these three kinds of models, especially the mathematical expression of the transfer probability density of CKLS model; We used the improved test method simulation analyzed the Vasicek model, CIR model and CKLS model, and compared with the method of Hong and Li.Finally, the Vasicek model, CIR model and CKLS model were used to examine the Shanghai inter-bank offered rate(daily) and the London inter-bank offered rate(daily). By analyzed the model test and fitting results, we found that the CIR model and the CKLS model were more consistent with the Shanghai inter-bank offered rate(daily) and the London inter-bank offered rate(daily) respectively.