Abstract: Nowadays,diffusion models are applied to the electronic and financial fields to describe the dynamics of the variables.Transition density,the most important variables to the diffusion models,is always a hot studying field.With the development of the matlab,it is very significant to find the optimal methods for the estimation of the transition density by making use of the simulation and numerical functions of it.The author compares two  methods of estimating transition densities of  diffusion model i.e.,Euler and Hermite.After the comparison of the approximation to the closed-form densities for the Vasicek and CIR models,it is found that the Hermite method can estimate the transition densities much more accurately in comparison with the Euler method.Then,the further estimation of the diffusion model parameters is conducted by these two methods,which proves that Hermite method can better recognize the model parameters than Euler method,and it can reduce the estimation errors.

Key words: diffusion model, transition density, matlab simulation