基于Matlab仿真的扩散模型转移密度估计方法比较

扩散模型目前被广泛的应用于现代电子、金融等领域用来描述变量的动态变化过程，转移密度作为反映扩散模型特征的重要变量一直是各国学者研究的重点，随着Matlab功能的日益完善，利用其强大的仿真和数值分析函数来定量研究扩散模型的转移密度，从而寻找出最优的估计方法无疑具有重要的意义.基于此，通过利用Matlab仿真技术，比较了2种估计扩散模型转移密度函数的方法，即Euler法和Hermite法，通过对存在闭端解的2个扩散模型的比较，发现用Hermite扩展确实比Euler法能更好的估计扩散模型的转移密度函数，在此基础上，进一步利用这2种方法估计了扩散模型的参数，证明了Hermite法比Euler法能更好的识别模型参数，减少估计中的错误.

Estimaiton Methods of the Transition Density of the Duffusion Model Based on the Matlab Simulation

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.