In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The parameter estimators are then derived by means of two procedures: the first is used to estimate the parameters in the drift coefficient by the maximum likelihood (ML) method, based on continuous sampling, and the second procedure approximates the diffusion coefficient by two methods. Finally, a simulation of the process is presented. Thus, a typical simulated trajectory of the process and its estimators is obtained.
翻译:在本文中,我们考虑一个基于Cox-Ingergol-Ross模型的随机模型,通过应用Itçóo的微积分和拟议过程的趋势功能进行分析,对随机模型进行参数化分析,然后通过两个程序得出参数估计:第一个程序用来根据连续抽样,用最大可能性(ML)方法估计漂移系数的参数,第二个程序用两种方法接近扩散系数。最后,对过程进行了模拟,从而获得了典型的模拟过程轨迹及其估计结果。