A NEW INHOMOGENEOUS VASICEK MODEL: STATISTICAL TREATMENT, SIMULATION STUDY AND APPLICATION

This paper proposes a new stochastic diffusion model, based on a Vasicek non-homogeneous diffusion process, in which only the speed mean reversion factor is affected by exogeneous factor. From the corresponding Itô stochastic differential equation, we obtain the probabilistic characteristics of the process as the transition probability density function and the trend functions. For the statistical inference of the parameters of the model, the method employed is the maximum likelihood using discrete sampling, which gives complex non-linear equations. To overcome this difficulty, we propose the use of the genetic algorithm to approximate these likelihood estimators. A simulation study is then carried out to validate the statistical treatment used. Finally, the model suggested, along with the methodology established, is applied to real data.