Parameter Estimation of the Extended Vasiček Model

Abstract

In this paper, an estimate of the drift and diffusion parameters of the extended Vasiček model is presented. The estimate is based on the method of maximum likelihood. We derive a closed-form expansion for the transition (probability) density of the extended Vasiček process and use the expansion to construct an approximate log-likelihood function of a discretely sampled data of the process. Approximate maximum likelihood estimators (AMLEs) of the parameters are obtained by maximizing the approximate log-likelihood function. The convergence of the AMLEs to the true maximum likelihood estimators is obtained by increasing the number of terms in the expansions with a small time step size.

Keywords

• The extended Vasiček model
• transition density
• maximum likelihood estimation