A connection between Gompertz diffusion model and Vasicek Interest Rate model

Abstract

The main goal of this paper is to establish a new connection between the Gompertz diffusion model and the Vasicek Interest Rate model. These connection focus on elementary stochastic calculus and Itô's calculus. Firstly, we prove that the exponential of the Vasicek Interest Rate model is a Gompertz diffusion process. Secondly, we prove that the logarithm of the Gompertz diffusion process is a Vasicek Interest Rate model. New computations of the probability transition density function and the mean functions of the processes have quite simple formulations.