Stochastic Brennan-Schwartz diffusion process: Statistical computation and application

Abstract

In this paper, we study the one-dimensional homogeneous stochastic Brennan-Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan-Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.