Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Ahmed Nafidi, Ghizlane Moutabir and Ramón Gutiérrez-Sánchez
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Ahmed Nafidi: Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, 26100 Berrechid, Morocco
Ghizlane Moutabir: Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, 26100 Berrechid, Morocco
Ramón Gutiérrez-Sánchez: Department of Statistics and Operational Research, Facultad de Ciencias, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain

Mathematics, 2019, vol. 7, issue 11, 1-16

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.

Keywords: Brennan–Schwartz diffusion model; stochastic differential equation; inference in diffusion processes; stationary distribution; application; electricity net consumption in Morocco (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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