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Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Author

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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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • Ramón Gutiérrez-Sánchez

    (Department of Statistics and Operational Research, Facultad de Ciencias, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1062-:d:283975
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    References listed on IDEAS

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