Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application
Metadatos
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MDPI
Materia
Brennan–Schwartz diffusion model Stochastic differential equation Inference in diffusion processes Stationary distribution Electricity net consumption in Morocco
Fecha
2019-11-06Referencia bibliográfica
Nafidi, A., Moutabir, G., & Gutiérrez-Sánchez, R. (2019). Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application. Mathematics, 7(11), 1062.
Patrocinador
This research was funded by LAMSAD from “Fonds propres de l’Université Hassan I” (Morroco) and FQM-147 from “Plan Andaluz de Investigaciòn” (Spain).Resumen
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.