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.

Strong consistency estimators of the Brennan‐Schwartz diffusion process based on martingales approach

“…It was also used by Courtadon (1982) to develop a discount bond option prices model. Later, this approach was applied to a variety of different domains, namely, Nafidi et al (2019) used a traditional maximum‐likelihood technique to estimate the drift parameters of the one‐dimensional homogeneous stochastic BSDP in order to illustrate the development of electricity net consumption based on continuous sampling. Handhika (2012) used the same approach to determine that the IRs of three major industrial countries (the United States, Japan and Canada) can be represented as a BSDP by modifying the measure on a discrete sample. …”

“…Nafidi et al (2019) used a traditional maximum‐likelihood technique to estimate the drift parameters of the one‐dimensional homogeneous stochastic BSDP in order to illustrate the development of electricity net consumption based on continuous sampling.…”

“…The asymptotic dynamic behaviour (El Ansari et al, 2018; Nafidi et al, 2019) and parameter estimation and forecasting (El Ansari et al, 2020; Handhika, 2012) of this model have been extensively studied in the literature. Brennan and Schwartz (1980) were the first to apply it in 1980 to create a model for convertible bond prices.…”

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

“…( 2020 ), where a hybrid growth is based on Gompertz and Vasicek models), resources consumption (for instance, Nafidi et al. ( 2019 ) use the Brennan-Schwartz process to model electricity consumption in Morocco) or particular fish species growth (cf. a stochastic version of the open-ended logistic model considered in Yoshioka et al.…”

A Stochastic Lomax Diffusion Process: Statistical Inference and Application

“…In addition to traditional applications, stochastic diffusion processes (SDPs) have attracted considerable attention as analytical tools in areas such as cell growth, population growth and environmental studies. In this respect, see for example: Lognormal [1]; Gompertz [2]; Logistic [3]; Hyperbolic [4]; Rayleigh [5]; Pearson [6]; Weibull [7] and Brennan-Schwartz [8].…”