.svg){kind=logo}
A NEW INHOMOGENEOUS VASICEK MODEL: STATISTICAL TREATMENT, SIMULATION STUDY AND APPLICATION
Keywords:
non-homogeneous Vasicek model, likelihood estimation, discrete sampling, genetic algorithm, methane emissionsDOI:
https://doi.org/10.17654/0972361725048Abstract
This paper proposes a new stochastic diffusion model, based on a Vasicek non-homogeneous diffusion process, in which only the speed mean reversion factor is affected by exogeneous factor. From the corresponding Itô stochastic differential equation, we obtain the probabilistic characteristics of the process as the transition probability density function and the trend functions. For the statistical inference of the parameters of the model, the method employed is the maximum likelihood using discrete sampling, which gives complex non-linear equations. To overcome this difficulty, we propose the use of the genetic algorithm to approximate these likelihood estimators. A simulation study is then carried out to validate the statistical treatment used. Finally, the model suggested, along with the methodology established, is applied to real data.
Received: April 24, 2025
Accepted: May 31, 2025
References
R. Gutiérrez, A. Nafidi and R. Gutiérrez Sánchez, Inference in the stochastic Gompertz diffusion model with continuous sampling, Monografías del Seminario Matemático García de Galdeano 31 (2004), 347-353.
A. Nafidi, A. El Azri and R. Gutiérrez-Sánchez, A stochastic Schumacher diffusion process: probability characteristics computation and statistical analysis, Methodology and Computing in Applied Probability 25 (2023), 66.
A. Nafidi, G. Moutabir and R. Gutiérrez-Sánchez, Stochastic Brennan-Schwartz diffusion process: statistical computation and application, Mathematics 7 (2019), 1062.
A. Nafidi, I. Makroz, R. Gutiérrez Sánchez and E. Ramos-Ábalos, Multivariate stochastic Vasicek diffusion process: computational estimation and application to the analysis of CO2 and concentrations N2O, Stochastic Environmental Research and Risk Assessment 38(1) (2024), 2581-2590.
A. Nafidi and A. El Azri, Emissions of greenhouse gases attributable to the activities of the land transport: modelling and analysis using I-CIR stochastic diffusion-the case of Spain, Environmetrics 19 (2007), 137-161.
A. Nafidi, R. Gutiérrez, R. Gutiérrez-Sánchez, E. Ramos-Ábalos and S. El Hachimi, Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors, Energy 113 (2016), 309-318.
A. Nafidi, I. Makroz, B. Achchab and R. Gutiérrez Sánchez, Stochastic Pareto diffusion process: Statistical analysis and computational issues, Simulation and Application, Moroccan J. of Pure and Appl. Anal. 9 (2023), 127-140.
Y. Chakroune and A. Nafidi, A new stochastic diffusion process based on the Rayleigh density function, Procedia Computer Science 201 (2022), 758-763.
O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics 5 (1977), 177-188.
J. C. Cox and S. A. Ross, The valuation of options for alternative stochastic processes, Journal of Financial Economics 3 (1976), 145-166.
J. Hull and A. White, The general Hull-White model and supercalibration, Financial Analysts Journal 57 (2001), 34-43.
R. Gutiérrez, R. Gutiérrez-Sánchez, A. Nafidi and A. Pascual, Detection, modelling and estimation of non-linear trends by using a nonhomogeneous Vasicek stochastic diffusion: application to CO2 emissions in Morocco, Stochastic Environmental Research and Risk Assessment 26 (2012), 533-543.
Y. Wu and X. Liang, Vasicek model with mixed-exponential jumps and its applications in finance and insurance, Advances in Differential Equations 2018 (2018), 138.
K. C. Chan, G. A. Karolyi, F. A. Longstaff and A. B. Sanders, An empirical comparison of alternative models of the short-term interest rate, J. Finance 47(3) (1992), 1209-1227.
K. G. Koedijk, F. G. J. A. Nissen, P. C. Schotman and C. C. P. Wolff, The dynamics of short-term interest rate volatility reconsidered, Rev. Finance 1(1) (1997), 105-130.
P. W. Zehna, Invariance of maximum likelihood estimators, The Annals of Mathematical Statistics 37(3) (1966), 744-744.
K. Es-sebaiy and M. Es-sebaiy, Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model, Stat. Methods. Appl. (2021), 409-436.
Nicholas Burgess, A Review of the Vasicek and Hull-White Models and the Likelihhod of Negative Rates, 2018.
J. H. Holland, Genetic algorithms, Scientific American 267(1) (1992), 66-73.
B. L. Miller and D. E. Goldberg, Genetic algorithms, tournament selection, and the effects of noise, Complex Systems 9(3) (1995), 193-212.
K. Chellapilla, Combining mutation operators in evolutionary programming, IEEE Transactions on Evolutionary Computation 2(3) (1998), 91-96.
F.-A. Fortin, F.-M. De Rainville, M.-A. Gardner, M. Parizeau and C. Gagné, DEAP: evolutionary algorithms made easy, Journal of Machine Learning Research 13 (2012), 2171-2175.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
