Hybrid estimation for a mixed fractional Black-Scholes model with random effects from discrete time observations

2025/08/11 by Chebli, Nesrine, Fathallah, Hamdi, Slaoui, Yousri
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2508.07936

Abstract

We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete time observations. Specifically, we consider N independent stochastic processes, each driven by a linear combination of standard Brownian motion and an independent fractional Brownian motion, and governed by a drift term that depends on an unobserved random effect with unknown distribution. Based on discrete-time statistics of process increments, we construct parametric estimators for the Brownian motion volatility, the scaling parameter for the fractional Brownian motion, and the Hurst parameter using a generalized method of moments. We establish strong consistency and joint asymptotic normality of these estimators. Then, from one trajectory, we consistently estimate the random effects, using a plug-in approach, and we study their asymptotic behavior under different asymptotic regimes as N and n grow. Finally, we construct a nonparametric estimator for the distribution function of these random effects using a Lagrange interpolation at Chebyshev-Gauss nodes based method, and we analyze its asymptotic properties as both the number of subjects N and the number of observations per-subject n increase. A numerical simulation framework is also investigated to illustrate the theoretical results of the estimators behavior.

Citations

• Random effects estimation in a fractional diffusion model based on continuous observations
• Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with random effects
• Maximum likelihood estimation for mixed fractional Vasicek processes
• Statistical inference for fractional diffusion process with random\n effects at discrete observations
• Nonparametric estimation for fractional diffusion processes with random effects
• Remarks on a Multivariate Transformation

Related

• Random effects estimation in a fractional diffusion model based on continuous observations
• Estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise
• Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with random effects
• Maximum Likelihood Estimation of Stochastic Differential Equations with Random Effects Driven by Fractional Brownian Motion
• Parametric Estimation for Processes Driven by Infinite Dimensional Mixed\n Fractional Brownian Motion