PARAMETER ESTIMATION FOR THE MIXED FRACTIONAL MERTON JUMP DIFFUSION MODEL WITH EM ALGORITHM

Author : Chidiogo Joy Agboeke, CHIDIOGO JOY AGBOEKE, HAMIDREZA MALEKI ALMANI, FOAD SHOKROLLAHI, TOMMI SOTTINEN, DARIO GASBARRA

Abstract : This paper develops a robust framework for parameter estimation in a Mixed Fractional Merton Jump Diffusion (MFMJD) model using an Expectation-Maximization (EM) algorithm combined with Markov Chain Monte Carlo (MCMC) sampling. The model integrates fractional Brownian motion to capture long-range dependence and a jump diffusion component to account for discontinuities in financial data. A Metropolis-Hastings scheme is employed in the E-step to estimate latent jump processes, while the M-step updates model parameters through likelihood optimization. The proposed method is applied to daily stock prices from the Helsinki Stock Index. Consistency and Asymptotic normality of the estimator were established. The results indicate strong evidence of persistence, heavy-tailed behaviour, and discrete shocks. Simulation based validation confirms that the model accurately reproduces both the statistical and structural properties of the observed data. Residual diagnostics and sensitivity analysis further demonstrate model adequacy and robustness. The framework provides a comprehensive tool for modeling financial markets characterized by memory effects and sudden discontinuities.

Keywords : fractional Brownian motion, jump diffusion, parameter estimation, Expectation-Maximization algorithm, Markov Chain Monte Carlo, financial modeling, and stock market analysis.

Conference Name : International Conference on Mathematical Modeling in Finance and Risk Analysis (ICMMFRA-26)

Conference Place : Oulu Finland

Conference Date : 3rd Jun 2026