Parameter Estimation for the Mixed Fractional Merton Jump Diffusion Model with EM Algorithm

Abstract

This paper proposes an Expectation--Maximization algorithm with Metropolis--Hastings sampling for parameter estimation in a Mixed Fractional Merton Jump Diffusion model. The model combines fractional Brownian motion to capture long-range dependence with a compound Poisson jump process to describe abrupt movements in financial returns. The latent jump process is inferred during the E-step using Markov Chain Monte Carlo sampling, while the M-step updates the model parameters by maximizing the expected complete-data likelihood. The consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. The methodology is applied to the Helsinki Stock Index (OMXH25). The proposed estimation framework provides a reliable and computationally efficient approach for modeling financial time series exhibiting both long-memory dependence and jump behavior.

Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise
Yongkang Li, Yaozhong Hu, Litan Yan
arXiv3 Oct 2026PreprintarXiv licenceFull textProbabilityarXiv
Spatio-Temporal Weighted Regression model with fractional-colored noise: Parameter estimation and consistency
Héctor Araya, Lisandro J Fermín, Silfrido Gómez +2
Journal of Statistical Planning and Inference21 Sep 2026Peer-reviewedCC BY 4.0Full textStatisticsHAL
An Adaptive Multi-Parameter ADMM Algorithm for Embedded MPC
Alberto Zaupa, Mikael Johansson
arXiv11 Sep 2026PreprintCC BY 4.0Full textOptimisation & controlarXiv
Subdivision-based collocation methods for time fractional convection diffusion reaction equation with environmental and biomedical applications
Saima Bibi, Syeda Tehmina Ejaz
Scientific Reports15 Oct 2026Peer-reviewedCC BY-NC-ND 4.0Full textGeneral mathematicsCrossref
PLADOS: A Parameter-free Landing Algorithm for Decentralized Optimization on the Stiefel Manifold
Shu Li, Jiang Hu
arXiv6 Oct 2026PreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeX RIS

BibTeX

@misc{agboeke2026parameter,
  title = {{Parameter Estimation for the Mixed Fractional Merton Jump Diffusion Model with EM Algorithm}},
  author = {Chidiogo Joy Agboeke and Hamidreza Maleki Almani and Dario Gasbarra and Foad Shokrollahi and Tommi Sottinen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20041},
  eprint = {2609.20041},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20041},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Parameter Estimation for the Mixed Fractional Merton Jump Diffusion Model with EM Algorithm
AU  - Chidiogo Joy Agboeke
AU  - Hamidreza Maleki Almani
AU  - Dario Gasbarra
AU  - Foad Shokrollahi
AU  - Tommi Sottinen
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20041
UR  - https://arxiv.org/abs/2609.20041
AB  - This paper proposes an Expectation--Maximization algorithm with Metropolis--Hastings sampling for parameter estimation in a Mixed Fractional Merton Jump Diffusion model. The model combines fractional Brownian motion to capture long-range dependence with a compound Poisson jump process to describe abrupt movements in financial returns. The latent jump process is inferred during the E-step using Markov Chain Monte Carlo sampling, while the M-step updates the model parameters by maximizing the expected complete-data likelihood. The consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. The methodology is applied to the Helsinki Stock Index (OMXH25). The proposed estimation framework provides a reliable and computationally efficient approach for modeling financial time series exhibiting both long-memory dependence and jump behavior.
ER  -

Abstract

Related

Cite