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

2026-09-17

AI Summary

本文针对混合分数Merton跳跃扩散模型，提出了一种结合Metropolis-Hastings采样的EM算法进行参数估计，以捕捉金融回报中的长程依赖性和跳跃行为。

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.

Problem

• Mixed Fractional Merton Jump Diffusion
• parameter estimation
• fractional Brownian motion
• compound Poisson jump process

Innovation

• Expectation--Maximization algorithm
• Mixed Fractional Merton Jump Diffusion model
• Metropolis--Hastings sampling
• long-range dependence
• jump behavior