Determination of the Binomial MSM Parameter Vector

Determine the parameter vector \(\psi_k=(m_0,\sigma,b)\) that fully specifies a binomial Markov-Switching-Multifractal model for a given number \(k\) of volatility components.

Background

For a fixed number of volatility components, the paper represents the free parameters of the binomial Markov-Switching-Multifractal model by the vector ψk=(m0,σ,b)\psi_k=(m_0,\sigma,b), comprising the high-state multiplier, the overall volatility scale, and the parameter governing the geometric progression of component switching probabilities. The paper notes that identifying this vector is unresolved in the existing literature and subsequently describes maximum-likelihood estimation as a general approach rather than solving the broader parameter-determination problem analytically.

References

Determining this vector is an open problem in the literature, and we will broadly illustrate the approach in of maximum likelihood estimation (MLE), which we detail in the following section.

— From Exponential to Polynomial: An Exact Filter for High-Dimensional MSM Models  (2608.22864 - Hameedi, 24 Aug 2026) in Section 2, subsection “The MSM Model”