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Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process.

Anas D Khalaf1, Tareq Saeed2, Reman Abu-Shanab3

  • 1General Directorate of Education in Saladin, Ministry of Education, Tikrit 34001, Iraq.

Entropy (Basel, Switzerland)
|May 28, 2022
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Summary

This study estimates drift parameters for the sub-fractional Vasicek process using discrete observations. New estimators demonstrate strong consistency and asymptotic normality, validated by simulations.

Keywords:
Berry–EsseenVasicek-type modelcentral limit theoremparameter estimationstrong consistency

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Area of Science:

  • Stochastic Calculus
  • Financial Mathematics
  • Time Series Analysis

Background:

  • The Vasicek model is a cornerstone in financial mathematics for modeling interest rates.
  • Sub-fractional Brownian motion (sfBm) introduces long-range dependence, requiring specialized estimation techniques.
  • Accurate parameter estimation is crucial for reliable financial modeling and risk management.

Purpose of the Study:

  • To develop and analyze new estimators for drift parameters (θ and μ) in the sub-fractional Vasicek process.
  • To establish the statistical properties (consistency and normality) of these novel estimators.
  • To validate the performance of the estimators through numerical simulations.

Main Methods:

  • Utilizing discrete time observations of the sub-fractional Vasicek process.
  • Applying Nordin-Peccati analysis techniques for parameter estimation.
  • Leveraging the properties of sub-fractional Brownian motion (sfBm) to prove theoretical results.

Main Results:

  • Introduction of novel estimators, denoted as θ^ and μ^, for the drift parameters.
  • Theoretical establishment of strong consistency for both θ^ and μ^.
  • Demonstration of asymptotic normality for the proposed estimators θ^ and μ^.

Conclusions:

  • The developed estimators provide a robust method for parameter estimation in sub-fractional Vasicek models.
  • The strong consistency and asymptotic normality confirm the reliability of the estimators.
  • Numerical simulations support the theoretical findings across various Hurst index values.