Volatility estimation in fractional Ornstein-Uhlenbeck models

Salwa Bajja, Khalifa Es-Sebaiy*, Lauri Viitasaari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

In this article, we study the asymptotic behavior of the realized quadratic variation of a process (Formula presented.) where u is a β-Hölder continuous process with (Formula presented.) and (Formula presented.) where (Formula presented.) and BH is a fractional Brownian motion with Hurst index (Formula presented.) By exploiting the concentration phenomena, we prove almost sure convergence of the quadratic variation, that holds uniformly in time and on the full range (Formula presented.) As an application, we construct strongly consistent estimator for the integrated volatility parameter in a model driven by (Formula presented.).

Original languageEnglish
Pages (from-to)94-111
JournalStochastic models
Volume36
Issue number1
Early online date1 Jan 2019
DOIs
Publication statusPublished - Jan 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional Brownian motion
  • quadratic variation
  • volatility

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