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

2 Citations (Scopus)

Abstract

In this article, we study the asymptotic behavior of the realized quadratic variation of a process ʃ t 0 u sdY (1) s, where u is a β-Hölder continuous process with β>1-H and Y (1) tt 0 e -sdB H as, where a t=He t/H and B H is a fractional Brownian motion with Hurst index H ϵ (0,1) By exploiting the concentration phenomena, we prove almost sure convergence of the quadratic variation, that holds uniformly in time and on the full range H ϵ (0,1) As an application, we construct strongly consistent estimator for the integrated volatility parameter in a model driven by Y (1).

Original languageEnglish
Pages (from-to)94-111
Number of pages18
JournalStochastic models
Volume36
Issue number1
Early online date1 Jan 2019
DOIs
Publication statusPublished - 2 Jan 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional Brownian motion
  • quadratic variation
  • volatility

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