Detecting rough volatility: a filtering approach

Camilla Damian*, Rüdiger Frey

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review

Abstract

In this paper, we focus on filtering and parameter estimation in stochastic volatility models when observations arise from high-frequency data. We are particularly interested in rough volatility models where spot volatility is driven by fractional Brownian motion with Hurst index (Formula presented.). Since volatility is not directly observable, we rely on particle filtering techniques for statistical inference regarding the current level of volatility and the parameters governing its dynamics. In order to obtain numerically efficient and recursive algorithms, we use the fact that a fractional Brownian motion can be represented through a superposition of Markovian semimartingales (Ornstein-Uhlenbeck processes). We analyze the performance of our approach on simulated data and we compare it to similar studies in the literature. The paper concludes with an empirical case study, where we apply our methodology to high-frequency data of a liquid stock.

Original languageEnglish
Pages (from-to)1493-1508
JournalQuantitative Finance
Volume24
Issue number10
Early online dateSept 2024
DOIs
Publication statusPublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Fractional Brownian motion
  • High-frequency data
  • Nested particle filter
  • Rough volatility
  • Stochastic filtering

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