Asymptotic behaviour of randomised fractional volatility models

Blanka Horvath, Antoine Jacquier, Chloé Lacombe

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail behaviours in particular). In order to do so, we extend some results on sample path large deviations for such diffusions. As an application, we show how these results characterise the small-time and tail estimates of the implied volatility for rough volatility models, recently proposed in mathematical finance.

Original languageEnglish
Pages (from-to)496-523
Number of pages28
JournalJournal of Applied Probability
Volume56
Issue number2
DOIs
StatePublished - 1 Jun 2019
Externally publishedYes

Keywords

  • Rough volatility
  • implied volatility asymptotics
  • large deviations

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