Show simple item record

Statistical inference for rough volatility: Minimax Theory

hal.structure.identifierColumbia University, New York, USA
dc.contributor.authorChong, Carsten
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHoffmann, Marc
dc.contributor.authorLiu, Yanghui
hal.structure.identifierCentre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
dc.contributor.authorSzymanski, Grégoire
hal.structure.identifierCentre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
dc.contributor.authorRosenbaum, Mathieu
dc.date.accessioned2023-03-10T14:19:42Z
dc.date.available2023-03-10T14:19:42Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/24557
dc.language.isoenen
dc.subjectwaveletsen
dc.subjectscalingen
dc.subjectminimax optimalityen
dc.subjectpre-averagingen
dc.subjectiterated estimation procedureen
dc.subjectRough volatilityen
dc.subjectfractional Brownian motionen
dc.subject.ddc519en
dc.titleStatistical inference for rough volatility: Minimax Theoryen
dc.typeDocument de travail / Working paper
dc.description.abstractenRough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter H. In this work, we provide a rigorous statistical analysis of these models. To do so, we establish minimax lower bounds for parameter estimation and design procedures based on wavelets attaining them. We notably obtain an optimal speed of convergence of n −1/(4H+2) for estimating H based on n sampled data, extending results known only for the easier case H > 1/2 so far. We therefore establish that the parameters of rough volatility models can be inferred with optimal accuracy in all regimes.en
dc.publisher.cityParisen
dc.identifier.citationpages54en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2023-03-10T14:12:58Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail
Name:
2210.01214.pdf
Size:
527.4Kb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record