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Statistical inference for rough volatility: Minimax Theory

Chong, Carsten; Hoffmann, Marc; Liu, Yanghui; Szymanski, Grégoire; Rosenbaum, Mathieu (2022), Statistical inference for rough volatility: Minimax Theory. https://basepub.dauphine.psl.eu/handle/123456789/24557

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Type
Document de travail / Working paper
Date
2022
Titre de la collection
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Ville d’édition
Paris
Pages
54
Métadonnées
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Auteur(s)
Chong, Carsten
Columbia University, New York, USA
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Liu, Yanghui
Szymanski, Grégoire
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Rosenbaum, Mathieu
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Résumé (EN)
Rough 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.
Mots-clés
wavelets; scaling; minimax optimality; pre-averaging; iterated estimation procedure; Rough volatility; fractional Brownian motion