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Short dated smile under Rough Volatility: asymptotics and numerics

Friz, Peter K.; Gassiat, Paul; Pigato, Paolo (2021), Short dated smile under Rough Volatility: asymptotics and numerics. https://basepub.dauphine.psl.eu/handle/123456789/22295

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Type
Document de travail / Working paper
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https://hal.archives-ouvertes.fr/hal-03099744
Date
2021
Titre de la collection
Cahier de recherche du CEREMADE
Pages
23
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Auteur(s)
Friz, Peter K.
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pigato, Paolo
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Résumé (EN)
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2020] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices, using the framework [Bayer et al; A regularity structure for rough volatility; Math. Fin. 2020]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.