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Precise asymptotics: robust stochastic volatility models

Friz, Peter K.; Gassiat, Paul; Pigato, Paolo (2021), Precise asymptotics: robust stochastic volatility models, Annals of Applied Probability, 31, 2, p. 896 - 940. 10.1214/20-AAP1608

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Annals of Applied Probability
Volume
31
Number
2
Publisher
Institute of Mathematical Statistics
Pages
896 - 940
Publication identifier
10.1214/20-AAP1608
Metadata
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Author(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]
Abstract (EN)
We present 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. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough volatility, 2017]. In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, Inahama--Kawabi on rough path space. When applied to rough volatility models, e.g. in the setting of [Forde-Zhang, Asymptotics for rough stochastic volatility models, 2017], one obtains precise asymptotic for European options which refine known large deviation asymptotics.
Subjects / Keywords
European option pricing; Regularity structures; Rough paths; Rough volatility; small-time asymptotics

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