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We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$.
Semi-stable stochastic processes
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Formule de Taylor stochastique et développement asymptotique d’intégrales de Feynman
Robert Azencott · 1982
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Large deviations and the Malliavin calculus
Jean-Michel Bismut · 1984
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Petites perturbations aléatoires des systemes dynamiques: développements asymptotiques
Robert Azencott · 1985
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Methods de Laplace et de la phase stationnaire sur l’espace de Wiener
Gérard Ben Arous · 1988
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Large deviations
Jean-Dominique Deuschel and Daniel W. Stroock · 1989
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A simple calibration procedure of stochastic volatility models with jumps by short term asymptotics
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On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility
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Approximation and calibration of short-term implied volatilities under jump-diffusion stochastic volatility
Alexey Medvedev and Olivier Scaillet · 2007
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The asymptotic expansion formula of implied volatility for dynamic SABR model and FX hybrid model
Yasufumi Osajima · 2007
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Densities for rough differential equations under Hörmander’s condition
Thomas Cass and Peter Friz · 2010
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Frank WJ Olver · 2010
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Yasufumi Osajima · 2015
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Christian Bayer, Peter K. Friz, and Jim Gatheral · 2016
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Decoupling the short- and long-term behavior of stochastic volatility
Mikkel Bennedsen, Asger Lunde, and Mikko S Pakkanen · 2016
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Omar El Euch and Mathieu Rosenbaum · 2016
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Archil Gulisashvili, Blanka Horvath, and Antoine Jacquier · 2016
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A new look at short-term implied volatility in asset price models with jumps
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Jean-Dominique Deuschel, Peter K. Friz, Antoine Jacquier, and Sean Violante · 2014
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A regularity structure for rough volatility
Christian Bayer, Peter K. Friz, Paul Gassiat, Jörg Martin, and Benjamin Stemper · 2017
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Mikkel Bennedsen, Asger Lunde, and Mikko S Pakkanen · 2017
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