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It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities.
A cluster process representation of a self-exciting process
A. G. Hawkes and D. Oakes · 1974
Earlier work this paper cites.
The stochastic behavior of common stock variances: Value, leverage and interest rate effects
A. A. Christie · 1982
Earlier work this paper cites.
A closed-form solution for options with stochastic volatility with applications to bond and currency options
S. L. Heston · 1993
Earlier work this paper cites.
Fractional integrals and derivatives
S. G. Samko, A. A. Kilbas, and O. I. Marichev · 1993
Earlier work this paper cites.
The variation of certain speculative prices
B. B. Mandelbrot · 1997
Earlier work this paper cites.
Option valuation using the fast Fourier transform
P. Carr and D. Madan · 1999
Earlier work this paper cites.
The fracpece subroutine for the numerical solution of differential equations of fractional order
K. Diethelm and A. D. Freed · 1999
Earlier work this paper cites.
Continuous martingales and Brownian motion
D. Revuz and M. Yor · 1999
Earlier work this paper cites.
A simple option formula for general jump-diffusion and other exponential lévy processes
A. L. Lewis · 2001
Earlier work this paper cites.
A predictor-corrector approach for the numerical solution of fractional differential equations
K. Diethelm, N. J. Ford, and A. D. Freed · 2002
Earlier work this paper cites.
Probability distribution of returns in the Heston model with stochastic volatility
A. A. Dragulescu and V. M. Yakovenko · 2002
Earlier work this paper cites.
Theory of financial risk and derivative pricing: from statistical physics to risk management
J.-P. Bouchaud and M. Potters · 2003
Earlier work this paper cites.
Detailed error analysis for a fractional Adams method
K. Diethelm, N. J. Ford, and A. D. Freed · 2004
Earlier work this paper cites.
Pricing options with VG model using FFT
A. Itkin · 2005
Earlier work this paper cites.
Not-so-complex logarithms in the Heston model
C. Kahl and P. Jäckel · 2005
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H. Albrecher, P. Mayer, W. Schoutens, and J. Tistaert · 2007
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A. M. Mathai and H. J. Haubold · 2008
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C. Li and C. Tao · 2009
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The Heston option pricing model
S.-H. Poon · 2009
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Option pricing formulae using Fourier transform: Theory and application
M. Schmelzle · 2010
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Critical reflexivity in financial markets: a Hawkes process analysis
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Limit theorems for stochastic processes
J. Jacod and A. Shiryaev · 2013
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Volatility is rough
J. Gatheral, T. Jaisson, and M. Rosenbaum · 2014
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Asymptotic behaviour of the fractional Heston model
H. Guennoun, A. Jacquier, and P. Roome · 2014
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Hybrid scheme for Brownian semistationary processes
M. Bennedsen, A. Lunde, and M. S. Pakkanen · 2015
Later among the works it cites.
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M. Fukasawa · 2011
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The volatility surface: a practitioner’s guide
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Mittag-leffler functions and their applications
H. J. Haubold, A. M. Mathai, and R. K. Saxena · 2011
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FX smile in the Heston model
A. Janek, T. Kluge, R. Weron, and U. Wystup · 2011
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The small-time smile and term structure of implied volatility under the Heston model
M. Forde, A. Jacquier, and R. Lee · 2012
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E. Bacry, S. Delattre, M. Hoffmann, and J.-F. Muzy · 2013
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T. Jaisson, M. Rosenbaum, et al · 2015
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The forward smile in local-stochastic volatility models
A. Mazzon and A. Pascucci · 2015
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The microstructural foundations of leverage effect and rough volatility
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Large-maturity regimes of the Heston forward smile
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Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
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