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Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling.
Complete models with stochastic volatility
D. G. Hobson and L. C. Rogers · 1998
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VIX: Cboe volatility index
CBOE · 2003
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Market heterogeneities and the causal structure of volatility
P. E. Lynch and G. Zumbach · 2003
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Path dependent volatility
P. Foschi and A. Pascucci · 2008
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Time reversal invariance in finance
G. Zumbach · 2009
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Volatility conditional on price trends
G. Zumbach · 2010
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A consistent pricing model for index options and volatility derivatives
R. Cont and T. Kokholm · 2013
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Consistent modelling of VIX and equity derivatives using a 3/2 plus jumps model
J. Baldeaux and A. Badran · 2014
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Path-dependent volatility
J. Guyon · 2014
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A regime-switching Heston model for VIX and S&P 500 implied volatilities
A. Papanicolaou and R. Sircar · 2014
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Linking vanillas and VIX options: a constrained martingale optimal transport problem
S. De Marco and P. Henry-Labordere · 2015
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Joint pricing of VIX and SPX options with stochastic volatility and jump models
T. Kokholm and M. Stisen · 2015
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Pricing under rough volatility
C. Bayer, P. Friz, and J. Gatheral · 2016
Cited alongside, same era.
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
T. Jaisson and M. Rosenbaum · 2016
Cited alongside, same era.
Quadratic Hawkes processes for financial prices
P. Blanc, J. Donier, and J.-P. Bouchaud · 2017
Cited alongside, same era.
Regime-switching stochastic volatility model: estimation and calibration to VIX options
S. Goutte, A. Ismail, and H. Pham · 2017
Cited alongside, same era.
Rough but not so tough: Fast hybrid schemes for fractional Riccati equations
G. Callegaro, M. Grasselli, and G. Pagès · 2018
Cited alongside, same era.
Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
Smiling twice: The Heston++ model
C. Pacati, G. Pompa, and R. Renò · 2018
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Affine Volterra processes
E. Abi Jaber, M. Larsson, and S. Pulido · 2019
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Inversion of convex ordering: Local volatility does not maximize the price of VIX futures
B. Acciaio and J. Guyon · 2019
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From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect
A. Dandapani, P. Jusselin, and M. Rosenbaum · 2019
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The Zumbach effect under rough Heston
O. El Euch, J. Gatheral, R. Radoičić, and M. Rosenbaum · 2019
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Roughening Heston
O. El Euch, J. Gatheral, and M. Rosenbaum · 2019
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C. Cuchiero and J. Teichmann · 2018
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The microstructural foundations of leverage effect and rough volatility
O. El Euch, M. Fukasawa, and M. Rosenbaum · 2018
Cited alongside, same era.
Perfect hedging in rough Heston models
O. El Euch and M. Rosenbaum · 2018
Cited alongside, same era.
Volatility is rough
J. Gatheral, T. Jaisson, and M. Rosenbaum · 2018
Cited alongside, same era.
On the joint calibration of SPX and VIX options
J. Guyon · 2018
Cited alongside, same era.
No-arbitrage implies power-law market impact and rough volatility
P. Jusselin and M. Rosenbaum · 2018
Cited alongside, same era.
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The characteristic function of rough Heston models
O. El Euch and M. Rosenbaum · 2019
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Rational approximation of the rough Heston solution
J. Gatheral and R. Radoičić · 2019
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Inversion of convex ordering in the VIX market
J. Guyon · 2019
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The joint S&P 500/VIX smile calibration puzzle solved
J. Guyon · 2019
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Deep learning volatility
B. Horvath, A. Muguruza, and M. Tomas · 2019
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