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The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.
A closed-form solution for options with stochastic volatility with applications to bond and currency options
Steven L Heston · 1993
Earlier work this paper cites.
Approximation of some Gaussian processes
Philippe Carmona, Laure Coutin, and G. Montseny · 1998
Earlier work this paper cites.
Affine processes and applications in finance
D. Duffie, D. Filipović, and W. Schachermayer · 2003
Earlier work this paper cites.
Volatility Markets – Consistent modeling, hedging and practical implementation
Hans Bühler · 2006
Earlier work this paper cites.
A didactic note on affine stochastic volatility models
J. Kallsen · 2006
Earlier work this paper cites.
Stochastic volatility’s orderly smiles
L. Bergomi and J. Guyon · 2012
Earlier work this paper cites.
Affine fractional stochastic volatility models
F. Comte, L. Coutin, and E. Renault · 2012
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The stochastic Fubini theorem revisited
Mark Veraar · 2012
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Stochastic equations in infinite dimensions
Giuseppe Da Prato and Jerzy Zabczyk · 2014
Cited alongside, same era.
Pricing under rough volatility
Christian Bayer, Peter Friz, and Jim Gatheral · 2016
Cited alongside, same era.
The characteristic function of rough Heston models
Omar El Euch and Mathieu Rosenbaum · 2016
Cited alongside, same era.
Eduardo Abi Jaber, Martin Larsson, and Sergio Pulido · 2017
Short-time at-the-money skew and rough fractional volatility
Masaaki Fukasawa · 2017
Later among the works it cites.
Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
Christa Cuchiero and Josef Teichmann · 2018
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Affine forward variance models
Jim Gatheral and Martin Keller-Ressel · 2018
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Volatility is rough
Jim Gatheral, Thibault Jaisson, and Mathieu Rosenbaum · 2018
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Asymptotic behavior of the fractional Heston model
Hamza Guennoun, Antoine Jacquier, Patrick Roome, and Fangwei Shi · 2018
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Affine representations of fractional processes with applications in mathematical finance
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Cited alongside, same era.
Multi-factor approximation of rough volatility models
Eduardo Abi Jaber and Omar El Euch
Cited in the paper.
Markovian structure of the Volterra Heston model
Eduardo Abi Jaber and Omar El Euch
Cited in the paper.
Philipp Harms and David Stefanovits · 2018
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