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We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models.
B. Mandelbrot and J. Van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Review
1968
Earlier work this paper cites.
X. Fernique. Intégrabilité des vecteurs Gaussiens. CRAS Paris
1970
Earlier work this paper cites.
F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Econ
1973
Earlier work this paper cites.
M.A. Berger and V.J. Mizel. Volterra Equations with Itô Integrals, I. Journal of Integral Equations
1980
Earlier work this paper cites.
M.A. Berger and V.J. Mizel. Volterra Equations with Itô Integrals, II. Journal of Integral Equations
1980
Earlier work this paper cites.
I. Gyöngy. Mimicking the one-dimensional marginal distributions of processes vaving an Itô differential. Probability Theory and Related Fields
1986
Earlier work this paper cites.
I. Karatzas and S. Shreve. Brownian motion and stochastic calculus. Springer-Verlag, New-York, 1988
1988
Earlier work this paper cites.
H. Lee. Neural algorithm for solving differential equations. Journal of Computational Physics
1990
Earlier work this paper cites.
G. Barles and PE. Souganidis. Convergence of approximation schemes for fully nonlinear second-order equation. Asymptotic Analysis
1991
Earlier work this paper cites.
B. Dupire. Pricing with a smile. Risk
1994
Earlier work this paper cites.
F. Comte and E. Renault. Long memory continuous time models. Journal of Econometrics
1996
Earlier work this paper cites.
L. Decreusefond and A. Ustünel. Stochastic analysis of fractional Brownian motion. Potential Analysis
1996
Earlier work this paper cites.
N. El Karoui, S. Peng and M.C. Quenez. Backward stochastic differential equations in Finance. Math. Fin
1997
Earlier work this paper cites.
M. Romano and N. Touzi. Contingent claims and market completeness in a stochastic volatility model. Mathematical Finance
1997
Earlier work this paper cites.
I. Lagaris, A. Likas, and D. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks
1998
Earlier work this paper cites.
M. Djehiche and M. Eddahbi. Hedging options in market models modulated by the fractional Brownian motion. Stochastic Analysis and Applications
2001
Earlier work this paper cites.
A. Lewis. A simple option formula for general jump-diffusion and other exponential Lévy processes, Available at optioncity.net/pubs/ExpLevy.pdf , 2001
2001
Earlier work this paper cites.
B. Bouchard and N. Touzi. Discrete time approximation and Monte-Carlo simulation of backward stochastic differential equation. Stochastic Processes and their Applications
2004
Earlier work this paper cites.
R. Cont. Modeling term structure dynamics: an infinite dimensional approach. IJTAF
2005
Earlier work this paper cites.
J. Gatheral. The Volatility Surface: a practitioner’s guide. John Wiley & Sons, 2006
2006
Earlier work this paper cites.
E. Alòs, J. León and J. Vives. On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility. Finance and Stochastics
2007
Earlier work this paper cites.
M. Fukasawa. Asymptotic analysis for stochastic volatility: martingale expansion. Finance and Stoch
2011
Earlier work this paper cites.
S. Peng and M. Xu. Numerical algorithms for backward stochastic differential equations with 1-d Brownian motion: Convergence and simulations. ESAIM: Mathematical Modelling and Numerical Analysis
2011
Earlier work this paper cites.
J. Picard. Representation formulae for the fractional Brownian motion. Séminaire de Probabilités
2011
Earlier work this paper cites.
L. Bergomi and J. Guyon. Stochastic volatility’s orderly smiles. Risk
2012
Earlier work this paper cites.
J. Guyon and P. Henry-Labordère. Being particular about calibration. Risk Magazine
2012
Earlier work this paper cites.
G. Da Prato and J. Zabczyk. Stochastic equations in infinite dimensions. CUP, 2014
2014
Cited alongside, same era.
I. Ekren, N. Touzi and J. Zhang. On viscosity solutions of path-dependent PDEs. Annals Proba
2014
Cited alongside, same era.
J. Gatheral and A. Jacquier. Arbitrage-free SVI volatility surfaces. Quantitative Finance
2014
Cited alongside, same era.
Z. Ren, N. Touzi and J. Zhang, An overview of viscosity solutions of path-dependent PDEs. Stochastic Analysis and Applications
2014
Cited alongside, same era.
J. Zhang and J. Zhuo. Monotone schemes for fully nonlinear parabolic path dependent PDEs. Journal Fin. Eng
2014
Cited alongside, same era.
J. Ba and D. Kingma. Adam: a method for stochastic optimization. Proceedings of the International Conference on Learning Representations
C. Bayer, P. Friz, A. Gulisashvili, B. Horvath and B. Stemper. Short-time near the money skew in rough fractional stochastic volatility models. Quantitative Finance
2019
Closest in time.
2019
Closest in time.
B. Dupire. Functional Itô Calculus. Quantitative Finance
2019
Closest in time.
O. El Euch and M. Rosenbaum. The characteristic function of rough Heston models. Math. Finance
2019
Closest in time.
O. El Euch, J. Gatheral and M. Rosenbaum. Roughening Heston. Risk
2019
Closest in time.
P. Gassiat. On the martingale property in the rough Bergomi model. Electronic Comm. Probability
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2015
Cited alongside, same era.
C. Bayer, P. Friz and J. Gatheral. Pricing under rough volatility. Quantitative Finance
2015
Cited alongside, same era.
I. Ekren, N. Touzi and J. Zhang. Viscosity solutions of fully nonlinear parabolic path-dependent PDEs: Part I. Annals of Probability
2016
Cited alongside, same era.
I. Ekren, N. Touzi and J. Zhang. Viscosity solutions of fully nonlinear parabolic path-dependent PDEs: Part II. Annals of Probability
2016
Cited alongside, same era.
M. Bennedsen, A. Lunde and M.S. Pakkanen. Hybrid scheme for Brownian semistationary processes. Finance and Stochastics
2017
Cited alongside, same era.
C. Cortes, X. Gonzalvo, V. Kuznetsov, M. Mohri and S. Yang. AdaNet: adaptive structural learning of artificial neural networks. Proceedings of Machine Learning Research
2017
Cited alongside, same era.
M. Forde and H. Zhang. Asymptotics for rough stochastic volatility models. SIAM Fin. Math
2017
Cited alongside, same era.
2019
Closest in time.
J. Gatheral and M. Keller-Ressel. Affine forward variance models. Finance and Stochastics
2019
Closest in time.
J. Gatheral and R. Radoičić. Rational approximation of the rough Heston solution. IJTAF
2019
Closest in time.
C. Heinrich, M. Pakkanen and AE.D. Veraart. Hybrid simulation scheme for volatility modulated moving average fields. Mathematics and Computers in Simulation
2019
Closest in time.
B. Horvath, A. Jacquier and C. Lacombe. Asymptotic behaviour of randomised fractional volatility models. Journal of Applied Probability
2019
Closest in time.
Q. Chan-Wai-Nam, J. Mikael and X. Warin. Machine Learning for semi linear PDEs Journal of Scientific Computing
2019
Closest in time.
2019
Closest in time.
F. Viens and J. Zhang. A martingale approach for fractional Brownian motions and related path-dependent PDEs. Annals of Applied Probability
2019
Closest in time.
C. Bayer, C. Ben Hammouda and R. Tempone. Hierarchical adaptive sparse grids for option pricing under the rough Bergomi model. Quantitative Finance
2020
Closest in time.
C. Bayer, P. Friz, P. Gassiat, J. Martin and B. Stemper. A regularity structure for rough volatility. Mathematical Finance
2020
Closest in time.
2020
Closest in time.
B. Horvath, A. Jacquier and P. Tankov. Volatility options in rough volatility models. SIFIN
2020
Closest in time.
C. Huré, H. Pham and X.Warin. Some machine learning schemes for high-dimensional nonlinear PDEs. Mathematics of Computation
2020
Closest in time.
B. Jourdain and A. Zhou. Existence of a calibrated regime switching local volatility model and new fake Brownian motions. Mathematical Finance
2020
Closest in time.
D. Lacker, M. Shkolnikov and J. Zhang. Inverting the Markovian projection, with an application to local stochastic volatility models. Annals of Probability
2020
Closest in time.
H. Stone. Calibrating rough volatility models: a convolutional neural network approach. Quantitative Finance
2020
Closest in time.
G. Callegaro, M. Grasselli and G. Pagès. Fast hybrid schemes for fractional Riccati equations (rough is not so tough). Mathematics of Operations Research
2021
Closest in time.
W. McGhee. An artificial neural network representation of the SABR stochastic volatility model. Journal of Computational Finance
2021
Closest in time.
C. Bayer, J. Qiu and Y. Yao. Pricing options under rough volatility with Backward SPDEs. SIAM Journal on Financial Mathematics
2022
Closest in time.
J. Guyon. The VIX Future in Bergomi models: Fast approximation formulas and joint calibration with S&P 500 skew. SIAM Journal on Financial Mathematics
2022
Closest in time.