Stefano De Marco
Associate Professor in Applied Mathematics at CMAP, Ecole Polytechnique.

Numerical probability, stochastic analysis and mathematical finance - with focus on

• Risk management of options, model risk, robust hedging
• Application of Monte-Carlo methods in risk computations, multi-level methods
• Volatility modeling, volatility derivatives
• Asymptotics for diffusion processes, large deviations, tail estimates, Malliavin calculus

• Marius Chevallier (2023- ). Consistent no-arbitrage market risk and counterparty risk metrics.
  Joint supervision with Pierre-Emmanuel Levy-dit-Vehel (Société Générale), thèse CIFRE.


• Jules Delemotte (2022- ). Smile dynamics and rough volatility modeling.
  Joint supervision with Mathieu Rosenbaum (Ecole Polytechnique) and Florent Ségonne (80 Technologies), thèse CIFRE.


• Arianna Mingone (2021-2023). Advanced implied volatility modeling for risk management and central clearing.
  Joint supervision with Claude Martini (Zeliade Systems), thèse CIFRE.


• Manon Rivoire (2020- ). Risk metrics in finance: forecast, backtesting, sensitivity, robustness.
  Joint supervision with Laurence Carassus, Matthieu Garcin, Emmanuel Gobet.


• Florian Bourgey (2017-2020). Stochastic approximations for financial risk computations.
  Joint supervision with Emmanuel Gobet.

• Membre du comité du Département de Mathématiques Appliquées, Ecole Polytechnique, collège des enseignants à temps complet

• Deep Learning in Finance MAP548, Ecole Polytechnique, Double degree Data and Finance (MScT). Page Moodle.


• Numerical processing of financial data MAP542, Ecole Polytechnique, Double degree Data and Finance (MScT). Page Moodle.


• Calibration de modèle, volatilité locale et stochastique. M2 Probabilités et Finance, Sorbonne Université - Ecole Polytechnique. Page Moodle.


• Stochastic Simulation and Monte-Carlo methods MAP556, Ecole Polytechnique, 3ème année cycle ingénieur (2012 - 2022).


• Modal MAP473D Simulation numérique aléatoire, Ecole Polytechnique, 2ème année cycle ingénieur (2013 - 2021)


• Local and stochastic volatility, model calibration. Master MMMEF Université Paris 1 - Ensta - Ensae (2015 - 2018)

Yet another analysis of the SP500 at-the-money skew: crossover of different power-law behaviours. With J. Delemotte, F. Ségonne
Preprint SSRN, 2023

Weak approximations and VIX option price expansions in forward variance curve models. With F. Bourgey, E. Gobet
Quantitative Finance, 23:9, 1259-1283, 2023. ArXiv version.

Local volatility from rough volatility. With F. Bourgey, P. Friz, P. Pigato.
Mathematical Finance, 33(4):1119-1145, 2023.


Publications

Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model. With F. Bourgey.
Journal of Computational Finance, 26(2):53-82, 2022.
Selected within the "online early" articles of the JCF. ArXiv version.

On the harmonic mean representation of the implied volatility.
SIAM J. Finan. Math, 12(2):551-565, 2021. ArXiv version.

Multilevel Monte-Carlo methods and lower/upper bounds in Initial Margin computations. With F. Bourgey, E. Gobet, A. Zhou.
Monte Carlo Methods and Applications, 26(2):131–161, 2020. Hal version.

Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements.
ESAIM: Proceedings and Surveys, Vol. 65, pp. 1-26, 2019. With A. Agarwal, E. Gobet, J. López-Salas, F. Noubiagain, A. Zhou. Hal

Study of new rare event simulation schemes and their application to extreme scenario generation. With A. Agarwal, E. Gobet, G. Liu.
Mathematics and Computer in Simulations, 143, pp. 89-98, 2018. Hal.

Local Volatility, Conditioned Diffusions, and Varadhan's Formula. With P. Friz.
SIAM J. Finan. Math., 9(2), 835–874, 2018. ArXiv.

Moment generating functions and Normalized implied volatilities: unification and extension via Fukasawa's pricing formula. With C. Martini
Quantitative Finance, 18, pp. 609–622, 2018. Journal eprint link (expires after 50 downloads), ArXiv.

Local volatility from American options. With P. Henry-Labordère.
Risk Magazine, November 2017. SSRN.

Shapes of implied volatility with positive mass at zero. With C. Hillairet and A. Jacquier.
SIAM J. Financ. Math. 8(1), pp. 709-737, 2017. ArXiv.

Two examples of non strictly convex large deviations. With A. Jacquier and P. Roome.
Electronic Communications in Probability, 21(1), p. 1-12, 2016. arXiv.

Linking Vanillas and VIX options: A constrained martingale optimal transport problem. With P. Henry-Labordère.
SIAM J. Financ. Math 6(1), pp. 1171–1194, 2015. journal link.

On small–noise equations with degenerate limiting system arising from volatility models. With G. Conforti and J-D. Deuschel.
Large Deviations and Asymptotic Methods in Finance, Springer Proceedings in Mathematics and Statistics, Vol. 110, 2015. arXiv.

Rational Shapes of the local volatility surface. With P. Friz and S. Gerhold.
Risk magazine, February 2013, p. 82-87. Available here.

The Term Structure of Implied Volatility in Symmetric Models, with applications to Heston. With C. Martini.
The International Journal of Theoretical and Applied Finance,15(4): 1250026 [27 pages], 2012. journal, ssrn.

Some estimates in extended Stochastic Volatility models of Heston type. With V. Bally.
Risk and Decision Analysis, 2(4): 195-206, 2011. journal, hal.

Smoothness and Asymptotic Estimates of densities for SDEs with locally smooth coefficients and applications to square-root diffusions.
Annals of Applied Probability, 21(4): 1282-1321, 2011. journal, arXiv.

Quasi-Explicit calibration of Gatheral's SVI model. 2009.
Zeliade Systems White Paper #5, available here. With C. Martini.

J'ai organisé jusqu'à juin 2017 le GT modèles stochastiques et finance du CMAP, en collaboration avec ENSTA et ENSAE. Mon collègue Thibaut Mastrolia a pris le relai en 2017-18.