Rama CONT: Research Publications


  1. R Cont: Functional Ito calculus and functional Kolmogorov equations, in: V Bally et al: Stochastic integration by parts and Functional Ito calculus (Lectures Notes of the Barcelona Summer School on Stochastic Analysis, Centro de Recerca de Matematica, July 2012), Springer: 2016. Lecture Notes.
  2. R Cont & P Tankov: Financial modelling with jump processes, Chapman and Hall/ CRC Press, 2003.
  3. R Cont (Editor in Chief) Encyclopedia of Quantitative Finance Wiley (2010).
  4. R Cont (ed.) : Frontiers in Quantitative Finance: credit risk and volatility modeling, Wiley, 2008.

Recent working Papers

  1. R Cont, A Rossier, Renyuan Xu (2022) Asymptotic analysis of Deep Residual Networks .
  2. R Cont, M Vuletic (2022) Simulation of arbitrage-free implied volatility surfaces .
  3. R Cont, P Degond, L Xuan (2022) A mathematical framework for modelling order book dynamics .
  4. R Cont, A Rossier, Renyuan Xu (2022) Convergence and Regularization Properties of Gradient Descent for Deep Residual Networks .
  5. R Cont, Wei Xiong (2022) Dynamics of Market Making Algorithms in Dealer Markets: Learning and Tacit Collusion, SSRN Working Paper.
  6. R Cont, Ruhong Jin (2021) Fractional Ito calculus.
  7. R Cont, P Das (2022) Rough volatility: fact or artefact?
  8. A Ananova, R Cont, R Xu (2021) Model-free analysis of dynamic trading strategies.
  9. A Ananova, R Cont, R Xu (2020) Excursion risk.
  10. R Cont, Mihai Cucuringu, Renyuan Xu, Chao Zhang (2021) TailGAN : Nonparametric scenario generation for tail risk estimation.
  11. Francesco Capponi, R Cont (2020) Multi-Asset Market Impact and Order Flow Commonality.
  12. Francesco Capponi, R Cont (2019) Trade Duration, Volatility and Market Impact.
  13. A Ananova and R Cont (2018) Functional calculus for controlled paths.
  14. R Cont (2018) Margin requirements for non-cleared derivatives.
  15. R Cont, Yuhua Yu (2018) Algorithmic trade execution and intraday market dynamics.
  16. R Cont, Eric Schaanning (2017) Fire sales, indirect contagion and systemic stress-testing.
    Highlighted in Central Banking Journal.
  17. P Blacque-Florentin, R Cont (2015) Functional calculus and martingale representation formula for integer-valued measures.
  18. R Cont, A Bentata (2009)Mimicking the marginals of a semimartingale.
  19. R Cont, M Avellaneda (2013) Close-Out Risk Evaluation.
  20. R Cont, Adrien de Larrard: (2012) Order book dynamics in liquid markets: limit theorems and diffusion approximations, Working Paper.
  21. Statistical Modeling of Credit default swap portfolios, 2011. With: YuHang KAN.
  22. Central Clearing of interest rate swaps: a comparison of offerings, 2011. With: YuHua YU and Radu MONDESCU.
  23. R Cont, Yu GU Local vs non-local forward equations for option prices, 2012.

Research Publications


  1. R Cont In memoriam: Marco Avellaneda (1955-2022), Mathematical Finance, Vol. 33, No. 1.
  2. R Cont, Purba Das (2023) Quadratic variation and quadratic roughness, Bernoulli, Vol. 29, No. 1 (Feb 2023), 496-522.
  3. H Chiu, R Cont (2021) A model-free approach to continuous-time finance., Mathematical Finance, Vol. 33, in press.
  4. R Cont, M Cucuringu, V Glukhov, F Prenzel (2023) Analysis and Modeling of Client Order Flow in Limit Order Markets, Quantitative Finance, Vol. 23, in press.
  5. 2022

  6. H Chiu, R Cont (2022) Causal Functional Calculus. Transactions of the London Mathematical Society, Volume 9, No. 1 December 2022, 237-269.
  7. R Cont, P Das (2022) Quadratic variation along refining partitions: constructions and examples, Journal of Mathematical Analysis and Applications, Volume 512, 126173.
  8. Felix Prenzel, Rama Cont, Mihai Cucuringu, Jonathan Kochems (2022) Dynamic Calibration of Order Flow Models with Generative Adversarial Networks, ICAIF '22: 3rd ACM International Conference on AI in Finance, November 2022, pages 446--453.
  9. 2021

  10. R Cont, Wei Xiong (2021) Interactions of market making algorithms: a study on perceived collusion, ICAIF '21: Proceedings of the Second ACM International Conference on AI in Finance.
  11. R Cont, M Mueller (2021) A stochastic partial differential equation model for limit order book dynamics. SIAM Journal on Financial Mathematics, Vol. 12 (2), 744 - 787.
  12. A Cohen, R Cont, A Rossier, Renyuan Xu (2021) Scaling properties of deep residual networks, International Conference on Machine Learning (ICML 2021).
  13. R Cont, A Kotlicki, R Xu (2021) Modelling COVID-19 contagion: risk assessment and targeted mitigation policies. Royal Society Open Science, Volume 8, No. 3.
  14. R Cont, X Guo, R Xu (2021) Interbank lending with benchmark rates: Pareto optima for a class of singular control games. Mathematical Finance Vol. 31.
  15. 2020

  16. R Cont, A Kalinin (2020) On the support of solutions of stochastic differential equations with path-dependent coefficients . Stochastic Processes and their Applications, Vol. 130, Issue 5, May 2020, Pages 2639-2674.
  17. R Cont, A Kotlicki and L Valderrama (2020) Liquidity at Risk: Joint Stress Testing of Solvency and Liquidity. Journal of Banking and Finance. Volume 118, September 2020, 105871.
    IMF Working Paper 20/082.
  18. 2019

  19. R Cont, N Perkowski (2019) Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity, Transactions of the American Mathematical Society (Series B), Volume 6, 161-186.
  20. R Cont, E Schaanning (2019) Monitoring indirect contagion, Journal of Banking and Finance, Volume 104, July 2019, Pages 85-102.
  21. Sirignano, J and Cont, R (2019) Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning, Quantitative Finance Vol. 19, No. 9, 1449-1459.
    Featured in RISK Magazine (March 2018): Neural network learns universal model for stock-price moves.
  22. 2018

  23. H Chiu, R Cont (2018) On pathwise quadratic variation for cadlag functions, Electronic Communications in Probability, Volume 23, paper no. 85.
  24. 2017

  25. A Ananova, R Cont (2017) Pathwise integration with respect to paths of finite quadratic variation, Journal de Mathematiques Pures et Appliquees, Volume 107, No 6, June 2017, 737-757.
  26. R Cont (2017) Central clearing and risk transformation, Financial Stability Review (Banque de France), No. 21, April 2017.

  27. R Cont, A Kukanov (2017) Optimal order placement in limit order markets, Quantitative Finance, Volume 17, No. 1, 21-39.
  28. 2016

  29. R Cont, Yi Lu (2016) Weak approximations for martingale representations, Stochastic Processes and Applications, Volume 126, Issue 3, March 2016, Pages 857--882.
  30. R Cont, D.A. Fournie Functional Kolmogorov equations, in: V Bally, L Caramellino, R Cont (2016)Stochastic integration by parts and Functional Ito calculus, pages 183-207.
  31. H Amini, R Cont, A Minca: Resilience to contagion in financial networks, Mathematical finance, Volume 26, Issue 2, pages 329--365, April 2016.
  32. R Cont: Functional Ito calculus and functional Kolmogorov equations, in: V Bally et al. Stochastic integration by parts and Functional Ito calculus (Lectures Notes of the Barcelona Summer School on Stochastic Analysis, Centro de Recerca de Matematica, July 2012), Birkhauser.
  33. R Cont, L Wagalath: Fire sale forensics: measuring endogenous risk. Mathematical Finance, Volume 26, Issue 4 (Oct. 2016) 835-866.
  34. R Cont, L Wagalath (2016) Institutional investors and the dependence structure of asset returns. Int. J. Theor. Appl. Finance, Volume 19 (March 2016), 1650010-1650047.
  35. R Cont, A Minca (2016) Credit default swaps and systemic risk, Annals Of Operations Research, December 2016, Volume 247, Issue 2, 523-547.
  36. R Cont, L Wagalath (2016) Risk management for whales, RISK, June 2016.
  37. 2015

  38. A Bentata, R Cont: Forward equations for option prices in semimartingale models, Finance and Stochastics, Volume 19, No. 3, 617-651, July 2015.
  39. R Cont (2015) The end of the waterfall: default resources of central counterparties, Journal of Risk management in Financial Institutions, Vol. 8, No. 4.
  40. 2014

  41. R Cont, Th Kokholm (2014) Central Clearing of OTC Derivatives: bilateral vs multilateral netting, Statistics and Risk Modeling, Vol 31, No. 1, 3-22, March 2014.
  42. R Cont, A Kukanov, S Stoikov (2014) The price impact of order book events, Journal of Financial Econometrics Vol 12, No 1, 47-88.
  43. 2013

  44. R Cont, D Fournie (2013) Functional Ito calculus and stochastic integral representation of martingales, Annals of Probability, Vol 41, No 1, 109-133.
  45. R Cont, A de Larrard (2013) Price dynamics in a Markovian limit order book market, SIAM Journal for Financial Mathematics, Vol 4, No 1, 1-25, 2013.
  46. R Cont, R Deguest, XueDong He (2013) Loss-based risk measures, Statistics and Risk Modeling, Vol 30, No. 2, 133-167, June 2013.
  47. R Cont, R Deguest (2013) Equity correlations implied by index options: estimation and model uncertainty analysis, Mathematical Finance, Vol. 23, No. 3 (July 2013), 496--530.
  48. R Cont, A Minca (2013) Recovering Portfolio Default Intensities Implied by CDO Quotes, Mathematical Finance, Vol 23, 94-121 (2013).
  49. R Cont, A Moussa and E. B. Santos (2013) Network structure and systemic risk in banking systems.
    in: JP Fouque & J Langsam (eds.): Handbook of Systemic Risk, Cambridge University Press, p 327-368.
  50. R Cont, L Wagalath (2013) Running for the exit: distressed selling and endogenous correlation in financial markets. Mathematical Finance Vol 23, Issue 4, p. 718-741, October 2013.
  51. R Cont, Th Kokholm: A Consistent Pricing Model for Index Options and Volatility Derivatives, Mathematical Finance, Vol 23, Issue 2, pages 248-274, April 2013.
  52. Benoit Mandelbrot et la modélisation mathématique en finance, Gazette des Mathématiciens No 136, 159-166 (April 2013).
  53. 2012

  54. H Amini, R Cont, A Minca: Stress testing the resilience of financial networks, International Journal of Theoretical and applied finance, Vol 15, (2012).
  55. R Cont, Cathrine Jessen: Constant Proportion Debt Obligations (CPDO): Modeling and Risk Analysis, Quantitative Finance, Vol 12, No 8, p 1199-1218.
  56. Amini H, Cont R, Minca A: Stress Testing the Resilience of Financial Networks, in: Finance at Fields, Editor(s): Grasselli, Hughston, World Scientific Publishing Company, 2012, Pages: 17-36, ISBN:9789814407885
  57. 2011

  58. R Cont : Statistical Modeling of High Frequency Financial Data: Facts, Models and Challenges. IEEE Signal Processing, Volume 28, No 5, 16-25 (2011).
  59. R Cont, YuHang Kan : Dynamic hedging of portfolio credit derivatives. SIAM Journal for Financial Mathematics, Vol 2 (2011), 112-140.
  60. R Cont, N Lantos and Olivier Pironneau: A reduced basis method for option pricing, SIAM Journal for Financial Mathematics, Vol 2 (2011), 287-316.
  61. R Cont, C Mancini: Nonparametric tests for the pathwise properties of semimartingales, Bernoulli, Vol 17, No 2, 781-813 (2011).
  62. 2010

  63. R Cont, D Fournié Change of variable formulas for non-anticipative functional on path space, Journal of Functional Analysis, 259 (2010) 1043-1072.
  64. R Cont (2010)Credit default swaps and financial stability, Financial Stability Review (Banque de France), No 14, 35-43, July 2010.
  65. R Cont, S Stoikov and R Talreja: A stochastic model for order book dynamics, Operations Research, Volume 58, 549-563.
  66. R Cont, R Deguest and G Scandolo: Robustness and Sensitivity Analysis of Risk Measurement Procedures, Quantitative Finance, Vol. 10, No. 6, June–July 2010, 593–606.
  67. R Cont, M Loewe (2010)Social distance, heterogeneity and social interactions. Journal of Mathematical Economics, Volume 46, 572-590, 2010.
  68. R Cont, R Deguest and Yu Hang Kan: Default Intensities implied by CDO Spreads: Inversion Formula and Model Calibration, SIAM Journal of Financial Mathematics, Volume 1, pp. 555-585 (2010)..
  69. Model Calibration, in: Encyclopedia of Quantitative Finance, Wiley (2010), pages 1210-1219.
  70. Credit Default Swaps, in: Encyclopedia of Quantitative Finance, Wiley (2010), pages 424-431.
  71. 2009

  72. R Cont, D Fournié (2009) A functional extension of the Ito formula , Comptes Rendus Mathematiques de l'Academie des Sciences, Volume 348, Issue 1-2, 57-61.
  73. R Cont, P Tankov (2009) Constant Proportion Portfolio Insurance in presence of jumps in asset prices, Mathematical Finance, Vol. 19, Issue 3, pp. 379-401, July 2009.
  74. Les statistiques face aux événements extremes (in French) Pour La Science, Dec 2009.
  75. 2008

  76. R Cont, Emily Tanimura (2008) Small world graphs: characterization and alternative constructions, Advances in Applied Probability, Volume 40, no 4 (December 2008), 939-965.
  77. R Cont, Ioana Savescu (2008): Forward equations for portfolio credit derivatives, in: R Cont (ed.): Frontiers in Quantitative Finance: credit risk and volatility modeling, Wiley, 269-293.
  78. La modélisation mathématique des risques financiers (in French) Pour La Science, Dec 2008, 24-27.
  79. 2007

  80. R Cont, P Tankov, E Voltchkova (2007) Hedging with options in presence of jumps, in : Benth, F.E.; Di Nunno, G.; Lindstrom, T.; Oksendal, B.; Zhang, T. (Eds.) Stochastic Analysis and Applications: The Abel Symposium 2005 in honor of Kiyosi Ito, Springer, 197-218.
  81. R Cont (2007)Volatility clustering in financial markets, in: A Kirman & G Teyssiere (Eds.): Long memory in economics, Springer, 289-310.
  82. Model-free representation of pricing rules as conditional expectations, in: Stochastic processes and applications to mathematical finance, Proceedings of the 6th Ritsumeikan International Symposium, World Scientific (2007), p 53-66. With: Sara Biagini.
  83. La notation de credit des produits structures (in French) Echanges , Dec 2007, 69-72.
  84. 2006

  85. Model uncertainty and its impact on derivative instruments, Mathematical Finance, Vol 16, 519-542, July 2006.
  86. R Cont, P Tankov (2006) Retrieving Lévy processes from option prices: regularization of a nonlinear inverse problem. SIAM Journal of Control and Optimization, 45, 1, 1-25.
  87. R Cont, E Voltchkova: Finite difference methods for option pricing in jump-diffusion and exponential Levy models. SIAM Journal of Numerical Analysis, Vol 43, No. 4, pp. 1596-1626.
  88. 2005

  89. Modeling term structure dynamics: an infinite dimensional approach,International Journal of Theoretical and Applied Finance, Vol 8, No 3, p 1-24 (2005).
  90. R Cont, S Ben Hamida: Recovering volatility from option prices by evolutionary optimization. Journal of Computational Finance, Vol. 8, No 3, 43-76.
  91. R Cont, E Voltchkova (2005) Integrodifferential equations for option prices in exponential Lévy models, Finance & Stochastics, Volume 9, Number 3, 299-325.
  92. Long range dependence in financial time series, in: E Lutton & J Lévy Vehel (Eds.): Fractals in Engineering, Springer, 2005.
  93. R Cont, F Ghoulmie and JP Nadal (2005) Heterogeneity and feedback in an agent-based market model, Journal of Physics: Condensed Matter 17 (2005) S1259-S1268.
  94. 2004

  95. R Cont, P Tankov (2004)Nonparametric calibration of jump-diffusion processes, Journal of Computational Finance, Vol .7, No 3, 1-49.
  96. R Cont, P Tankov, E Voltchkova (2005)Option pricing models with jumps: integrodifferential equations and inverse problems.in: P Neittanmaki et al (Eds.): European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004).
  97. 2002

  98. R Cont, J Da Fonseca, V Durrleman: Stochastic models of implied volatility surfaces, Economic Notes, vol. 31, No. 2, 361 - 377.
  99. R Cont, Jose da Fonseca: Dynamics of implied volatility surfaces,Quantitative Financs, Vol 2, No 2, ( 2002 ) 45-60.
  100. 2001

  101. Empirical properties of asset returns: stylized facts and statistical issues in: Quantitative Finance, Vol 1, No 2, (March 2001) 223-236.
  102. 20-th century

  103. Herd behavior and aggregate fluctuations in speculative markets, Macroeconomic dynamics, Vol. 4, No.2, 170-196 (with: J.P. Bouchaud).
  104. JP Bouchaud, R Cont, N ElKaroui, N Sagna, M Potters.Phenomenology of the interest rate curve: a statistical analysis of term structure deformations", Applied Mathematical Finance, Vol. 6, No. 3 (Sept 1999), 209-232.
  105. Are financial crashes predictable?, Europhysics Letters, Vol. 45, No. 1, pp. 1-5 (1999). With: JP Bouchaud, M Potters and L Laloux.
  106. Modeling economic randomness: statistical mechanics of market phenomena, in: M Batchelor, L Wille (Eds.): Statistical Physics in the 21st century, World Scientific: 1998.
  107. J-Ph Bouchaud, R Cont: "A Langevin approach to stock market fluctuations and crashes", European Physical Journal B 6 (1998) 4, 543-550.
  108. Des marches aléatoires aux marchés aléatoires: modélisation statistique des fluctuations boursieres. Doctoral thesis, Université de Paris IX.
  109. R Cont, D Sornette: Convergent multiplicative processes repelled from zero: power laws and truncated power laws, Journal de Physique I , Vol. 7, March 1997, 431-444.
  110. J-Ph Bouchaud, R Cont, M Potters (1997) Scaling in stock market data: stable laws and beyond, in: B. Dubrulle, F. Graner, D. Sornette (Eds.):Scale invariance and beyond, Springer.
    Introduced the class of `tempered stable' Lévy processes in financial modelling.