Séminaire thématique de l’Observatoire des impacts territoriaux de la crise
Le Centre Cournot et la Banque postale partagent leurs réflexions sur les effets de la crise sanitaire sur les finances des collectivité
Luc-Alain Vervisch (Banque Postale) et Jean-Philippe Touffut (Centre Cournot) présenteront une analyse croisée de la géographie de la crise.
Pour vous inscrire, c'est par ici : https://lnkd.in/eXbR4HKZ
Sloan conference series
Organized with École polytechnique and the University of California at Irvine
PROGRAM - PRESENTATIONS - VIDEOS
WEDNESDAY, 31 AUGUST 2022
Welcome and Introduction to the Conference
Jean-Philippe Touffut (Fondation Cournot) and Josselin Garnier (École Polytechnique)
Video – Introduction
PART 1 - Chaired by David Mordecai (Courant Institute, NYU)
The fractional Brownian motion in volatility modeling
Elisa Alòs (Universitat Pompeu Fabra, Barcelona)
Presentation – Alòs
Video – Alòs
This talk focuses on the properties of volatilities driven by the fractional Brownian motion (fBm) or related processes. In particular, we study the short-end behaviour of the at-the-money level, skew and curvature of fractional volatilities, and we see how this behaviour is more consistent with real market data.
Rough volatility: Fact or artefact?
Rama Cont (University of Oxford)
Based on joint work with Purba Das
We investigate the statistical evidence for the use of "rough" fractional processes with Hurst exponent H<0.5 for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on a discrete sample, using the concept of normalized p-th variation along a sequence of partitions. We investigate the finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits "rough" behaviour with an apparent Hurst index Ĥ <0.5. These results suggest that the origin of the roughness observed in realized volatility time series lies in the estimation noise rather than the volatility process itself.
A GMM approach to estimate the roughness of stochastic volatility
Mikko Pakkanen (Imperial College London)
Presentation – Pakkanen
Video – Pakkanen
I present an approach to estimate log normal stochastic volatility models, including rough volatility models, using the generalized method of moments (GMM). In this GMM approach, estimation is done directly using realized measures (e.g., realized variance), avoiding the biases that arise from using a proxy of spot volatility. I also present asymptotic theory for the GMM estimator, lending itself to inference, and apply the methodology to Oxford–Man realized volatility data. This presentation is based on joint work with Anine Bolko, Kim Christensen and Bezirgen Veliyev.
PART 2 – Chaired by Knut Sølna (University of California at Irvine)
Quadratic Gaussian models: Analytic expressions for pricing in rough volatility models
Eduardo Abi Jaber (Université Paris I)
Presentation – Abi Jaber
Video – Abi Jaber
Stochastic models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets, such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive explicit analytic expressions for Fourier–Laplace transforms of quadratic functionals of Gaussian processes. Such analytic expression can be approximated by closed form matrix expressions stemming from Wishart distributions. We highlight the applicability of such results in the context of rough volatility modeling: (i) fast pricing and calibration in the (rough) fractional Stein–Stein model; (ii) explicit solutions for the Markowitz portfolio allocation problem in a multivariate rough Stein—Stein model.
Efficient inference for large and high-frequency data
Alexandre Brouste (Université du Maine)
Presentation – Brouste
Video – Brouste
Although a lot of attention has been paid to the high-frequency data due to their increasing availability in different applications, several statistical experiments under the high-frequency scheme remain not fully understood. For instance, at high frequency, the variance and the Hurst exponent for the fractional Gaussian noise (fGn) or the scale and the stability index for the stable Lévy process are melting. Weak LAN property with a singular Fisher information matrix was obtained for the fGn and for the stable Lévy process.
Due to this singularity, no minimax theorem can be applied and it has been unclear for a long time whether the maximum likelihood estimator (MLE) possesses any kind of asymptotic optimality property. More recently, we established a non-singular LAN property for the fGn and for the stable Lévy process making it possible to define the asymptotic optimality in these statistical experiments.
The LAN theory does not directly provide the construction of efficient estimators. In regular statistical experiments, the MLE generally achieves optimality. Nevertheless, its computation is time consuming, and alternatives should be found to handle big or high-frequency datasets available in the fields of insurance and finance. In this direction, the Le Cam one-step estimation can be proposed in the aforementioned statistical experiments (and in others).
Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness
Archil Gulisashvili (Ohio University)
Presentation – Gulisashvili
Video – Gulisashvili
The talk concerns time-inhomogeneous stochastic volatility models in which the volatility is described by a non-negative function of a Volterra type continuous Gaussian process that may have very rough sample paths. We prove small-noise large deviation principles for the log-price process in a Volterra type Gaussian model under very mild restrictions. These results are used to study the small-noise asymptotic behavior of binary barrier options, exit time probability functions, and call options.
Background papers:
Concluding remarks
THURSDAY, 1 SEPTEMBER 2022
PART 3 – Chaired by Jean-Philippe Touffut (Fondation Cournot)
Rough volatility: Challenges for Macroeconomists
Xavier Timbeau (OFCE)
Presentation – Timbeau
Video – Timbeau
Rough volatility and regime shifts: Views from a macroeconomist
Jean-Bernard Chatelain (Université Paris I)
Presentation – Chatelain
Video – Chatelain
The presentation focuses on rough volatility on stock market returns, endogenous persistence and regime shifts with feedback from other variables.
Concluding Remarks
Josselin Garnier (École Polytechnique), Knut Sølna (University of California at Irvine), Jean-Philippe Touffut (Fondation Cournot)
Video – Concluding Remarks
WEDNESDAY, 31 AUGUST 2022
8:00 AM–11:30 AM (LOS ANGELES) / 11:00 AM–2:30 PM (NEW YORK) / 5:00–8:30 PM (PARIS)
THURSDAY, 1 SEPTEMBER 2022
9:00–11:00 AM (LOS ANGELES) / 12:00–2:00 PM (NEW YORK) / 6:00–8:00 PM (PARIS)
Sloan conference series
Organized with École Polytechnique and the University of California at Irvine
PROGRAM
WEDNESDAY, 31 AUGUST 2022
8:00 AM–11:30 PM (LA) / 11:00 AM–14:30 PM (NY) / 5:00–8:30 PM (PARIS)
Welcome and Introduction to the Conference
Josselin Garnier (École Polytechnique)
Knut Sølna (University of California at Irvine)
Jean-Philippe Touffut (Fondation Cournot)
Part 1 - 5:00–6:30 PM (Paris) (Chair: David Mordecai, Courant Institute, NYU)
The fractional Brownian motion in volatility modeling
Elisa Alòs (Universitat Pompeu Fabra, Barcelona)
This talk focuses on the properties of volatilities driven by the fractional Brownian motion (fBm) or related processes. In particular, we study the short-end behaviour of the at-the-money level, skew and curvature of fractional volatilities, and we see how this behaviour is more consistent with real market data.
Rough volatility: Fact or artefact?
Rama Cont (University of Oxford)
Based on joint work with Purba Das
We investigate the statistical evidence for the use of "rough" fractional processes with Hurst exponent H<0.5 for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on a discrete sample, using the concept of normalized p-th variation along a sequence of partitions. We investigate the finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits "rough" behaviour with an apparent Hurst index Ĥ <0.5. These results suggest that the origin of the roughness observed in realized volatility time series lies in the estimation noise rather than the volatility process itself.
A GMM approach to estimate the roughness of stochastic volatility
Mikko Pakkanen (Imperial College London)
I will present an approach to estimate log normal stochastic volatility models, including rough volatility models, using the generalized method of moments (GMM). In this GMM approach, estimation is done directly using realized measures (e.g., realized variance), avoiding the biases that arise from using a proxy of spot volatility. I will also present asymptotic theory for the GMM estimator, lending itself to inference, and apply the methodology to Oxford–Man realized volatility data. Joint work with Anine Bolko, Kim Christensen and Bezirgen Veliyev.
Part 2 - 7:00–8:30 PM (Paris) (Chair: Knut Sølna, University of California at Irvine)
Quadratic Gaussian models: Analytic expressions for pricing in rough volatility models
Eduardo Abi Jaber (Université Paris I)
Stochastic models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets, such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive explicit analytic expressions for Fourier–Laplace transforms of quadratic functionals of Gaussian processes. Such analytic expression can be approximated by closed form matrix expressions stemming from Wishart distributions. We highlight the applicability of such results in the context of rough volatility modeling: (i) fast pricing and calibration in the (rough) fractional Stein–Stein model; (ii) explicit solutions for the Markowitz portfolio allocation problem in a multivariate rough Stein—Stein model.
Efficient inference for large and high-frequency data
Alexandre Brouste (Université du Maine)
Although a lot of attention has been paid to the high-frequency data due to their increasing availability in different applications, several statistical experiments under the high-frequency scheme remain not fully understood. For instance, at high frequency, the variance and the Hurst exponent for the fractional Gaussian noise (fGn) or the scale and the stability index for the stable Lévy process are melting. Weak LAN property with a singular Fisher information matrix was obtained for the fGn and for the stable Lévy process.
Due to this singularity, no minimax theorem can be applied and it has been unclear for a long time whether the maximum likelihood estimator (MLE) possesses any kind of asymptotic optimality property. More recently, we established a non-singular LAN property for the fGn and for the stable Lévy process making it possible to define the asymptotic optimality in these statistical experiments.
The LAN theory does not directly provide the construction of efficient estimators. In regular statistical experiments, the MLE generally achieves optimality. Nevertheless, its computation is time consuming, and alternatives should be found to handle big or high-frequency datasets available in the fields of insurance and finance. In this direction, the Le Cam one-step estimation can be proposed in the aforementioned statistical experiments (and in others).
Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness
Archil Gulisashvili (Ohio University)
The talk concerns time-inhomogeneous stochastic volatility models in which the volatility is described by a non-negative function of a Volterra type continuous Gaussian process that may have very rough sample paths. We prove small-noise large deviation principles for the log-price process in a Volterra type Gaussian model under very mild restrictions. These results are used to study the small-noise asymptotic behavior of binary barrier options, exit time probability functions, and call options.
Concluding remarks
THURSDAY, 1 SEPTEMBER 2022
9:00–11:00 AM (LA) / 12:00–2:00 PM (NY) / 6:00–8:00 PM (PARIS)
Part 3 - 6:00–7:30 PM (Paris) (Chair: Jean-Philippe Touffut, Fondation Cournot)
Rough volatility and regime shifts: Views from a macroeconomist
Jean-Bernard Chatelain (Université Paris I)
The presentation will focus on rough volatility on stock market returns, endogenous persistence and regime shifts with feedback from other variables.
Intervenant :
Jean-Philippe Touffut (Centre Cournot)
Un extrait de Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique (1851) de Cournot a été l'un des trois sujets qui figurait au baccalauréat général de philosophie ce mercredi 15 juin 2022.
10H00-12H00 (Los Angeles) | 13H00-15H00 (New York) | 19H00-21H00 (Paris)
Débat autour du Climate Extended Risk Model (CERM)
avec Josselin Garnier (École polytechnique) et Anne Gruz (Iggaak)
Pour suivre ce débat, inscrivez-vous via ce lien
ou contacter : augustin[at]centre-cournot.org
Intervenants :
Jean-Philippe Touffut (Centre Cournot) : Dynamique de l'économie russe depuis 2007 : dans quelle mesure la guerre s'inscrit-elle dans une logique économique ?
Julien Vercueil (Inalco-CREE, séminaire BRICs) : Entre guerre et sanctions : quel horizon pour l'économie russe ?
Ce séminaire est organisé en partenariat avec le Séminaire BRICs (Brésil, Russie, Inde, Chine : approche comparative et avenir de l’économie mondiale).
Auditorium Georges Dumézil
Inalco
Maison de la recherche
2, rue de Lille
75007 Paris
Métro Saint Germain des Près
CONFÉRENCE SLOAN : Régimes de prix
Organisée avec l'École polytechnique et l'Université de la Californie à Irvine
Jean-Philippe Touffut (Centre Cournot) et Josselin Garnier (École polytechnique)
Quadratic Hawkes processes: A microfoundation for rough volatility models?
Jean-Philippe Bouchaud (Capital Fund Management/École polytechnique)
Présentation - Bouchaud
Vidéo - Bouchaud
From no-arbitrage to rough volatility via market impact
Mathieu Rosenbaum (École polytechnique)
Présentation - Rosenbaum
Vidéo - Rosenbaum
Modeling rough covariance processes
Christa Cuchiero (University of Vienna)
Présentation - Cuchiero
Vidéo - Cuchiero
L'intervention repose sur les travaux de Nadine Levratto coécrits avec Matthieu Chtioui (EconomiX).
Intervenante :
Nadine Levratto (EconomiX, CNRS-Université Paris-Nanterre)
Discutant :
Matthieu Leprince (Université de Bretagne Occidentale)
En ce début 2022, les perspectives macroéconomiques de part et d’autre de l’Atlantique semblent être à l’avantage de l’Union Européenne et notamment de la France.
Du côté des EU, une relance entravée, entre autres, par de nombreux goulots d’étranglement et des pénuries de main-d’œuvre, accompagnée par une nette montée de l’inflation, le rythme dépassant les 7% annuels. Du côté de l’UE, des goulots d’étranglement et des pénuries de main-d’œuvre aussi, certes, mais moins affirmés, et une reprise de l’inflation pour l’instant plus modérée ; dans le cas français l’inflation est autour de 2-3% en rythme annuel et des perspectives de rebond économique restent fortes.
Il en résulte des priorités différentes de politique monétaire (Monperrus – Veroni 2022) : aux EU la crainte d’une spirale prix-salaires est forte, dans un contexte où la contraction de la population active résultant des confinements de 2020 n’est qu’à moitié résorbée. Il en résulte une posture « agressive » de la Banque Fédérale de Réserve, qui envisage des hausses de taux pouvant en retour freiner la relance. En Europe la population active a retrouvé intégralement son niveau moyen de 2019, et la Banque Centrale Européenne est plus attentiste et cherche en priorité à ne pas casser le rebond des économies.
Ces bonnes performances relatives sont largement à mettre au compte des dispositifs d’activité réduite (« chômage partiel » selon l’ancienne dénomination) qui ont permis à l’Europe d’absorber le choc de la pandémie en préservant pour de très nombreux travailleurs leur lien à l’emploi tout en les indemnisant, et donc d’éviter le gonflement du chômage ouvert.
L'intervention repose sur les travaux de Nadine Levratto coécrits avec Matthieu Chtioui (EconomiX).
Intervenante :
Nadine Levratto (EconomiX, CNRS-Université Paris-Nanterre)
Discutant :
Matthieu Leprince (Université de Bretagne Occidentale)
Pour suivre ce séminaire, inscrivez-vous via ce lien
ou contacter : augustin[at]centre-cournot.org
CONFÉRENCE SLOAN : Régimes de prix
Organisée avec l'École polytechnique et l'Université de la Californie à Irvine
Ces dernières années, la modélisation non markovienne a été l’objet de beaucoup d'attention dans la modélisation financière. Il est fondamental et utile de comprendre comment un comportement non markovien ou fractionnaire, tel qu'observé à l'échelle macroscopique, peut résulter de modèles élaborés à l'échelle microscopique. Une telle analyse présente des similitudes, mais aussi des différences, avec l'analyse des systèmes physiques du point de vue des limites d'échelle. Cette conférence présente quelques aspects de l'analyse du comportement rugueux à l'échelle macro résultant de certaines dynamiques microscopiques.
VISIOCONFÉRENCE EN ANGLAIS
PROGRAMME
Quadratic Hawkes processes: A microfoundation for rough volatility models?
Jean-Philippe Bouchaud (Capital Fund Management/École polytechnique)
We discuss a natural generalization of the Hawkes processes that accounts for a feedback from past price trends and volatility onto current activity. The model naturally explains the power-law nature of price returns and the violation of time reversal invariance. It can be extended in various directions, in particular to model the activity in the order book and the occurrence of liquidity crises.
From no-arbitrage to rough volatility via market impact
Mathieu Rosenbaum (École polytechnique)
Slide presentation - Rosenbaum
Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that under no-arbitrage assumption, the market impact function can only be of a power-law type. Furthermore, we prove that this implies that the macroscopic price is diffusive with rough volatility, with a one-to-one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence, we simply explain the universal rough behavior of the volatility as a consequence of the no-arbitrage property. From a mathematical viewpoint, our study relies, in particular, on new results about hyper-rough stochastic Volterra equations.
Modeling rough covariance processes
Christa Cuchiero (University of Vienna)
The rough volatility paradigm asserts that the trajectories of assets’ volatility are rougher than Brownian motion, a revolutionary perspective that has changed certain persistent views of volatility. It provides via stochastic Volterra processes a universal approach to capture important features of time series and option price data, as well as microstructural foundations of markets. We provide an infinite dimensional point of view on stochastic Volterra processes, which makes it possible to dissolve a generic non-Markovanity of the at-first-sight naturally low dimensional volatility process. This approach makes it possible to go beyond the univariate case and to treat multivariate rough covariance models, in particular of affine and Wishart type, for more than one asset.
Discussion
Closing remarks
Étude Cournot publiée dans Les Cahiers de recherche de la Caisse des Dépôts Auteur : Jean-Philippe Touffut (économiste, Directeur du Centr...
