26 sept. 2022

Les impacts de la crise sanitaire sur la fiscalité des collectivités locales

 Mercredi 28 septembre 2022, 10H00–12H00









Séminaire thématique de lObservatoire 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 



12 sept. 2022

The Modeling of Markets with Complex and Rough Regimes

 Visioconférence mise en ligne le 12 septembre 2022










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



12 août 2022

The modeling of markets with complex and rough regimes

Visioconference

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 MordecaiCourant Institute, NYU)

The fractional Brownian motion in volatility modeling
Elisa Alòs (Universitat Pompeu Fabra, Barcelona)

Presentation – 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

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.

Break: 6:30–7:00 PM (Paris)

Part 2 - 7:00–8:30 PM (Paris) (Chair: Knut SølnaUniversity of California at Irvine)

Quadratic Gaussian models: Analytic expressions for pricing in rough volatility models
Eduardo Abi Jaber (Université Paris I)

Presentation – 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

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

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 TouffutFondation Cournot)

Rough volatility: Challenges for Macroeconomists
Xavier Timbeau (OFCE)

Rough volatility and regime shifts: Views from a macroeconomist
Jean-Bernard Chatelain
(Université Paris I)

Presentation – Chatelain

The presentation will focus on rough volatility on stock market returns, endogenous persistence and regime shifts with feedback from other variables.

Concluding Remarks - 7:30–8:00 PM (Paris)
Josselin Garnier (École Polytechnique)
Knut Sølna (University of California at Irvine)
Jean-Philippe Touffut (Fondation Cournot)


REGISTER


15 juin 2022

Cournot au bac de philo

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.













Voici l'extrait :

Pour qu’une observation puisse être qualifiée de scientifique, il faut qu’elle soit susceptible d’être faite et répétée dans des circonstances qui comportent une définition exacte, de manière qu’à chaque répétition des mêmes circonstances on puisse toujours constater l’identité des résultats, au moins entre les limites de l’erreur qui affecte inévitablement nos déterminations empiriques. Il faut en outre que, dans les circonstances définies, et entre les limites d’erreurs qui viennent d’être indiquées, les résultats soient indépendants de la constitution de l’observateur ; ou que, s’il y a des exceptions, elles tiennent à une anomalie de constitution, qui rend manifestement tel individu impropre à tel genre d’observation, sans ébranler notre confiance dans la constance et dans la vérité intrinsèque du fait observé. Mais rien de semblable ne se rencontre dans les conditions de l’observation intérieure sur laquelle on voudrait fonder une psychologie scientifique ; d’une part, il s’agit de phénomènes fugaces, insaisissables dans leurs perpétuelles métamorphoses et dans leurs modifications continues ; d’autre part, ces phénomènes sont essentiellement variables avec les individus en qui se confondent le rôle d’observateur et celui de sujet d’observation ; ils changent, souvent du tout au tout, par suite des variétés de constitution qui ont le plus de mobilité et d’inconsistance, le moins de valeur caractéristique ou d’importance dans le plan général des œuvres de la nature. Que m’importent les découvertes qu’un philosophe a faites ou cru faire dans les profondeurs de sa conscience, si je ne lis pas la même chose dans la mienne ou si j’y lis tout autre chose ? Cela peut-il se comparer aux découvertes d’un astronome, d’un physicien, d’un naturaliste qui me convie à voir ce qu’il a vu, à palper ce qu’il a palpé, et qui, si je n’ai pas l’œil assez bon ou le tact assez délicat, s’adressera à tant d’autres personnes mieux douées que je ne le suis, et qui verront ou palperont si exactement la même chose, qu’il faudra bien me rendre à la vérité d’une observation dont témoignent tous ceux en qui se trouvent les qualités du témoin ?

COURNOT, Essai sur les fondements de nos connaissances
et sur les caractères de la critique philosophique
(1851)




17 mai 2022

Comment les banques peuvent-elles prendre en compte le risque de climat ?

Débat en visioconférence en anglais le mardi 31 mai 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


11 avr. 2022

L'économie russe en perspective : de la rente à la guerre - et après ?

 Séminaire à Paris le mardi 19 avril 2022 - 18H00

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

L'inscription est gratuite et obligatoire via ce lien.

Les impacts de la crise sanitaire sur la fiscalité des collectivités locales

 Mercredi 28 septembre 2022, 10H00–12H00 Séminaire thématique de l ’ Observatoire des impacts territoriaux de la crise Le Centre Cournot et ...