Volatility in electricity derivative markets: the Samuelson effect revisited

couverture-cahier-73-lautier-jaeckby Edouard Jaeck & Delphine Lautier

This article proposes an empirical study of the Samuelson effect in electricity markets. Our motivations are twofold. First, although the literature largely assesses the decreasing pattern in the volatilities along the price curve in commodity markets, it has not extensively tested the presence of such a dynamic feature in electricity prices. Second, the analysis of a non-storable commodity enriches the literature on the behavior of commodity prices. Indeed, it has been sometimes asserted that the Samuelson effect results from the presence of inventories. We examine the four most important electricity futures markets worldwide for the period from 2008 to 2014: the German, Nordic, Australian, and US markets. We also use the American crude oil market as a benchmark for a storable commodity negotiated on a mature futures market. Our analysis has two steps: i) in addition to the traditional tests, we propose and test a new empirical implication of the Samuelson effect: price shocks should spread from the physical market to the paper market, and not the reverse; ii) based on the concept of “indirect storability”, we investigate the link between the Samuelson effect and the storability of the commodity. We find evidence of a Samuelson effect in all of the electricity markets and show that storage is not a necessary condition for such an effect to appear. These results should be taken into account for the understanding of the dynamic behavior of commodity prices, for the valuation of electricity assets, and for hedging operations.

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A Long-Term Mathematical Model for Mining Industries

couverture-cahier-72-achdou-et-alby Yves Achdou, Pierre-Noel Giraud, Jean-Michel Lasry & Pierre-Louis Lions

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problems with two controls, first the ux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton-Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to t the historical data is carried out.

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Negotiated Red Zones Around Hazardous Plants

couverture-cahier-71-villeneuve-glby Céline Grislain-Letrémy & Bertrand Villeneuve

The industrialists are liable for any damage they cause to neighboring households. Consequently, households do not have to pay for the risk they create by locating in exposed areas. To contain their liabilities, the firm can purchase or rent land, establishing an exclusion zone, also called a red zone. This paper studies the negotiations of red zones in urban areas exposed to industrial disasters. We compare typical scenarios regarding the distribution of bargaining power between the firm and the city. Using a microeconomic model, we explain how red zones are revised as technology, climate, or demography change, and we show how and why responses are neatly distinct across scenarios. Further, we give and explain the conditions for industrial sanctuaries (as the population grows) and city cores (as the risk grows).

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Natural Disasters, Land-Use, and Insurance

couverture-cahier-70-villeneuve-glby Céline Grislain-Letrémy & Bertrand Villeneuve

This paper addresses the urbanization of areas exposed to natural disasters and studies its dependency on land-use and insurance policies. The risk-map paradox that we describe explains why an insurance system with simplistic maps and tariffs is the rule. Indeed, in practice we observe simple policies, consisting of a prohibited red zone and a zone without insurance tariff differentiation. We show that they implement the optimal land-use in specific cases. Even if there are fixed damages per dwelling, the red-zone policy is relatively efficient. In a central proposition, we detail the effects redefining the optimal red zone as the climate or the population changes. We use this analysis to expose and comment plausible cases in which, as the population grows, the red zone shrinks, the red zone grows, and the red zone shrinks and then grows.

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StOpt: A New Stochastic Optimization Library

Scr_StOptThe STochastic OPTimization library (StOpt)   was developped at OSIRIS department at EDF R&D  and used in some operational projects as an open source project.

The StOpt library aims at providing tools in C++ for solving some stochastic optimization problems encountered in finance or in the industry. A python binding is available for some C++ objects provided permitting to easily solve an optimization problem by regression.

Different methods are available :
– dynamic programming methods based on Monte Carlo  with regressions (global, local and  sparse regressors), for underlying states following some uncontrolled Stochastic Differential Equations (python binding provided). Continue reading

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Jeux à champ moyen – Bilan et perspectives

Vignette_conf_PLLpar Pierre-Louis Lions
16 juin 2016, Abbaye des Vaux de Cernay

Présentation donnée dans le cadre des journées ateliers FiME à l’Abbaye des Vaux de Cernay.

Lien vers la video (vimeo)

 

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Journées ateliers FiME

Abbaye_des_Vaux-de-Cernay_Building_12Abbaye des Vaux de Cernay
16-17 juin 2016

L’objectif de ces deux journées était de faire le point sur les travaux conduits au sein de l’IdR FiME, les résultats déjà obtenus et les perspectives de développement de ces travaux. Les travaux était présentés au travers d’ateliers co-animés par les ingénieurs chercheurs d’EDF R&D et les chercheurs académiques, et de quelques exposés magistraux (G. Stolz, PL Lions, B Villeneuve, I Ekeland).

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Micro-finance et lutte contre la pauvreté: le rapport annuel de la Fondation Grameen – Crédit Agricole

Rapport Fond G-CA CouvAu 31 décembre 2015, la Fondation est active dans 27 pays en développement parmi les plus pauvres, auprès de 59 institutions de microfinance ou entreprises de social business. Les institutions de microcrédit partenaires de la Fondation comptent 3,3 millions d’emprunteurs actifs, dont 85% sont des femmes et 79% vivent en zone rurale. Fin 2015, le portefeuille d’engagements de la Fondation auprès de ses partenaires en microfinance s’élève à près de 30 millions d’Euros. Elle a développé la «Facilité Africaine de décollage pour la Microfinance» lancée en 2013, en partenariat avec l’AFD, qui associe financement et assistance technique en vue d’accompagner un plus grand nombre d’institutions de microcrédit à vocation agricole et rurale en Afrique sub-saharienne : 16 institutions ont bénéficié en 2015 de ce dispositif innovant.

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Macrofinancial models for long-term asset returns

IHP_FACADE-150x150A lecture by Jean-Paul Renne (Université de Lausanne)
July 7-8, Institut Henri Poincaré

This lecture offers an extensive study of macro-founded asset pricing models which explicitly integrate the role of key macroeconomic variables (revenue growth, inflation and uncertainty). One of its main objectives is to shed light on the critical effects of macroeconomic risk structures on long run portfolio returns. The analysis will therefore target modelling approaches of the joint dynamics of macroeconomic factors and asset prices. It will focuses on the so-called affine models family – which include the long run risk models pioneered by Bansal and Yaron (2004), that solved popular asset pricing puzzles – equity risk premium puzzle and risk free rate puzzle. These tractable and flexible approaches open the route to valuation tools integrating consistently equilibrium asset prices and macroeconomic scenarios. The introduction of the lecture will review the literature investigating how macroeconomic variables affect asset returns. A first part will present the above mentioned affine pricing models. It will be shown how they help to understand the effects of macroeconomic changes on asset returns. As an illustration, we will present a method for generating asset price scenarios contingent to exogenous macroeconomic trajectories. A second and last part will carefully examine numerical resolution and calibration issues on real data.

Lecture description

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Les communs numériques : éléments d’économie politique

couverture cahier 69 verdier murcipar Henri Verdier & Charles Murciano 

Cet article interroge l’actualité intellectuelle et légale des communs. Plus précisément, notre travail explore la notion de commun numérique (ou informationnel) et ses spécificités au regard du concept classique de communs en théorie économique. Les communs numériques désignent les nouveaux modes d’administration d’une ressource informationnelle par une communauté, qui sont permis par les technologies de l’information et de la communication. Ils constituent un mode de partage de ressources socialement valorisées. Les économistes s’accordent sur une conception classique des biens communs, désignant une ressource rivale et non-exclusive. Les communs numériques étant immatériels, cette définition est insatisfaisante. En outre, les travaux d’Elinor Ostrom ont souligné la dualité des communs, à la fois ressource exploitée en commun et régime de droits de propriété dérogeant au paradigme de la propriété privée. Notre article spécifie ainsi cette ambivalence à l’ère numérique. L’examen attentif d’exemples de communs numériques promus par l’Etat permet d’expliciter la logique contributive à l’oeuvre dans ces communs. Nous soutenons que cette logique autorise une nouvelle forme d’action publique. Alliée à la « multitude », en promouvant et en encadrant les communs, la puissance publique pourrait s’armer contre l’hégémonie croissante de grandes plateformes monopolistiques, dont les logiques s’opposent de plus en plus à celles des Etats.

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The digital commons: a political and economic game-changer

COUV_CAHIER_FDD_68by Henri Verdier and Charles Murciano

This paper addresses the current intellectual and legal status of the commons. Specifically, we explore the notion of the digital (or information) commons and its specificities with regard to the classic concept of the commons in economic theory. The digital commons concerns new ways of administering an information resource by a community, made possible by information and communications technology. It constitutes a means of sharing socially valued resources. Economists agree on a classic conception of common goods, designating a rival and non-exclusive resource. Because the digital commons is immaterial, this definition is unsatisfactory. In addition, the work of Elinor Ostrom emphasizes the duality of the commons: both a resource used in common and a property-rights regime running counter to the paradigm of private property. Our paper thus examines this ambiguity in the digital age. Careful study of examples of digital commons promoted by the state can clarify the contributory logic at work in these commons. We argue that this approach authorizes a new form of public action. Allied with the “multitude”, the public authorities could, by nurturing and supervising the commons, arm themselves against the growing hegemony of big monopolistic platforms, whose logic is increasingly opposed to that of the state.

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Resource Conservation Across Generations in a Ramsey-Chichilnisky Model

couverture cahier 67 ekeland asheimby Geir B. Asheim & Ivar Ekeland 

The Chichilnisky criterion is an explicit social welfare function that satisfies compelling conditions of intergenerational equity. However, it is time inconsistent and has no optimal solution in the Ramsey model. By investigating stationary Markov equilibria in the game that generations with Chichilnisky preferences play, this paper shows how nevertheless this criterion can be practically implemented in the Ramsey model, leading to attractive consequences. The time-discounted utilitarian optimum is the unique equilibrium path with a high-productive initial stock, implying that the weight on the infinite future in the Chichilnisky criterion plays no role. However, this part of the Chichilnisky criterion may lead to more stock conservation than the timediscounted utilitarian optimum with a low-productive initial stock. Based on the notion of von Neumann-Morgenstern abstract stability, we obtain uniqueness by assuming that each generation coordinates on an almost best equilibrium and takes into account that future generations will do as well.

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Thematic Semester on “Commodity Derivatives Markets: Industrial Organization, Regulation and Financialization”

AfficheA3-ThematicSemester-DerivativesMarkets_v8d-vectoredInformation related to the thematic semester on « Commodity Derivatives Markets » and the closing conference to be held in Paris on November 6th can be found on the following website:

http://thematicsemester.com/

 

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Optimal Pits and Optimal Transportation

couverture cahier 66 ekelandby Ivar Ekeland and Maurice Queyranne

In open pit mining, one must dig a pit, that is, excavate the upper layers of ground before reaching the ore. The walls of the pit must satisfy some mechanical constraints, in order not to collapse. The question then arises how to mine the ore optimally, that is, how to find the optimal pit. We set up the problem in a continuous (as opposed to discrete) framework, and we show, under weak assumptions, the existence of an optimum pit. For this, we formulate an optimal transportation problem, where the criterion is lower semi-continuous and is allowed to take the value +∞. We show that this transportation problem is a strong dual to the optimum pit problem, and also yields optimality (complementarity slackness) conditions.

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Thematic Semester on “Commodity Derivatives Markets:
Industrial Organization, Regulation and Financialization”

AfficheA3-ThematicSemester-DerivativesMarkets_v8d-vectored
This project aims to examine recent developments in commodity derivatives markets. The changed industrial organization and the financialization of these markets are major phenomena, both of which call for changes in regulation.

Organized from March to November 2015, the thematic semester will include an opening conference, a series of thematic seminars, a summer school and a closing conference.

Link to the Thematic Semester’s webpage

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Probabilistic Representation of a Class of Non Conservative Nonlinear Partial Differential Equations

couverture cahier 65 oudjaneby Anthony Lecavil, Nadia Oudjane & Francesco Russo

We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.

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Mean Field Games and Related Topics (3)

AfficheA3-MFGJune2015-pourImpression June 10-12 2015,
Paris (Institut Henri Poincare)

      The meeting will be a continuation of the workshops on Mean Fields Games and Related Topics, held in Rome (May 12-13 2011) and Padova (September 4-6 2013).

Further information on the Conference website

The conference is supported by:
The “Finance and Sustainable Development”Chair
The CEREMADE, Université Paris-Dauphine
The Laboratoire Jacques-Louis Lions
The Institut Louis Bachelier
The Projet ANR ISOTACE
The Institut Henri Poincaré
Université Franco-Italienne

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Some PDE Methods in Mean Field Games Theory

Affiche_cours_A. Poretta

A Course by Professor Alessio Porretta

From March 9th to April 16th 2015

Institut Henri Poincaré (IHP), Paris

Mean field games theory was initiated by J.-M. Lasry and P.-L. Lions since 2006 in order to describe control processes with large number of agents (say, a population of identical individuals) whose strategy is influenced by the overall distribution of the agents. The macroscopic description, suggested as an asymptotic regime of Nash equilibria of N-players games when N goes to infinity, is given in terms of a new system of PDEs, where a backward Hamilton-Jacobi-Bellman equation (describing the individual strategy) is coupled with a forward Kolmogorov-Fokker-Planck equation (describing the evolution of the distribution law). The goal of this course is to present several problems and methods recently developed in the study of those systems, addressing questions such as the long time behavior and its connection with the turnpike property of controlled systems, the optimal transport of the distribution law, the well-posedness of weak theories and other possible related directions of research.

Further information on the FSMP Website

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Opening Conference of the Thematic Semester on “Commodity Derivatives Markets: Industrial Organization, Regulation and Financialization”

AfficheA3-ThematicSemester-DerivativesMarkets_v8d-vectored26-27 March 2015 – Institut Henri Poincaré (IHP), Paris

To launch the thematic semester, the opening conference will aim to show the state of the art and especially to identify new research problems. Special emphasis will be given to the identification of unsolved problems.

Program, practical information and online registration

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Information Flows across the Futures Term Structure: Evidence from Crude Oil Prices

couverture cahier 64 lautier copyby Delphine Lautier, Franck Raynaud & Michel A. Robe

We apply the concepts of conditional entropy, information transfers and directed graphs to investigate empirically the propagation of price fluctuations across a futures term structure. We focus on price relationships for North American crude oil futures because this key market experienced several structural changes between 2000 and 2014: financialization (starting in 2003), infrastructure limitations (in 2008-2011) and regulatory changes (in 2012-2014) in addition to big demand and supply shocks in the underlying asset market. We find large variations over time in the amount of information shared by contracts with different maturities. Although on average short-dated contracts (up to 6 months) emit more information than backdated ones, a dynamic analysis reveals that, after 2012, similar amounts of information flow backward and forward along the futures maturity curve. The mutual information share increased substantially starting in 2004 but fell back sharply in 2012-2014. In the crude oil space, our findings point to a puzzling re-segmentation of the futures market by maturity in 2012-2014. More broadly, they have implications for the Samuelson effect and raise questions about the causes of market segmentation.

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