Category Rapports

Nov
2009

Comonotonic Measures of Multivariate Risks

Ivar Ekeland, Alfred Galichon, Marc Henri We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invari- ance, subadditivity and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural Read more [...]

Oct
2009

Market Design for Emission Trading Schemes

René Carmona, Max Fehr, Juri Hinz, Arnaud Porchet This paper is concerned with the mathematical analysis of emissions markets. We review the existing quantitative analyses on the subject and introduce some of the mathematical challenges posed by the implementation of the new phase of the European Union Emissions Trading Scheme as well as the cap-and-trade schemes touted by the US, Canada, Australia and Japan. From a practical point of view, the main thrust of the paper is the design and numerical Read more [...]

Sep
2009

L2 Density Estimation Under Constraints

Christian Musso, Nadia Oudjane This paper presents a general methodology to estimate a probability density under linear constraints (on the support, bounded moments or quantiles,. . . ). The proposed approximation is the projection of the free density estimation on the set of the probability densities satisfying the constraints. In some cases, the solution of this projection problem can be expressed in a simple parametric form as a function of the free density estimate. Plus d'infos. Read more [...]

Juin
2009

A Structural Risk-Neutral Model of Electricity Prices

René Aïd, Luciano Campi, Adrien Nguyen Huu, Nizar Touzi The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity T, and on the random available capacity of each production means. Read more [...]

Fév
2009

Hedging and Vertical Integration in Electricity Markets

René Aïd, Gilles Chemla, Arnaud Porchet, Nizar Touzi This paper analyzes the interactions between vertical integration and (wholesale) spot, forward and retail markets in risk management. We develop an equilibrium model that fits electricity markets well. We point out that vertical integration and forward hedging are two separate levers for demand and spot price risk diversification. We show that they are imperfect substitutes as to their impact on retail prices and agents’ utility because the Read more [...]

Déc
2008

Generation Capacity Expansion Under Long-Term Uncertainties in the Us Electric Market

Alexandre Klein, Julian Bouchard, Sabine Goutier In this paper, we deal with generation capacity expansion under long-term uncertainties regarding fuel prices and CO2 emissions regulation. We present a model based on stochastic dynamic programming which gives optimal generation investment planning for perfectly competitive power markets. It is applied to the US continuous electricity market with DOE's fuel price scenarios. We show that taking into account uncertainties on fuel costs and on CO2 emissions Read more [...]

Déc
2008

Long-Term Risk Management for Utility Companies: the Next Challenges

René Aïd Since the energy markets liberalisation at the beginning of the 1990s in Europe, electricity monopolies have gone through a profound evolution process. From an industrial organisation point of view, they lost their monopoly on their historical business, but gained the capacity to develop in any sector. Companies went public and had to upgrade their financial risk management process to international standards and implement modern risk management concepts and reporting processes (VaR, EaR...). Read more [...]

Oct
2008

Garch (1,1) Models with Exogeneously Driven Volatility:Structure and Estimation

Nazim Regnard, Jean-Michel Zakoïan This paper considers GARCH(1,1) models in which the time-varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of non-explosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi-maximum likelihood estimator are derived under mild assumptions and Read more [...]

Sep
2007

Strategic Storage and Market Power in the Natural Gas Market

Laure Durand-Viel In a competitive setting, storage is traditionally used to smooth production costs or face demand variations. However, oligopolistic sellers can also use inventories as a commitment tool. We analyze strategically motivated storage in a model where, as in the European gas market, both producers and suppliers have market power. In this two-tier oligopolistic structure, storage allows suppliers not only to preempt future demand, but also to counter producers' market power.This, in Read more [...]

Jan
2007

Valuation of a Power Plant Under Production Constraints and Market Incompleteness

Arnaud Porchet, Nizar Touzi, Xavier Warin This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. Existence of non-hedgeable uncertainties is also an important feature of energy markets whose impact on assets value is often neglected. We use the utility indifference Read more [...]

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