Category Rapports

Déc
2009

Environmental Policies in an Electricity Sector: Test on the French Electricity Sector

Corinne Chaton Marie-Laure Guillerminet Feed-in Tariffs promoting renewable energy sources and quotas of CO2 emissions have been implemented jointly in France to reduce CO2 emissions. We develop on GAMS a supply-demand model applied to the electricity sector. Demand is uncertain and is characterized by load curves. We find that if both policies reduce emissions, feed-in tariffs involve a substantial extra-cost without significant gain for sure in terms of emissions. Read more [...]

Déc
2009

Structure and Estimation of a Class of Nonstationary Yet Nonexplosive GARCH Models

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. Read more [...]

Déc
2009

Variance Optimal Hedging for Continuous Time Processes with Independent Increments and Applications

Stéphane Goutte, Nadia Oudjane, Francesco Russo For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market are performed. Plus d'infos. Read more [...]

Nov
2009

An Arbitrage-Free Interest Rate Model Consistent with Economic Constraints for Long-Term Asset Liability Management

René Aïd, Olivier Féron, Nizar Touzi, Christine Vialas This paper proposes an Heath-Jarrow-Morton model of the yield curve that can fit the particular requirements of long-term asset and liability management (ALM). In particular, the proposed HJM model can reproduce expected long-term statistical properties of any two interest rates, while still satisfying the no-arbitrage constraints. We describe the methodology to calibrate the model in this particular constrainted setting, i.e. to find the Read more [...]

Nov
2009

A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

Arash Fahim, Nizar Touzi, Xavier Warin We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [10], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step. An explicit implementable scheme Read more [...]

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 [...]

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