Category Reports

Oct
2011

Variance Optimal Hedging for Discrete Time Processes with Independent Increments. Application to Electricity Markets

RR-FiME-11-10 Stéphane GOUTTE, Nadia OUDJANE, Francesco RUSSO We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Föllmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitly, for Read more [...]

Oct
2011

Variance Optimal Hedging for Discrete Time Processes with Independent Increments. Application to Electricity Markets

RR-FiME-11-10 Stéphane GOUTTE, Nadia OUDJANE and Francesco RUSSO We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Föllmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitly, Read more [...]

Mar
2011

Gas storage hedging

RR-FiME-11-04 Xavier WARIN Gaz storage valuation has been an intense subject of research during the recent years. This problem is related to optimal control problems [17], [15] and more precisely to the class of optimal switching problem. On the energy market, the gaz storage management can be seen as a so called swing option [12] with some operational contraints : each day the manager of the gas storage has to decide either to inject gaz in the storage, buying it on the gas market, either to withdraw Read more [...]

Feb
2011

Swing Options Valuation: a BSDE with Constrained Jumps Approach

M. Bernhart, H. Pham, P. Tankov, X. Warin We introduce a new of probabilistic method for solving a class of impulse control problems based on their representation as Backward Stochastic Differential Equations (BDSE) with constrained jumps. As an example, our method is used to price swing options. We deal with the jump contraints by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method with Read more [...]

Feb
2011

On the Robustness of the Snell envelope

Pierre Del Moral, Peng Hu, Nadia Oudjane, Bruno Remillard We analyze the robustness properties of the Snell envelope backward evolution equation for the discrete time optimal stopping problem. We consider a series of approximation schemes, including cut-off type approximations, Euler discretization schemes, interpolation models, quantization tree models, and the Stochastic Mesh method of Broadie-Glasserman. In each situation, we provide non asymptotic convergence estimates, including Lp-mean error Read more [...]

Feb
2011

A Finite Dimensional Approximation for Pricing Moving Average Options

M. Bernhart, P. Tankov, X. Warin We propose a method for pricing American options whose pay-o depends on the moving average of the underlying asset price. The method uses a nite dimensional approximation of the in nite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a finite-dimensional optimal stopping problem, which we propose to solve with a least squares Monte-Carlo approach. We analyze the theoretical convergence Read more [...]

Nov
2010

Plaquette de présentation du laboratoire FiME

   

Nov
2010

A Class of DCC Asymmetric GARCH Models Driven by Exogenous Variables

Jean-Michel Zakoïan This paper considers Dynamic Conditional Correlations (DCC) GARCH models in which the time-varying coefficients, including the conditional correlation matrix, 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 second-order moments of these solutions. Potential applications concern Read more [...]

Oct
2010

Hubbert’s Oil Peak Revisited by a Simulation Model

Pierre-Noël Giraud, Aline Sutter, Timothée Denis, Cédric Léonard As conventional oil reserves are declining, the debate on the oil production peak has become a burning issue. An increasing number of papers refer to Hubbert's peak oil theory to forecast the date of the production peak, both at regional and world levels. However, in our views, this theory lacks microeconomic foundations. Notably, it does not assume that exploration and production decisions in the oil industry depend on market Read more [...]

Oct
2010

A Structural Risk-Neutral Model for Pricing and Hedging Power Derivatives

René Aïd, Luciano Campi, Nicolas Langrené We develop a structural risk-neutral model for energy market modifying along several directions the approach introduced in [Aïd et al., 2009]. In particular a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities Read more [...]

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