Category Rapports

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 [...]

<h3><strong><span style="color: #005d63;">M. Bernhart, P. Tankov, X. Warin</span></strong></h3> 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 Read more [...]

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 [...]

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 [...]

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 [...]

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 [...]

Moahamed Ben Abdelhamid, Chaker Aloui, Corinne Chaton Given the volatility of the prices of fossil fuels and of environmental constraints, the nuclear power plants can be the least expensive solution to satisfy the demand of electricity. In this paper, we present a dynamic modeling for an optimal operational planning by considering the possibility to switch from natural gas to nuclear power. A switching options approach is applied to address an optimal power generation strategy. We show that, when Read more [...]

Bruno Bouchard, Xavier Warin The aim of this paper is to discuss efficient algorithms for the pricing of American options by two recently proposed Monte-Carlo type methods, namely the Malliavian calculus and the regression based approaches. We explain how both technics can be exploded with improved complexity and effciency. We also discuss several technics for the estimation of the corresponding hedging strategies. Numerical tests and comparisons, including the quantization approach, are performed. Plus Read more [...]

Bruno Bouchard, Adrien Nguyen Huu We consider a class of production-investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no-arbitrage of the second kind condition introduced by M. Rasonyi [13]. We show that this condition implies the closedness of the set of attainable claims and is equivalent to the existence of a strictly consistent price system under which the evaluation of future production profits are strictly Read more [...]

Corinne Chaton, Laure Durand-Viel Real assets are usually valued by assuming a liquid spot market with competitive traders who buy or sell until arbitrage opportunities are exhausted; the value of a real asset is computed as the stream of profits resulting from such transactions. This method ignores market fundamentals by assuming that all the relevant information is included in the spot price. This paper analyses the bias resulting from such an approach when the market is imperfectly competitive. Read more [...]