Category Rapports

Adrien Nguyen Huu We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods. This general framework covers the interesting case of an electricity producer who wants to hedge a financial position and can trade commodities which are also inputs for his system. This extends the framework of Bouchard & Nguyen Read more [...]

RR-FiME-11-09 Pierre Del Moral, Peng Hu, Nadia Oudjane We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this Read more [...]

RR-FiME-11-08 Nazim Regnard This paper establishes the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of a GARCH(1,1) process with time-varying cofficients driven by an exogenous variable, when some true coefficients may be null. The QMLE is shown to be consistent. Its asymptotic distribution is a projection of a normal vector distribution onto a convex cone. Furthermore, the QMLE is shown to converge to its asymptotic distribution locally uniformly. We then consider the Read more [...]

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 [...]

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 [...]