Category Rapports

Nov
2011

Snell Envelope with Small Probability Criteria

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 …

Oct
2011

Testing the Nullity of Coefficients of a GARCH Model with Exogenously-Driven Volatility

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 …

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 …

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] …

Fév
2011

A Finite Dimensional Approximation for Pricing Moving Average Options

<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 …

Fév
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 …

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 …

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 …

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, …

Juin
2010

Modeling Power Generation Switch as a Real Switching Option: Nucleus Vs. Gas

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 …

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