Modeling and valuation methods for gas contracts: stochastic control approaches.

Summary The work presented in this thesis was motivated by issues raised by the valuation of contracts traded in the gas market: gas storage and supply contracts. These contracts incorporate optionality and constraints, which makes their valuation difficult in a context of random commodity prices. The valuation of these contracts leads to complex stochastic control problems: optimal switching or impulse control and high dimensional stochastic control. The first part of this thesis is a relatively exhaustive review of the literature, putting in perspective the different existing valuation approaches. In a second part, we consider a numerical method for solving impulse control problems based on their representation as a solution of constrained jumping EDSRs. We propose a discrete time approximation using a penalty to handle the constraint and give a convergence rate of the introduced error. Combined with Monte Carlo techniques, this method has been numerically tested on three problems: optimal biomass management, evaluation of swing options and gas storage contracts. In a third part, we propose a method for the valuation of options whose payoff depends on moving averages of underlying prices. It uses a finite dimensional approximation of the dynamics of moving average processes, based on a truncated Laguerre series development. The numerical results provided include examples of gas swings with strike prices indexed to moving averages of oil prices.