Modelization and valuation methods of gas contracts: Stochastic control approaches

Abstract : The work presented in this PhD dissertation was motivated by issues raised by the valuation of contracts commonly traded in the gas market: gas storage and gas supplying contracts. Both of them include optionality and constraints, which make tough their valuation in a context of uncertain commodity prices. The valuation of such contracts leads to particularly complex stochastic control problems: optimal switching or impulse control and optimal control in high dimension. The first part of this dissertation is a relatively exhaustive review of the existing valuation methods. In a second part, we introduce a numerical method for solving impulse control problems by using their representations as BSDEs with constrained jumps. We propose a discrete-time approximation using a penalization of the constraint on the jump component and provide a rate of convergence of the approximation error. Combining this approach with Monte Carlo techniques, we perform numerical tests on three problems: optimal forest management, valuation of Swing options and gas storage facilities. In a third part, we introduce a method for pricing options whose payoff depends on moving averages of underlying prices. We use a finite-dimensional approximation of the infinite-dimensional dynamics of moving average processes, based on a truncated Laguerre series expansion. We present numerical results including examples of gas Swing contracts involving strike prices indexed on moving averages of oil prices.
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Submitted on : Monday, March 14, 2011 - 11:00:41 AM
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Marie Bernhart. Modelization and valuation methods of gas contracts: Stochastic control approaches. Mathematics [math]. Université Paris-Diderot - Paris VII, 2011. English. ⟨tel-00576355⟩

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