The robustness of modified unit root tests in the presence of GARCH

We consider the valuation of energy storage facilities within the framework of stochastic control. Our two main examples are natural gas dome storage and hydroelectric pumped storage. Focusing on the timing flexibility aspect of the problem we construct an optimal switching model with inventory. Thus, the manager has a constrained compound American option on the inter-temporal spread of the commodity prices. Extending the methodology from Carmona and Ludkovski [Appl. Math. Finance, 2008], we then construct a robust numerical scheme based on Monte Carlo regressions. Our simulation method can handle a generic Markovian price model and easily incorporates many operational features and constraints. To overcome the main challenge of the path-dependent storage levels, two numerical approaches are proposed. The resulting scheme is compared with the traditional quasi-variational framework and illustrated with several concrete examples. We also consider related problems of interest, such as supply guarantees and mines management.