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We develop least squares Monte Carlo (LSM) and approximate linear programming (ALP) methods for valuing multiple exercise options, such as energy swing and storage options, using term structure models. Our numerical and theoretical investigation shows the superiority of a rarely used LSM variant for estimating lower and upper bounds on the option value over the standard LSM version and the ALP approach. We also structurally relate the seemingly different LSM and ALP methods using the concept of surrogate relaxations. This analysis motivates further research into surrogate relaxations of approximate linear programs.

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