Fast Lower and Upper Estimates for the Price of Constrained Multiple Exercise American Options by Single Pass Lookahead Search and Nearest-Neighbor Martingale

Abstract: This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport options with multiple lookback rights. The lower estimate algorithm uses the artificial intelligence method of lookahead search. The upper estimate algorithm uses the dual approach to option pricing on a nearest-neighbor basis for the martingale space. Probabilistic convergence guarantees are provided. Several numerical examples illustrate the approaches including a swing option with four constraints, and a passport option with 16 constraints.