Fast Lower and Upper Estimates for the Price of Constrained Multiple Exercise American Options by Single Pass Lookahead Search and Nearest-Neighbor Martingale
This provides efficient pricing methods for complex financial derivatives with multiple constraints, which is incremental but practically useful for quantitative finance professionals.
The authors developed fast algorithms for estimating lower and upper bounds on the price of constrained multiple exercise American options, such as swing and passport options, using lookahead search and nearest-neighbor martingale methods, with probabilistic convergence guarantees demonstrated through numerical examples including options with up to 16 constraints.
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.