Abstract
Simulation is a powerful tool for pricing path-dependent options. However, the possibility of early exercise has limited the use of such methods for valuing American options. Recently, a few methodologies have been presented for pricing American options, such as the least-squares-Monte-Carlo approach proposed by Longstaff and Schwartz [16]. In this paper, we propose a hybrid methodology combining simulation and the Cox-Ross-Rubinstein [10] binomial method to value American barrier and Parisian options. Our methodology uses the insight that once the barrier condition is met, the exercise strategy of an up-and-in or down-and-in barrier option is identical to that of an option without the restriction. This insight allows us to use the binomial method to determine the optimal exercise strategy. The simulation then incorporates both the optimal exercise strategy and the barrier condition to value the option.
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