Valuing American options using multi-step rebate options

The determination of optimal exercise boundaries is a critical aspect of pricing American options, which often requires costly numerical methods. This paper proposes a new approach that employs multi-step rebate options to approximate American option prices. Since the rebate options offer payoffs when the multi-step boundaries are touched, the prices of American options are estimated by maximizing the multi-step rebate option prices, and the optimal multi-step barriers replace the true optimal exercise boundaries. To this end, the closed-form pricing formulas for multi-step rebate options are derived and utilized to approximate several American option prices. Through extensive numerical experiments, we demonstrate the validity and performance of our approach.