Valuing American Options Using Multi-Step Barrier Derivatives with a Rebate

Determining optimal exercise boundaries has been central to pricing American options. Ingersoll (1998) offers an alternative to approximating option prices using simple barrier derivatives. Using pricing formulas for multi-step barrier options with a rebate, we generalize it to value American options. An optimal exercise boundary is replaced with the multi-step boundary, which maximizes the pricing formula, and the maximum price serves the approximate American option value. We demonstrate that it provides tight lower bounds to true prices by applying the method to valuing standard American and American barrier options