Recursive Lower- and Dual Upper-Bounds for Bermudan-Style Options

Bermudan-style options are priced by simulation by computing lower- and (dual) upper-bounds. However, much less is known about the associated two optimal bounds. This paper adresses this gap and shows that the exercise strategy that maximizes the Bermudan price (Ibanez and Velasco (2016) local least-squares method) also minimizes (no the dual upper-bound itself, but) the gap between the lower- and the upper-bound in a recursive way. We then price Bermudan max-call options with an up-and-out barrier, which is a difficult stopping-time problem, reducing the gap produced by state-of-the-art methods (including least-squares and pathwise optimization) from 200 basis points -- or more to just one figure. Our results indicate that upper-bounds are tighter than lower-bounds, and hence a mid-point will be lower biased (contrary to conventional wisdom).