ESADE Spain

We study lower- and dual upper-bounds for Bermudan options in a MonteCarlo/MC setting and provide four contributions. 1) We introduce a local least-squares MC method, based on maximizing the Bermudan price and which provides a lower-bound, which "also" minimizes (not the dual upper-bound itself, but) the gap between these two bounds; where both bounds are specified recursively. 2) We confirm that this method is near optimal, for both lower- and upper-bounds, by pricing Bermudan max-call options subject to an up-and-out barrier; state-of-the-art methods including Longstaff-Schwartz produce a large gap of 100--200 basis points/bps (Desai et al. (2012)), which we reduce to just 5--15 bps (using the same linear basis of functions). 3) For dual upper-bounds based on continuation values (more biased but less time intensive), it works best to reestimate the continuation value in the continuation region only. And 4) the difference between the Bermudan option Delta and the intrinsic value slope at the exercise boundary gives the sensitivity to suboptimal exercise (up to a 2nd-order Taylor approximation). The up-and-out feature flattens the Bermudan price, lowering the Bermudan Delta well below one when the call-payoff slope is equal to one, which implies that optimal exercise "really" matters.