Pricing Bermudan options by simulation: When optimal exercise matters

The pricing of Bermudan options by simulation is solved by using a least-squares lower-bound and a duality-based upper-bound, but a recent paper by Desai et al.(2012) shows that up to five state-of-the-art methods fail to price a max-call option subject to an up-and-out barrier. The "gap" between their best lower- and best upper-bounds reaches 100--200 basis points, bps. This implies that these bounds are not tight and could be dramatically improved and rises two questions. If there is a practical method which easily improves upon these bounds and why all methods fail. The contribution of this paper is threefold. First, our local least-squares method (Ibáñez and Velasco (2012a)) yields lower-bounds which improve upon their best lower-bounds by 85--160 bps. An upper-bound based on the exercise strategy associated to our lower-bound reduces de "gap" to just 6--15 bps. Second, we show that this same exercise strategy, indeed, optimizes both bounds. And third, the sensitivity to suboptimal exercise depends on the difference between the option Delta and the payoff slope. The up-and-out feature flattens the Bermudan Delta well below one, when the call-payoff slope is equal to one, implying that optimal exercise "really" matters.