A Simple Derivation of and Improvements to Jamshidian's and Rogers' Upper Bound Methods for Bermudan Options

The additive method for upper bounds for Bermudan options is rephrased in terms of buyer's and seller's prices. It is shown how to deduce Jamshidian's upper bound result in a simple fashion from the additive method, including the case of possibly zero final pay-off. Both methods are improved by ruling out exercise at sub-optimal points. It is also shown that it is possible to use sub-Monte Carlo simulations to estimate the value of the hedging portfolio at intermediate points in the Jamshidian method without jeopardizing its status as upper bound.