  The subject of this study is an iterative Bermudan option pricing algorithm
based on (high-dimensional) cubature. We show that the sequence of Bermudan
prices (as functions of the underlying assets' logarithmic start prices)
resulting from the iteration is bounded and increases monotonely to the
approximate perpetual Bermudan option price; the convergence is linear in the
supremum norm with the discount factor being the convergence factor.
Furthermore, we prove a characterisation of this approximated perpetual
Bermudan price as the smallest fixed point of the iteration procedure.
