We introduce a new method to price American-style options on underlying
investments governed by stochastic volatility (SV) models. The method does not
require the volatility process to be observed. Instead, it exploits the fact
that the optimal decision functions in the corresponding dynamic programming
problem can be expressed as functions of conditional distributions of
volatility, given observed data. By constructing statistics summarizing
information about these conditional distributions, one can obtain high quality
approximate solutions.