We introduce a new numerical approach, called the \u201csingular points
method\u201d, for pricing American path-dependent options. This method, which
is based on a continuous representation of the price at each node of the
binomial tree, allows us to obtain very precise upper and lower bounds
for the discrete binomial price. Moreover, the method provides a priori
estimates of the difference between the upper and lower bounds. The
algorithm is convergent and provides efficient estimates of the continuous
price value. We apply the method to the case of Asian and lookback
American options
