  Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by
Longstaff and Schwartz (2001) for pricing American style securities. This
algorithm is based on the projection of the value of continuation onto a
certain set of basis functions via the least squares problem. We analyze the
stability of the algorithm when the number of exercise dates increases and
prove that, if the underlying process for the stock price is continuous, then
the regression problem is ill-conditioned for small values of the time
parameter.
