This paper analyzes 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 parameter t, time .
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 .
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This paper analyzes
Consider
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parameter t, time
the time parameter