On the Stability the Least Squares Monte Carlo

Details On the Stability the Least Squares Monte Carlo On the Stability the Least Squares Monte Carlo

2011-02-16

arxiv.org/abs/1102.3218v2

Economy

Quantitative Finance

Computational Finance

9 pages, 2 figures

Scientific paper

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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