On the stability the least squares Monte Carlo

On the stability the least squares Monte Carlo

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Article ID: iaor2013653
Volume: 7
Issue: 2
Start Page Number: 259
End Page Number: 265
Publication Date: Feb 2013
Journal: Optimization Letters
Authors:
Keywords: finance & banking
Abstract:

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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