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On the stability the least squares Monte Carlo

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Abstract

Consider least squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (Rev Financial Studies 14:113–147, 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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  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Oleksii Mostovyi

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  1. Oleksii Mostovyi
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Correspondence to Oleksii Mostovyi.

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Mostovyi, O. On the stability the least squares Monte Carlo. Optim Lett 7, 259–265 (2013). https://doi.org/10.1007/s11590-011-0414-z

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  • DOI: https://doi.org/10.1007/s11590-011-0414-z

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