Refining the least squares Monte Carlo method by imposing structure

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Abstract
The least squares Monte Carlo method of Longstaff and Schwartz has become a standard numerical method for option pricing with many potential risk factors. An important choice in the method is the number of regressors to use and using too few or too many regressors leads to biased results. This is so particularly when considering multiple risk factors or when simulation is computationally expensive and hence relatively few paths can be used. In this paper we show that by imposing structure in the regression problem we can improve the method by reducing the bias. This holds across different maturities, for different categories of moneyness and for different types of option payoffs and often leads to significantly increased efficiency.

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