AMERICAN OPTION PRICING WITH REGRESSION: CONVERGENCE ANALYSIS

The Longstaff-Schwartz (LS) algorithm is a popular least square Monte Carlo method for American option pricing. We prove that the mean squared sample error of the LS algorithm with quasi-regression is equal to c(1)/N asymptotically,(a) where c(1) > 0 is a constant, N is the number of simulated paths. We suggest that the quasi-regression based LS algorithm should be preferred whenever applicable. Juneja & Kalra (2009) and Bolia & Juneja (2005) added control variates to the LS algorithm. We prove that the mean squared sample error of their algorithm with quasi-regression is equal to c(2)/N asymptotically, where c(2) > 0 is a constant and show that c(2) < c(1) under mild conditions. We revisit the method of proof contained in Clement et al. [E. Clement, D. Lamberton & P. Protter (2002) An analysis of a least squares regression method for American option pricing, Finance and Stochastics, 6 449-471], but had to complete it, because of a small gap in their proof, which we also document in this paper.