AMERICAN OPTION PRICING WITH REGRESSION: CONVERGENCE ANALYSIS

Chen Liu, Henry Schellhorn () and Qidi Peng ()
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Chen Liu: Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711, USA
Henry Schellhorn: Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711, USA
Qidi Peng: Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 08, 1-31

Abstract: 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 c1/N asymptotically,a where c1 > 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 c2/N asymptotically, where c2 > 0 is a constant and show that c2 < c1 under mild conditions. We revisit the method of proof contained in Clément et al. [E. Clément, 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.

Keywords: American option pricing; convergence rate; Monte Carlo methods; optimal stopping; control variates (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500444

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