Comparisons of Alternative Quasi-Monte Carlo Sequences for American Option Pricing

2004 ◽  
Author(s):  
Jennifer X.F. Jiang ◽  
John R. Birge
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
American Option ◽  
American Option Pricing ◽  
Quasi Monte Carlo

AMERICAN OPTION PRICING WITH REGRESSION: CONVERGENCE ANALYSIS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950044
Author(s):  
CHEN LIU ◽  
HENRY SCHELLHORN ◽  
QIDI PENG
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
American Option ◽  
Regression Method ◽  
Least Square ◽  
Least Squares Regression ◽  
American Option Pricing ◽  
Mild Conditions ◽  
Sample Error ◽  
The Mean

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 [Formula: see text] asymptotically, a where [Formula: see text] is a constant, [Formula: see text] 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 [Formula: see text] asymptotically, where [Formula: see text] is a constant and show that [Formula: see text] 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.

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