CONVERGENCE OF A LEAST-SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA

2016 ◽  
Vol 28 (1) ◽  
pp. 447-479 ◽  
Author(s):  
Daniel Z. Zanger
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Least Squares ◽  
American Option ◽  
Monte Carlo Algorithm ◽  
American Option Pricing ◽  
Least Squares Monte Carlo ◽  
Sample Data ◽  
Dependent Sample

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.

scholarly journals Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xisheng Yu ◽  
Qiang Liu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Legendre Polynomials ◽  
American Options ◽  
Computational Cost ◽  
Monte Carlo Algorithm ◽  
Convergence Properties ◽  
Entropy Model ◽  
Least Squares Monte Carlo ◽  
Convergence Results

The paper by Liu (2010) introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

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