Canonical least-squares Monte Carlo valuation of American options: convergence and empirical pricing analysis
Summary: The paper by \textit{Q. Liu} [``Pricing American options by canonical least-squares Monte Carlo'', J. Futures Mark. 30, No. 2, 175--187 (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.
scientific article; zbMATH DE number 7017218