Pricing American-Style Options by Monte Carlo Simulation ...

multi-collinearity problem. We find that the quality of the approximation using OLSregression deteriorates as the number of exercise opportunities increases, indicating thatbias introduced at an early stage in the backward induction framework propagates andresults in an approximate option price far from the true value. A potential explanation tothe underperformance of OLS regression is that the estimates computed using Tikhonovregularization, MPP and MMPP have lower variance than the OLS estimates, althoughthey may be biased. The larger variance of OLS regression leads to a rapid deteriorationin the OLS estimates, as the results of one estimation are used in a recursive fashion tocompute the previous — in terms of exercise dates — estimate.The rest of this paper is organized as follows: Section I describes the general valuationalgorithm and alternative methods to OLS regression. Section II presents the fivetestcases that we use to evaluate the performance of the different methods. Section IIIdiscusses the experimental design of our study and the measures we use to evaluateperformance. Section IV presents our computational results. Section V concludes thepaper.I. Valuation AlgorithmA. General Valuation FrameworkPricing American-style options through Monte Carlo simulation involves the generalframework of dynamic programming and function approximation. We describe the LeastSquares Monte Carlo (LSM) algorithm below and in Figure 1. Further details can befound in Longstaff and Schwartz (2001).3