Pricing American-Style Options by Monte Carlo Simulation

Abstract

We replicate (in some parts) and extend Tompaidis and Yang’s (2014) analysis by comparing the performance of Ordinary Least-Squares (OLS) Regression to Tikhonov Regularization and Classification & Regression Trees (CART), and study whether any polynomial among Chebyshev, Hermite, Laguerre, Legendre and Powers perform superiorly when used in the pricing function. We analyze each method’s performance by testing five option types (of which two barrier option types are new research in this thesis) in-the-money, at-the-money and outof- the-money, and by varying the polynomial degree between zero and five. We find no evidence of superiority among the tested polynomials. Like Tompaidis and Yang (2014), we find that OLS regression tend to underperform when the number of simulation paths is small. Despite this issue, we find that OLS regression performs best among the methods tested – which is also observable for one of the tested barrier options.