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

as well as European option prices. 9 From the table we notice that OLS regressionperforms better when the number of exercise opportunities is smaller, and that theperformance of OLS regression deteriorates faster than the performance of alternativessuch as Tikhonov regularization, the MPP and MMPP methods as the number of exercisedates increases. This behavior can be understood by the nature of the methods: sinceTikhonov regularization, MPP and MMPP methods penalize the size of the coefficientsof the basis functions, the estimates of the coefficients obtained from these methods arelikely to be smaller and less variable than those obtained by OLS regression. For the samereason, their out-of-sample performance is likely to be close to in-sample performancecompared to OLS regression. Given that the estimates of the coefficients are used ina recursive manner, we conjecture that the more variable coefficient estimates of OLSregression result in the faster propagation of errors compared to the other methods.V. ConclusionsWe investigated the performance of OLS regression in Monte Carlo simulation methodsof pricing American options. We found that OLS regression is prone to overfitting andproducing inaccurate estimates when the number of simulation paths is small, when thenumber of functions used to approximate the continuation value function is large, whenEuropean option prices are included in the basis functions, and when the number ofexercise dates increases. In the case of polynomial bases, an alternative that performsas well as OLS regression and often better is the MMPP method. When Europeanoption prices are added to the polynomial bases, Tikhonov regularization, the MPP andMMPP methods outperform OLS regression. Given the increased use of Monte Carlosimulation methods for pricing American options, and the fact that it is often difficult tocheck whether the number of paths used is sufficiently large for the option being priced,9 Additional details are available from the authors.25