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

and 100,000 paths are used. Given our focus on evaluating the performance ofdifferent estimation methods, we investigate bases that consist of polynomials ofdifferent degrees, as well as bases that include functions corresponding to Europeanoption prices with different strikes and maturities. Our motivation for includingsuch functions is that they are likely to be more similar to the continuation valuethan polynomials. While one would expect that including basis functions that aremore similar to the function being estimated would improve the approximation, itis possible that the opposite is true, especially since European option prices withdifferent strikes and maturities are highly correlated.• Computational efficiency: A concern when using alternatives to OLS regression is thepotential additional computational cost. The methods we have chosen to study,while less familiar than OLS regression, are nonetheless similar in terms of computationalefficiency: quantile regression reduces to a linear optimization problem;similarly to OLS the computational time of Tikhonov regularization increases linearlywith the number of observations; MPP and MMPP also scale linearly withthe number of observations as they reduce to matrix-vector multiplication, wherethe matrix has a number of rows equal to the number of basis functions and a numberof columns equal to the number of simulation paths. In numerical experimentswe have confirmed that CART also scales linearly with the number of simulationpaths. In our computations there were very small differences in computationaltime between OLS regression and the alternative estimation methods.19