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

Panel B. Polynomial and European price basisN b Asymptotic OLS Quantile Tikhonov MPP MMPP CARTNumber of Paths = 1000 7.89±0.01 9.76±0.20*** 8.86±0.25*** 8.22±0.19 8.13±0.21 8.53±0.21*** 9.67±0.14***1 7.88±0.00 9.88±0.16*** 8.78±0.20*** 8.50±0.17*** 8.46±0.23** 8.33±0.19**2 7.88±0.01 10.69±0.21*** 9.33±0.21*** 8.56±0.19*** 8.71±0.20*** 8.90±0.25***3 7.89±0.00 10.69±0.19*** 9.49±0.30*** 8.57±0.22*** 8.52±0.15*** 8.75±0.26***4 7.88±0.00 10.54±0.16*** 9.59±0.24*** 8.78±0.22*** 8.64±0.22*** 8.18±0.175 7.88±0.01 10.87±0.24*** 9.71±0.29*** 8.48±0.16*** 8.22±0.14** 8.55±0.29**6 7.88±0.00 10.65±0.17*** 9.85±0.18*** 8.83±0.27*** 8.36±0.22** 8.31±0.18**7 7.89±0.00 10.68±0.30*** 10.14±0.22*** 8.62±0.23*** 8.72±0.21*** 8.85±0.23***8 7.88±0.01 11.01±0.23*** 9.93±0.18*** 8.90±0.23*** 8.31±0.15** 8.75±0.22***9 7.88±0.00 10.66±0.20*** 9.62±0.27*** 9.02±0.21*** 8.47±0.21** 8.25±0.15**10 7.88±0.00 10.77±0.25*** 10.07±0.16*** 8.71 ±0.18*** 8.64±0.25*** 8.42±0.18**Number of Paths = 10000 7.89±0.01 8.35±0.07*** 7.43±0.08*** 7.88±0.06 7.82±0.05 8.01±0.06 8.65±0.07***1 7.88±0.00 8.18±0.09*** 7.49±0.10*** 7.96±0.06 7.95±0.06 7.93±0.072 7.88±0.01 8.30±0.05*** 7.43±0.08*** 7.98±0.06 7.98±0.05 7.95±0.073 7.89±0.00 8.24±0.07*** 7.39±0.05*** 7.93±0.04 7.99±0.05 7.92±0.044 7.88±0.00 8.31±0.04*** 7.44±0.09*** 7.94±0.05 7.94±0.08 7.80±0.065 7.88±0.01 8.28±0.06*** 7.35±0.09*** 7.88±0.05 7.86±0.05 8.02±0.06**6 7.88±0.00 8.33±0.06*** 7.53±0.08*** 7.95±0.06 7.99±0.05** 8.00±0.067 7.89±0.00 8.37±0.06*** 7.50±0.05*** 8.00±0.06 7.93±0.05 7.89±0.068 7.88±0.01 8.37±0.06*** 7.65±0.06*** 7.98±0.05 7.81±0.05 7.89±0.089 7.88±0.00 8.49±0.05*** 7.48±0.07*** 7.90±0.08 7.95±0.05 7.89±0.0610 7.88±0.00 8.40±0.06*** 7.73±0.09 8.01±0.03*** 7.91±0.08 8.08±0.05***Number of Paths = 50000 7.89±0.01 7.93±0.02 7.32±0.04*** 7.88± 0.02 7.86±0.03 7.91±0.02 7.91±0.041 7.88±0.00 7.93±0.03 7.28±0.06*** 7.90± 0.01 7.87±0.02 7.93±0.032 7.88±0.01 7.96±0.02*** 7.39±0.04*** 7.86±0.03 7.84±0.02 7.92±0.023 7.89±0.00 7.86±0.02 7.32±0.05*** 7.91± 0.03 7.84±0.02** 7.87±0.034 7.88±0.00 7.94±0.03 7.33±0.07*** 7.90± 0.03 7.87±0.03 7.86±0.035 7.88±0.01 7.96±0.02*** 7.29±0.06*** 7.86±0.03 7.84±0.03 7.90±0.036 7.88±0.00 8.00±0.02*** 7.31±0.08*** 7.91±0.02 7.87±0.02 7.90±0.037 7.89±0.00 7.94±0.02** 7.43±0.05*** 7.86±0.03 7.90±0.02 7.90±0.028 7.88±0.01 7.95±0.03** 7.47±0.07*** 7.91±0.02 7.86±0.02 7.91±0.039 7.88±0.00 7.96±0.02*** 7.50±0.04*** 7.92±0.02 7.88±0.02 7.88±0.0210 7.88±0.00 7.95±0.02*** 7.55±0.07*** 7.90±0.02 7.91±0.03 7.88±0.03Number of Paths = 100000 7.89±0.01 7.89±0.01 7.28±0.04*** 7.90± 0.02 7.90±0.02 7.88±0.02 7.81±0.02***1 7.88±0.00 7.92±0.02 7.38±0.04*** 7.89± 0.02 7.88±0.02 7.88±0.012 7.88±0.01 7.84±0.02 7.27±0.04*** 7.87± 0.02 7.88±0.02 7.89±0.013 7.89±0.00 7.91±0.02 7.40±0.06*** 7.88± 0.02 7.91±0.02 7.89±0.014 7.88±0.00 7.92±0.01*** 7.41±0.04*** 7.89±0.01 7.88±0.02 7.90±0.025 7.88±0.01 7.90±0.02 7.24±0.06*** 7.85± 0.02 7.88±0.01 7.86±0.026 7.88±0.00 7.90±0.02 7.40±0.06*** 7.87± 0.02 7.88±0.01 7.86±0.027 7.89±0.00 7.89±0.02 7.41±0.05*** 7.85± 0.02 7.88±0.02 7.91±0.028 7.88±0.01 7.89±0.02 7.47±0.04*** 7.90± 0.01 7.88±0.02 7.91±0.029 7.88±0.00 7.93±0.02** 7.45±0.06*** 7.89±0.01 7.89±0.02 7.89±0.0210 7.88±0.00 7.90±0.02 7.42±0.06*** 7.88±0.02 7.89±0.01 7.86±0.02Notes: The parameters are: σ = 0.2, r = 0.05, T = 3, D = 5.0, S 0 = 100, K = 100,and exercise points t ∈ {0, 0.5, 1, 1.5, 2, 2.5, 3}. N b denotes the highest degree of thepolynomial basis functions. The standard errors are reported after the ± sign basedon 20 replications. The asymptotic value is computed by the OLS regression methodwith 100,000 paths. The “**” sign means two to three standard errors away from theasymptotic value. The “***” sign means more than three standard errors away.