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 7.87±0.01 7.57±0.19 7.73±0.21 7.61± 0.22 7.79±0.19 7.84±0.23 8.77±0.20***1 7.86±0.01 7.81±0.23 7.44±0.21 7.99± 0.25 7.99±0.25 7.83±0.252 7.86±0.01 8.74±0.31** 7.19±0.23** 8.05±0.20 8.26±0.20 8.44±0.25**3 7.86±0.00 9.33±0.23*** 7.44±0.26 8.78± 0.25*** 8.24±0.22 8.49±0.24**4 7.86±0.01 9.16±0.27*** 7.86±0.19 8.66± 0.26*** 8.23±0.18** 8.15±0.255 7.87±0.01 9.75±0.25*** 8.24±0.31 8.76± 0.29*** 8.17±0.30 8.06±0.226 7.87±0.01 9.51±0.19*** 8.53±0.26** 8.64±0.31** 8.58±0.21*** 8.32±0.18**7 7.87±0.01 9.12±0.21*** 8.32±0.20** 8.63±0.24*** 8.58±0.18*** 7.99±0.248 7.87±0.01 10.05±0.32*** 8.60±0.20*** 8.90±0.25*** 8.08±0.20 8.73±0.21***9 7.86±0.01 9.87±0.20*** 8.59±0.24*** 8.56±0.31** 8.23±0.19 8.37±0.2610 7.86±0.01 9.80±0.23*** 8.90±0.27*** 8.63±0.19*** 8.11±0.20 8.25±0.29Number of Paths = 10000 7.87±0.01 7.76±0.07 7.66±0.08** 7.45± 0.05*** 7.74±0.06** 7.91±0.07 8.63±0.05***1 7.86±0.01 7.98±0.07 6.89±0.11*** 7.85± 0.06 7.93±0.08 7.98±0.062 7.86±0.01 7.88±0.06 7.02±0.08*** 7.79± 0.08 7.86±0.07 7.97±0.083 7.86±0.00 7.93±0.06 7.14±0.11*** 7.90± 0.06 7.83±0.05 7.80±0.064 7.86±0.01 8.02±0.07** 7.25±0.11*** 7.92±0.09 7.85±0.05 7.84±0.065 7.87±0.01 8.02±0.05** 7.36±0.09*** 7.81±0.05 7.81±0.06 7.85±0.056 7.87±0.01 8.05±0.08** 7.08±0.10*** 7.84±0.07 7.93±0.06 7.92±0.067 7.87±0.01 8.01±0.08 7.17±0.09*** 7.95± 0.08 7.79±0.03** 7.93±0.078 7.87±0.01 8.09±0.07*** 7.10±0.09*** 7.88±0.08 7.88±0.05 7.94±0.079 7.86±0.01 8.04±0.06** 7.31±0.11*** 7.94±0.07 7.81±0.05 7.83±0.0810 7.86±0.01 8.16±0.06*** 7.18±0.08*** 7.82±0.05 7.87±0.05 7.86±0.06Number of Paths = 50000 7.87±0.01 7.78±0.03** 7.73±0.05** 7.48±0.02*** 7.81±0.03 7.80±0.04 7.91±0.031 7.86±0.01 7.83±0.02 6.89±0.07*** 7.79± 0.03** 7.77±0.03** 7.80±0.032 7.86±0.01 7.88±0.03 7.22±0.04*** 7.82± 0.03 7.84±0.03 7.91±0.043 7.86±0.00 7.90±0.03 7.20±0.06*** 7.86± 0.03 7.86±0.04 7.82±0.034 7.86±0.01 7.87±0.03 7.26±0.05*** 7.86± 0.03 7.84±0.04 7.84±0.035 7.87±0.01 7.90±0.02 7.34±0.05*** 7.80± 0.03** 7.89±0.04 7.89±0.026 7.87±0.01 7.91±0.02 7.32±0.05*** 7.90± 0.03 7.82±0.02** 7.84±0.047 7.87±0.01 7.91±0.02 7.32±0.04*** 7.85± 0.03 7.81±0.03 7.90±0.038 7.87±0.01 7.90±0.02 7.40±0.06*** 7.88± 0.03 7.81±0.03 7.85±0.039 7.86±0.01 7.91±0.03 7.32±0.05*** 7.88± 0.03 7.83±0.03 7.84±0.0310 7.86±0.01 7.88±0.03 7.35±0.05*** 7.87±0.03 7.84±0.03 7.85±0.03Number of Paths = 100000 7.87±0.01 7.79±0.02*** 7.61±0.04*** 7.43±0.02*** 7.74±0.02*** 7.74±0.02*** 7.82±0.021 7.86±0.01 7.78±0.02*** 6.90±0.05*** 7.75±0.03*** 7.85±0.02 7.82±0.022 7.86±0.01 7.88±0.01 7.18±0.03*** 7.76± 0.02*** 7.84±0.02 7.83±0.033 7.86±0.00 7.87±0.02 7.26±0.03*** 7.81± 0.02** 7.86±0.02 7.84±0.024 7.86±0.01 7.89±0.02 7.28±0.04*** 7.84± 0.02 7.84±0.02 7.86±0.025 7.87±0.01 7.87±0.02 7.27±0.03*** 7.85± 0.01 7.84±0.02 7.82±0.02**6 7.87±0.01 7.84±0.01** 7.30±0.04*** 7.85±0.02 7.84±0.02 7.86±0.027 7.87±0.01 7.85±0.01 7.29±0.05*** 7.83± 0.02 7.87±0.02 7.85±0.028 7.87±0.01 7.91±0.02 7.31±0.04*** 7.83± 0.02 7.82±0.02** 7.84±0.029 7.86±0.01 7.89±0.02 7.24±0.04*** 7.88± 0.02 7.85±0.02 7.86±0.0210 7.86±0.01 7.89±0.02 7.23±0.05*** 7.85±0.01 7.85±0.02 7.86±0.02Notes: The parameters are: σ = 0.2, r = 0.05, T = 3, δ = 0.1, 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.