Table 1 Comparison of the value of an...

Table 1

Comparison of the value of an American put option for a set of parameter values with default parameters r = 0.1, K = 1, T = 1, σ_L = 0.2, λ_L = 0.5

Parameters			Pentanomial tree		3-Point Richardson
S	σ_H	λ_H	P_H(0, S)	P_L(0, S)	${\tilde{P}}_{H}^{3} (0, S)$	${\tilde{P}}_{L}^{3} (0, S)$
0.9	0.4	1.0	0.1483	0.1106	0.1483	0.1106
0.9	0.4	2.0	0.1390	0.1093	0.1393	0.1094
0.9	0.5	1.0	0.1738	0.1150	0.1737	0.1149
0.9	0.5	2.0	0.1594	0.1128	0.1597	0.1127
1.0	0.4	1.0	0.1015	0.0594	0.1014	0.0592
1.0	0.4	2.0	0.0904	0.0574	0.0905	0.0572
1.0	0.5	1.0	0.1293	0.0660	0.1292	0.0658
1.0	0.5	2.0	0.1128	0.0629	0.1131	0.0626

Parameters			Pentanomial tree		3-Point Richardson
S	σ_H	λ_H	P_H(0, S)	P_L(0, S)	${\tilde{P}}_{H}^{3} (0, S)$	${\tilde{P}}_{L}^{3} (0, S)$
0.9	0.4	1.0	0.1483	0.1106	0.1483	0.1106
0.9	0.4	2.0	0.1390	0.1093	0.1393	0.1094
0.9	0.5	1.0	0.1738	0.1150	0.1737	0.1149
0.9	0.5	2.0	0.1594	0.1128	0.1597	0.1127
1.0	0.4	1.0	0.1015	0.0594	0.1014	0.0592
1.0	0.4	2.0	0.0904	0.0574	0.0905	0.0572
1.0	0.5	1.0	0.1293	0.0660	0.1292	0.0658
1.0	0.5	2.0	0.1128	0.0629	0.1131	0.0626

Note(s): The values in Columns 4 and 5 are obtained by the pentanomial-tree method in Bollen (1998) with 10³ time steps and those in Columns 6 and 7 are obtained by our accelerated method with a three-point Richardson extrapolation

Source(s): Authors' own work

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