A Robust Spline Collocation Method for Pricing American Put Options

Table 3

Comparison of the American put option values at for some different values of with parameters: .

Stock price		Binomial method	Analytic approx. method	Compact method 1	Compact method 2	Compact method 3	Our stable scheme	True values
75.9572		25.33949	25.4509	25.10042	25.32570	25.32739	25.32892	25.32986
	error	0.00963	0.12104	0.22944	0.00416	0.00247	0.00094
83.9457		19.49101	19.6617	19.34597	19.49193	19.49383	19.49565	19.49691
	error	0.00590	0.16479	0.15094	0.00498	0.00308	0.00126
92.7743		14.27957	14.4477	14.16375	14.25707	14.25914	14.26121	14.26265
	error	0.01692	0.18505	0.09890	0.00558	0.00351	0.00144
102.5315		9.87092	10.0278	9.78167	9.83789	9.84000	9.84216	9.84354
	error	0.02738	0.18426	0.06187	0.00565	0.00354	0.00138
113.3148		6.35580	6.53401	6.32881	6.36044	6.36241	6.36458	6.36558
	error	0.00978	0.16843	0.03677	0.00514	0.00317	0.00100
125.2323		3.84473	3.97728	3.81244	3.82898	3.83064	3.83268	3.83337
	error	0.01136	0.14391	0.02093	0.00439	0.00273	0.00069
138.4031		2.14801	2.25467	2.12653	2.13452	2.13578	2.13757	2.13784
	error	0.01017	0.11683	0.01131	0.00332	0.00206	0.00027