New Methods with Capped Options for Pricing American Options

Table 4

Numerical results for Example 4.

Steps	Tian binomial tree	Error	Rate	Improved binomial tree	Error	Rate
100	4.775829512	0.0067634	—	4.787677204	0.00508421	—
200	4.779289543	0.0033034	1.0337934	4.785271837	0.00267884	0.92441183
300	4.780385169	0.0022078	0.9938233	4.784452498	0.00185950	0.90038471
400	4.780947507	0.0016454	1.0218663	4.784022516	0.00142952	0.9140937
500	4.781290534	0.0013024	1.0476757	4.783750356	0.00115736	0.94645693
600	4.78151052	0.0010824	1.0147265	4.783567205	0.00097421	0.94486630
700	4.781671345	0.0009216	1.0433990	4.783434838	0.00084185	0.94733429
800	4.781788327	0.0008046	1.0165205	4.783334956	0.00074196	0.94581474
900	4.781878368	0.0007146	1.0075284	4.783260037	0.00066704	0.90371784
1000	4.781950499	0.0006424	1.0098803	4.783199437	0.00060644	0.90397488
1100	4.782010723	0.0005822	1.0326610	4.783148553	0.00055556	0.91947996
1200	4.782060177	0.0005328	1.0200962	4.783105294	0.00051230	0.93163122
1300	4.782102211	0.0004907	1.0266497	4.783068897	0.00047590	0.92069405
1400	4.782138982	0.0004540	1.0509063	4.783037294	0.00044430	0.92722175
1500	4.782170649	0.0004223	1.0479512	4.783010233	0.00041724	0.91082254
1600	4.782198327	0.0003946	1.0502588	4.78298612	0.00039313	0.92234362