A Simple Numerical Method for Pricing an American Put Option

Table 2

Comparison of the values of the American put options.

(𝑆,𝑇,𝑟,𝜎,𝛿)	Binomial	Front fixing	MBM-FDM	Our method
( 80, 0.5, 0.05, 0.20, 0.00)	20.0000	20.0000	20.0000	20.0000
( 90, 0.5, 0.05, 0.20, 0.00)	10.6661	10.6643	10.6680	10.6661
(100, 0.5, 0.05, 0.20, 0.00)	4.6556	4.6501	4.6504	4.6549
(110, 0.5, 0.05, 0.20, 0.00)	1.6681	1.6629	1.6631	1.6686
(120, 0.5, 0.05, 0.20, 0.00)	0.4976	0.4961	0.4993	0.4985
( 80, 0.5, 0.05, 0.20, 0.03)	20.0000	20.0000	20.0000	20.0000
( 90, 0.5, 0.05, 0.20, 0.03)	11.1551	11.1513	11.1526	11.1544
(100, 0.5, 0.05, 0.20, 0.03)	5.1496	5.1435	5.1444	5.1496
(110, 0.5, 0.05, 0.20, 0.03)	1.9491	1.9461	1.9455	1.9509
(120, 0.5, 0.05, 0.20, 0.03)	0.6132	0.6113	0.6155	0.6153
( 80, 1.0, 0.05, 0.20, 0.00)	20.0000	20.0000	20.0000	20.0000
( 90, 1.0, 0.05, 0.20, 0.00)	11.4928	11.4924	11.4857	11.4929
(100, 1.0, 0.05, 0.20, 0.00)	6.0903	6.0893	6.0829	6.0905
(110, 1.0, 0.05, 0.20, 0.00)	2.9866	2.9856	2.9854	2.9868
(120, 1.0, 0.05, 0.20, 0.00)	1.3672	1.3654	1.3643	1.3674
( 80, 1.0, 0.07, 0.40, 0.03)	24.0068	24.0054	23.9987	24.0057
( 90, 1.0, 0.07, 0.40, 0.03)	18.2760	18.2741	18.2697	18.2746
(100, 1.0, 0.07, 0.40, 0.03)	13.7886	13.7879	13.7852	13.7873
(110, 1.0, 0.07, 0.40, 0.03)	10.3317	10.3312	10.3235	10.3307
(120, 1.0, 0.07, 0.40, 0.03)	7.7027	7.7014	7.7016	7.7018
( 80, 3.0, 0.08, 0.20, 0.00)	20.0000	20.0000	20.0000	20.0000
( 90, 3.0, 0.08, 0.20, 0.00)	11.6974	11.9029	11.6892	11.6977
(100, 3.0, 0.08, 0.20, 0.00)	6.9320	7.2527	6.9221	6.9321
(110, 3.0, 0.08, 0.20, 0.00)	4.1550	4.4841	4.1443	4.1548
(120, 3.0, 0.08, 0.20, 0.00)	2.5102	2.7760	2.4997	2.5102
( 80, 3.0, 0.08, 0.20, 0.03)	20.1345	20.2396	20.1282	20.1349
( 90, 3.0, 0.08, 0.20, 0.03)	12.9694	13.1798	12.9611	12.9697
(100, 3.0, 0.08, 0.20, 0.03)	8.3791	8.5901	8.3690	8.3792
(110, 3.0, 0.08, 0.20, 0.03)	5.4152	5.5223	5.4041	5.4151
(120, 3.0, 0.08, 0.20, 0.03)	3.4981	3.5983	3.4879	3.4979