Algorithms of Finite Difference for Pricing American Options under Fractional Diffusion Models

Table 1

First-order numerical estimates computed by iterative algorithm and second-order estimates obtained by extrapolation.

	First-order approximation				First-order approximation				Second-order
		itns	Value	Change		itns	Value	Change	Value	Change
25	128	5.92	0.5386		256	8.00	0.5267		0.5148
50	256	6.04	0.5275	0.0111	512	8.94	0.5199	0.0068	0.5123	0.0025
100	512	6.18	0.5203	0.0072	1024	9.90	0.5167	0.0032	0.5131	0.0008
200	1024	6.63	0.5169	0.0034	2048	11.03	0.5149	0.0018	0.5129	0.0002
400	2048	7.20	0.5150	0.0019	4096	12.24	0.5139	0.0010	0.5128	0.0001

“itns” is the average number of iterations per time step. is the number of time steps. is the number of spatial points. “value” is a sample of the put option values.