Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach

Table 3

American put, time of computation: FDS & WH versus FDS.

Parameters		Relative difference		Time of computation, sec.
Space step Δ𝑥	Number of time steps 𝑁𝜏	𝜖𝑝	𝜖𝑏	FDS	FDS & WH
0.002	65	0.21%	0.2%	14	1
0.001	112	0.21%	0.2%	64	3
0.0005	203	0.2%	0.2%	536	13

KoBoL parameters: 𝜎=0, 𝜈=0.2, 𝜆₊=3.2, 𝜆₋=−5.4, 𝑐=1.
𝐾=100, 𝑟=0.03, 𝑇=0.5.
𝜖_𝑝 and 𝜖_𝑏 are the maximums of the relative differences between correspondent prices and boundaries, respectively, in the region 𝑆≤1.3𝐾.