Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System

Table 1

Prices of American put option with parameters and different values of .

		Regime 1			Regime 2
		LTM	FDM	RE (%)	LTM	FDM	RE (%)
	3.00	6.0000	6.0000	0.0000	6.0000	6.0000	0.0000
	4.50	4.4924	4.5431	1.1160	4.5278	4.5117	0.3568
	6.00	3.3692	3.4138	1.3065	3.3071	3.3502	1.2865
	7.50	2.5536	2.5835	1.1573	2.4741	2.5026	1.1388
	9.00	1.9512	1.9712	1.0146	1.8630	1.8816	0.9885
	10.50	1.5047	1.5177	0.8566	1.4146	1.4265	0.8342
	12.00	1.1717	1.1795	0.6613	1.0847	1.0915	0.6230
	3.00	6.0000	6.0000	0.0000	6.0000	6.0000	0.0000
	4.50	4.5084	4.5436	0.7747	4.5181	4.5149	0.0709
	6.00	3.3787	3.3988	0.5914	3.3229	3.3420	0.5715
	7.50	2.5258	2.5381	0.4846	2.4442	2.4537	0.3872
	9.00	1.9016	1.9089	0.3824	1.7972	1.8037	0.3604
	10.50	1.4633	1.4672	0.2658	1.3659	1.3691	0.2337
	12.00	1.1517	1.1531	0.1214	1.0668	1.0678	0.0937
	3.00	6.0000	6.0000	0.0000	6.0000	6.0000	0.0000
	4.50	4.5275	4.5370	0.2094	4.5067	4.5112	0.0998
	6.00	3.3630	3.3677	0.1396	3.3102	3.3146	0.1327
	7.50	2.4738	2.4749	0.0444	2.3871	2.3877	0.0251
	9.00	1.8271	1.8257	0.0767	1.7102	1.7085	0.0995
	10.50	1.3915	1.3883	0.2305	1.2882	1.2849	0.2568
	12.00	1.0940	1.0891	0.4499	1.0094	1.0046	0.4778
CPU time	1.98 s for LTM; 532.47 s for FDM