A Continuous-Time Model for Valuing Foreign Exchange Options

Table 1

Prices for European call and put FX options when time to maturity 𝑇=1 month.

𝑆𝑡/𝑋	Call𝑂	CallGK	Bias𝑐	Put𝑂	PutGK	Bias𝑝
0.70	0.000000	0.000000		0.617117	0.617122	−0.0008
0.72	0.000000	0.000000		0.560023	0.560026	−0.0005
0.74	0.000000	0.000000		0.506014	0.506017	−0.0006
0.76	0.000000	0.000000		0.454848	0.454851	−0.0007
0.78	0.000000	0.000000		0.406307	0.406308	−0.0002
0.80	0.000001	0.000001		0.360193	0.360194	−0.0003
0.82	0.000006	0.000006		0.316332	0.316333	−0.0003
0.84	0.000029	0.000029		0.274579	0.274578	0.0004
0.86	0.000115	0.000115		0.234832	0.234830	0.0009
0.88	0.000387	0.000385	0.5195	0.197081	0.197077	0.0020
0.90	0.001109	0.001105	0.3620	0.161470	0.161464	0.0037
0.92	0.002753	0.002746	0.2549	0.128360	0.128351	0.0070
0.94	0.006003	0.005992	0.1836	0.098336	0.098322	0.0142
0.96	0.011655	0.011639	0.1375	0.072100	0.072081	0.0264
0.98	0.020408	0.020390	0.0883	0.050267	0.050245	0.0438
1.00	0.032643	0.032624	0.0582	0.033139	0.033116	0.0695
1.02	0.048284	0.048267	0.0352	0.020568	0.020547	0.1022
1.04	0.066823	0.066811	0.0180	0.011981	0.011964	0.1421
1.06	0.087482	0.087475	0.0080	0.006538	0.006525	0.1992
1.08	0.109419	0.109416	0.0027	0.003339	0.003330	0.2703
1.10	0.131898	0.131898	0.0000	0.001596	0.001590	0.3774
1.12	0.154374	0.154377	−0.0019	0.000714	0.000711	0.4219
1.14	0.176497	0.176502	−0.0028	0.000300	0.000298	0.6711
1.16	0.198075	0.198082	−0.0035	0.000118	0.000117	0.8547
1.18	0.219023	0.219031	−0.0037	0.000044	0.000043	2.3256
1.20	0.239317	0.239324	−0.0029	0.000015	0.000015
1.22	0.258962	0.258970	−0.0031	0.000005	0.000005
1.24	0.277980	0.277988	−0.0029	0.000002	0.000002
1.26	0.296397	0.296405	−0.0027	0.000000	0.000000
1.28	0.314238	0.314247	−0.0029	0.000000	0.000000
1.30	0.331531	0.331540	−0.0027	0.000000	0.000000

𝑆_𝑡 is the exchange rate at initial time 𝑡, 𝑋 is the exercise price, Call_𝑂 and Put_𝑂 are call and put prices for our model, Call_GK and Put_GK are call and put prices for the G-K model, Bias_𝑐=100(Call_𝑂−Call_GK)/Call_GK, and Bias_𝑝=100(Put_𝑂−Put_GK)/Put_GK.