Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification

Table 1

Fuzzy EUR/USD currency option price.

𝛼-level set of this paper		𝛼-level set of paper [16, 18]	WPM		Market price
𝛼	[(𝐶^∼𝑡)^𝐿𝛼,(𝐶^∼𝑡)^𝑈𝛼]	[(𝐶^∼𝑡)^𝐿𝛼,(𝐶^∼𝑡)^𝑈𝛼]	𝑛	𝑀𝑓𝑛(𝐶^∼𝑡)
0.0	[0.022898,0.032859]	[−0.05526,0.11108]	0	0.02787
0.1	[0.023394,0.032360]	[−0.04644,0.10225]	1	0.027589
0.2	[0.023890,0.031860]	[−0.037785,0.093576]	2	0.02745
0.3	[0.024386,0.031360]	[−0.029274,0.085052]	3	0.027312
0.4	[0.024883,0.030860]	[−0.020886,0.076652]	4	0.027174
0.5	[0.025379,0.030361]	[−0.012604,0.068359]	5	0.027036	0.0274
0.6	[0.025876,0.029861]	[−0.0044076,0.060155]	6	0.0269
0.7	[0.026373,0.029362]	[0.0037199,0.052020]	7	0.026763
0.8	[0.026870,0.028862]	[0.011796,0.043938]	8	0.026628
0.9	[0.027367,0.028363]	[0.019839,0.035892]	9	0.026492
1.0	[0.027864,0.027864]	[0.027864,0.027864]	10	0.026358