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334 國際金融市場實務
表 12-4: 2014 年 1 月 30 日的收益率
國庫券 國庫券 遠期國庫券 遠期利率 波動性
價格 價格 價格
期限 ( f )
(T) 收益率 ( B i T , 0 ) ( B , 0 T i 1 ) ( F i T , i T +1 ) i T , i T +1 (σ)
(1) (2) (3) (4) (5) (6) (7)
T 1 =182 / 360 3.75% $0.9816 $0.9615 $0.9795 4.18% 0.1%
T 2 =365 / 360 4.00% $0.9615 $0.9401 $0.9777 4.55% 0.1%
4.25% $0.9401 $0.9174 $0.9759 4.95% 0.1%
T 3 =547 / 360
4.50% $0.9174 $0.8939 $0.9744 5.26% 0.1%
T 4 =730 / 360 4.75% $0.8939 $0.8697 $0.9729 5.57% 0.1%
T 5 =912 / 360 5.00% $0.8697
T 6 =1094 / 360
註: (3)=$1/[1+(2)×(1)],(4) 為 (3) 之 T 2 至 T 6 的價格,(5)=(4) / (3),(6)=[$1 / (5)-1]
×360 / 182。
表12-5: 利率上限與下限的價格計算資料
選擇權 f i T , i T +1 X σ T i d 1 d 2 N(d 1 ) N(d 2 )
1 4.18% 6% 0.1% 0.5 -5.0549 -5.1259 0 0
2 4.55% 6% 0.1% 1.0 -2.7163 -2.8163 0.0033 0.0024
3 4.95% 6% 0.1% 1.5 -1.5094 -1.6319 0.0655 0.0516
4 5.26% 6% 0.1% 2.0 -1.0657 -1.1798 0.1440 0.1190
5 5.57% 6% 0.1% 2.5 -0.3915 -0.5498 0.3483 0.2912
N (-d 2 ) N (-d 1 ) C T (X) P T (X) B , 0 T i 1 C(X) P(X)
1 1 0 0.0182 0.9615 0 0.0175
0.9976 0.9967 0.0001 0.0146 0.9401 0.0001 0.0137
0.9484 0.9345 0.0001 0.0106 0.9174 0.0001 0.0097
0.8810 0.8560 0.0005 0.0079 0.8939 0.0004 0.0071
0.7088 0.6517 0.0019 0.0062 0.8697 0.0017 0.0054