April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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14.6 Black-Scholes 歐式選擇權公式
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567
而對波動性的敏感度則使用 vega（或稱 kappa）指標，即定價函數對波動性微分。
我們試著計算買權的 delta 指標，假設履約價格為 60 元，距履約日期還有半年，目前股
價為 40 元，無風險利率則是 4%，由以下計算可得到股價每上升 1 元，選擇權的價格會
增加約 0.038 元。[Page-569]
直接計算股價為 40.5 與 39.5 元時的選擇權價格之差額也可得到接近的結果。
將 delta 指標對股價與時間的關係繪製為 3D 圖形將更有感覺。
注意在接近履約日期時（
t
接近 0 時），delta 指標對股價非常敏感。
ch14.indd 567 2014/4/2 下午 02:58:58
568
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第十四章
在接近履約日期時，delta 指標對股價的高敏感度也反映在 gamma 指標上，gamma 指標
是 delta 的一次微分，即定價函數對股價的二次微分。[Page-570]
從時間敏感度 theta 的圖形可看出隨著股價增加，在接近履約日期時，衰退的速度相對
較快。
ch14.indd 568 2014/4/2 下午 02:58:59
14.6 Black-Scholes 歐式選擇權公式
|
569
上圖顯示隨著履約
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