一千萬個為什麽

搜索

如何計算Black Scholes模型的Vomma

這個 source(PDF)給出了vomma(或volga,即volga)的封閉形式Black Scholes期權定價模型的價格波動的二階導數):

$$ S_ {0}ë^ { - qT的} \ SQRT {T】\壓裂{1} {\ SQRT {2 \ PI}}ë^ { - \壓裂{D_ {1} ^ {2}} {2} } \壓裂{D_ {1} D_ {2}} {\西格瑪} $$

哪裏

$$ d_ {1} = \ frac {ln(S_ {0}/K)+(r-q)T + \ sigma ^ {2}/2T} {\ sigma \ sqrt {T}} $$

$$ d_ {2} = \ frac {ln(S_ {0}/K)+(r-q)T - \ sigma ^ {2}/2T} {\ sigma \ sqrt {T}} $$

兩個問題:

  • Is this correct? Please provide additional source 和/or proof.
  • What is $q$? (it's not defined in the referenced document)

Edit: I think there's a missing set of parentheses around $\sigma^{2}/2$ in the formulas for $d_{1}$ 和 $d_{2}$. E.g. $d_{1}$ should be

$$ d_ {1} = \ frac {ln(S_ {0}/K)+(r-q)T +(\ sigma ^ {2}/2)T} {\ sigma \ sqrt {T}} $$

最佳答案

這看起來是正確的

伏爾加:S * Sqrt(T)* d1 * d2 * N'(d1)/σ

編輯:我提供了以下書籍pdf的鏈接:

http://books.google.co.jp/books/about/The_complete_guide_to_option_pricing_for.html?id=tuoJAQAAMAAJ&redir_esc=y

但是因為它是一個掃描版本而取消它,我不確定它是否侵犯了版權。

轉載註明原文: 如何計算Black Scholes模型的Vomma