派生美式期權隱含波動率的修正二等分公式

我正在嘗試制定計算派息股票的美式期權隱含波動率（離散支付或年化收益率）的公式。

在豪格的第 171 頁

為二分法算法提供了以下程式碼，並附有註釋：“稍作修改，該函式也可用於查找美式和奇異期權的隱含波動率”。但是，我無法在書中（或線上）中找到更多資訊，其中提供了有關所需修改的說明。

我包括下面的功能程式碼，希望有人可以提出所需的修改：

function BisectionAlgorithm(CallPutFlag As String, S As Double, X as Double, T As Double,
                           r As Double, b as Double, cm As Double) As Double
  Dim vLow as Double, vHigh As Double, vi as Double
  Dim cLow As Double, cHigh As Double, epsilon as Double, tempval As Double

  vLow=0.01
  vHigh=1
  epsilon=0.000001
  cLow = GBlackScholes(CallPutFlag,S,X,T,r,b,vLow)
  cHigh = GBlackScholes(CallPutFlag,S,X,T,r,b,vHigh)
  vi=vLow+(cm-cLow)*(vHigh-vLow)/(cHigh-cLow)
  tempval=GBlackScholes(CallPutFlag,S,X,T,r,b,vi)

  While Abs(cm-tempval) > epsilon
      if tempval < cm Then
          vLow=vi
      Else
          vHigh=vi
      End If

      cLow = GBlackScholes(CallPutFlag,S,X,T,r,b,vLow)
      cHigh = GBlackScholes(CallPutFlag,S,X,T,r,b,vHigh)
      vi=vLow+(cm-cLow)*(vHigh-vLow)/(cHigh-cLow)
      tempval=GBlackScholes(CallPutFlag,S,X,T,r,b,vi)
  Wend

  BisectionAlgorithm=vi
End Function

算法是相同的，您只需要使用適當的（美國/異國情調）定價器而不是 black-scholes。

引用自：https://quant.stackexchange.com/questions/3027