Take the 2-minute tour ×
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield).

On page 171 of Haug

The following code is provided for the Bisection algorithm, along with the comment: "With small modifications, the function can also be used to find the implied volatility for American and exotic options". However, I am unable to find further information in the book (or online), which provides instructions on the required modification(s).

I include the function code below, hopefully, someone may be able to suggest the required modifications:

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
share|improve this question
add comment

1 Answer 1

up vote 4 down vote accepted

The algorithm is the same, you just need to use appropriate (American/Exotic) pricer instead of black-scholes.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.