Implied Volatility - Black Scholes

[rogerioct]

Dear forum members,

I have been trying (along 3 nights) to implement an algorith to calculate implied volatility.
Calculation of calls and puts prices is OK (follow the code).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Public Function normal(x)
normal = Application.WorksheetFunction.NormSDist(x)
End Function


Public Function precobs(S, sigma, r, strike, T, div, tipo)
Dim d1 As Single
Dim d2 As Single

T = T / 252
r = 1 * Log(1 + r / 1)

d1 = (Log(S / strike) + (r + (sigma ^ 2) / 2) * T) / (sigma * Sqr(T))
d2 = d1 - sigma * Sqr(T)

If tipo = "Call" Then
precobs = S * normal(d1) * Exp(-div * T) - strike * Exp(-r * T) * normal(d2)
Else
precobs = strike * Exp(-r * T) * normal(-d2) - S * normal(-d1) * Exp(-div * T)
End If

End Function

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
legend: precobs=price of option from black scholes formula
tipo=call/put

the rest is intuitive

User gives the inputs and the function calculates the price.

Well done.

But, implied volatility requires such a routine which finds the volatility (sigma) whose lets price from black scholes be equal to market price.

I tryed something like this:

Public Function impv(mktprice,S,r,T,tipo,div,strike)

dim dif as double
dim sigma as double
dim cont as double
dim limit as double
cont=0
dif=abs(mktprice-precobs(S,sigma,strike,r,T,tipo,div))
limit=10^(-2)

Do While dif>limit and cont<2000 and sigma>0

sigma=sigma-0.01
dif=abs(mktprice-precobs(S,sigma,strike,r,T,tipo,div))
cont=cont+1
loop

if cont>2000 or sigma<0 then
impv="fail!"
else
impv=sigma
end if
End Function


It doesn't work.
I tried other codes I found on web but neither works.

Thank You

Regards,
Rogerio.

 

[rogerioct]

Somebody?

I need help on creating an algorithm which the output is the implied volatility.

The user will enter with S,r,T,tipo,strike and market price (mktprice)

The program has to find the value for "sigma" which makes the difference "mktprice-precobs" be almost zero. [in other words, I need to find sigma which lets the value of the BS equation be equal to the value of market price, the last is given by the user and the BS price is an output from the function "precobs".

Thank you.

 

[Norie]

That is the worst code I think I've ever seen in my life.

the rest is intuitive

How?

 

[rogerioct]

Dude, if you can't help, you better stay quiet.

The code for the BS price is working and it is simple, thats what matters, How would you improve it? Creating useless accessories to it?

PS: I didn't knew about code tags.

 

[Norie]

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